🔗 Problem

Problem: John has been learning to add and subtract fractions at school. He was given a problem during his homework that puzzled him. He had to take the sum of 48/56 and 95/23 and then subtract 34/26 from the result. What was the value that John found for this operation? Answer in simplest form.

Gemma 2B:

    Let's solve this problem step by step:

    1. First, we need to find the sum of 48/56 and 95/23.
       To add fractions, we need to find the least common denominator (LCD).
       The LCD of 56 and 23 is 1288 (56 × 23 = 1288).

       Now, we convert the fractions to equivalent fractions with the LCD:
       48/56 = (48 × 23) / 1288 = 1104/1288
       95/23 = (95 × 56) / 1288 = 5320/1288

       Add the fractions: 1104/1288 + 5320/1288 = 6424/1288

    2. Next, we subtract 34/26 from the result.
       The LCD of 1288 and 26 is 1288 (1288 is already divisible by 26).

       Convert 34/26 to an equivalent fraction with the LCD:
       34/26 = (34 × 49) / 1288 = 1666/1288

       Subtract the fractions: 6424/1288 - 1666/1288 = 4758/1288

    3. Simplify the result:
       4758/1288 can be simplified by dividing both the numerator and denominator by their greatest common factor (GCF).
       The GCF of 4758 and 1288 is 14.

       4758/1288 = (4758 ÷ 14) / (1288 ÷ 14) = 339/92

    Therefore, the value John found for this operation, in simplest form, is 339/92.

    ### Answer: 339/92

Expected answer: 7702/2093

Correct? No

🔗 Problem

Problem: First, add the fractions 88/9 and 28/65. Then subtract the fraction 18/37 from the result. What is the result expressed as a simple fraction?

Gemma 2B:

    Okay, let's solve this problem step by step:

    1. Add the fractions 88/9 and 28/65:
       To add fractions with different denominators, we need to find the least common denominator (LCD).
       LCD of 9 and 65 = 9 × 65 = 585
       Now, we convert both fractions to equivalent fractions with the LCD:
       88/9 = 88 × 65/9 × 65 = 5720/585
       28/65 = 28 × 9/65 × 9 = 252/585
       Add the numerators: 5720/585 + 252/585 = 5972/585

    2. Subtract the fraction 18/37 from the result:
       The result from step 1 is 5972/585. Now we need to subtract 18/37 from this fraction.
       First, find the LCD of 585 and 37:
       LCD of 585 and 37 = 21645
       Convert both fractions to equivalent fractions with the LCD:
       5972/585 = 5972 × 37/585 × 37 = 220964/21645
       18/37 = 18 × 585/37 × 585 = 10530/21645
       Subtract the numerators: 220964/21645 - 10530/21645 = 210434/21645

    3. Simplify the resulting fraction:
       210434/21645 can be simplified by dividing both the numerator and denominator by their greatest common factor (GCF).
       GCF of 210434 and 21645 = 1
       Therefore, the fraction cannot be simplified further.

    ### Answer: 210434/21645

Expected answer: 210434/21645

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, you calculated the sum of 88/9 and 28/65, then subtracted 18/37 from the result. If you add 5/62 to this result, what is the newly resulting fraction?

Gemma 2B:

    Great! Let's continue from where we left off in the previous problem and add 5/62 to the result.

    Given:
    - The result from the previous problem is 210434/21645.
    - We need to add 5/62 to this result.

    Step 1: Find the least common denominator (LCD) of 21645 and 62.
    LCD = 21645 × 62 = 1342990

    Step 2: Convert both fractions to equivalent fractions with the LCD.
    210434/21645 = 210434 × 62/21645 × 62 = 13046908/1342990
    5/62 = 5 × 21645/62 × 21645 = 108225/1342990

    Step 3: Add the numerators of the equivalent fractions.
    13046908/1342990 + 108225/1342990 = 13155133/1342990

    Step 4: Simplify the resulting fraction by dividing both the numerator and denominator by their greatest common factor (GCF).
    GCF of 13155133 and 1342990 = 1
    Therefore, the fraction cannot be simplified further.

    ### Answer: 13155133/1342990

Expected answer: 13155133/1341990

Correct? No

🔗 Follow-up

Problem: In the previous problem, you had the sum of 88/9 and 28/65, and then subtracted 18/37 from the result. Now, imagine instead of having 88/9, you have 44/9. What is the result if you first add 44/9 and 28/65, then subtract 18/37 from the sum? Answer as a simplified fraction.

Gemma 2B:

    Great! Let's solve this problem step by step, similar to the previous one:

    1. Add the fractions 44/9 and 28/65:
       LCD of 9 and 65 = 9 × 65 = 585
       Convert both fractions to equivalent fractions with the LCD:
       44/9 = 44 × 65/9 × 65 = 2860/585
       28/65 = 28 × 9/65 × 9 = 252/585
       Add the numerators: 2860/585 + 252/585 = 3112/585

    2. Subtract the fraction 18/37 from the result:
       The result from step 1 is 3112/585. Now we need to subtract 18/37 from this fraction.
       First, find the LCD of 585 and 37:
       LCD of 585 and 37 = 21645
       Convert both fractions to equivalent fractions with the LCD:
       3112/585 = 3112 × 37/585 × 37 = 115144/21645
       18/37 = 18 × 585/37 × 585 = 10530/21645
       Subtract the numerators: 115144/21645 - 10530/21645 = 104614/21645

    3. Simplify the resulting fraction:
       104614/21645 can be simplified by dividing both the numerator and denominator by their GCF.
       GCF of 104614 and 21645 = 2
       104614 ÷ 2 / 21645 ÷ 2 = 52307/10822

    ### Answer: 52307/10822

Expected answer: 104614/21645

Correct? No

🔗 Problem

Problem: What is the result of (63 / 41) + (44 / 50) when simplified to the lowest terms?

Gemma 2B:

    To simplify (63 / 41) + (44 / 50) to the lowest terms, we need to perform the division and addition, and then find a common denominator to add the fractions.

    1. Simplify 63 / 41:
       63 / 41 = 1.536585... (rounded)
       This cannot be simplified further as the result is not a rational number.

    2. Simplify 44 / 50:
       44 / 50 = 22 / 25 (divide both numerator and denominator by their common factor of 2)

    3. Add the fractions:
       (63 / 41) + (22 / 25)

       To add fractions, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 41 and 25.
       LCM(41, 25) = 1025

       Now, we convert both fractions to equivalent fractions with the common denominator:

       (63 / 41) = (63 * 25) / (41 * 25) = 1575 / 1025
       (22 / 25) = (22 * 41) / (25 * 41) = 902 / 1025

       Add the fractions:
       (1575 / 1025) + (902 / 1025) = (1575 + 902) / 1025 = 2477 / 1025

       This fraction cannot be simplified further as the numerator and denominator have no common factors other than 1.

    ### Answer: 2477 / 1025

Expected answer: 2477/1025

Correct? Yes

🔗 Follow-up

Problem: After finding the result of (63 / 41) + (44 / 50), what is the answer if you add up the result twice? Answer as a simplified fraction.

Gemma 2B:

    Let's continue from the previous result:

    (63 / 41) + (44 / 50) = 2477 / 1025

    Now, we need to add this result twice:

    (2477 / 1025) + (2477 / 1025)

    To add fractions with the same denominator, we simply add the numerators and keep the denominator the same:

    (2477 + 2477) / 1025 = 4954 / 1025

    Simplifying the fraction:
    Both 4954 and 1025 are divisible by 41.
    4954 / 41 = 121
    1025 / 41 = 25

    Therefore, the simplified fraction is 121 / 25.

    ### Answer: 121 / 25

Expected answer: 4954/1025

Correct? No

🔗 Follow-up

Problem: Instead of the previous scenario, now consider a change to the operation. What will be the result if we use (63 / 37) instead of (63 / 41) to find the sum of (63 / 37) + (44 / 50)?. Remember to simplify your answer to its lowest form.

Gemma 2B:

    Let's solve the problem with the new fraction (63 / 37) instead of (63 / 41).

    1. Simplify 63 / 37:
       63 / 37 = 1.702702... (rounded)
       This cannot be simplified further as the result is not a rational number.

    2. Simplify 44 / 50:
       44 / 50 = 22 / 25 (divide both numerator and denominator by their common factor of 2)

    3. Add the fractions:
       (63 / 37) + (22 / 25)

       To add fractions, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 37 and 25.
       LCM(37, 25) = 925

       Now, we convert both fractions to equivalent fractions with the common denominator:

       (63 / 37) = (63 * 25) / (37 * 25) = 1575 / 925
       (22 / 25) = (22 * 37) / (25 * 37) = 814 / 925

       Add the fractions:
       (1575 / 925) + (814 / 925) = (1575 + 814) / 925 = 2389 / 925

    4. Simplify the result:
       2389 and 925 have a common factor of 37.
       2389 / 37 = 64.5675...
       925 / 37 = 25

       Therefore, the simplified fraction is 64.5675... / 25, which cannot be further simplified as the numerator is not a whole number.

    ### Answer: 2389 / 925

Expected answer: 2389/925

Correct? Yes

🔗 Problem

Problem: John had 71/41 of a cake left and Emily added 41/77 of another cake to it. How much cake is there in total? Give your answer as a simplified fraction.

Gemma 2B:

    Let's solve this problem step by step:

    1. John had 71/41 of a cake left.
    2. Emily added 41/77 of another cake to it.
    3. To find the total amount of cake, we need to add these two fractions:

       71/41 + 41/77

    4. To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators.
       LCM(41, 77) = 3157

    5. Now, we can convert both fractions to equivalent fractions with the common denominator of 3157:

       71/41 = (71 × 77) / (41 × 77) = 5467/3157
       41/77 = (41 × 41) / (77 × 41) = 1681/3157

    6. Add the fractions:

       5467/3157 + 1681/3157 = (5467 + 1681) / 3157 = 7148/3157

    7. Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD):
       GCD(7148, 3157) = 1

       The fraction 7148/3157 is already in its simplest form.

    ### Answer: 7148/3157

Expected answer: 7148/3157

Correct? Yes

🔗 Follow-up

Problem: In the same scenario as before, imagine that John had less cake initially, only 28/41 of his cake was left instead of 71/41. If Emily still added 41/77 of another cake to it, how much cake is there now in total? Give your answer as a simplified fraction.

Gemma 2B:

    Let's solve this problem step by step:

    1. John had 28/41 of a cake left.
    2. Emily added 41/77 of another cake to it.
    3. To find the total amount of cake, we need to add these two fractions:

       28/41 + 41/77

    4. To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators.
       LCM(41, 77) = 3157

    5. Now, we can convert both fractions to equivalent fractions with the common denominator of 3157:

       28/41 = (28 × 77) / (41 × 77) = 2156/3157
       41/77 = (41 × 41) / (77 × 41) = 1681/3157

    6. Add the fractions:

       2156/3157 + 1681/3157 = (2156 + 1681) / 3157 = 3837/3157

    7. Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD):
       GCD(3837, 3157) = 1

       The fraction 3837/3157 is already in its simplest form.

    ### Answer: 3837/3157

Expected answer: 3837/3157

Correct? Yes

🔗 Problem

Problem: Calculate the result of 10/65 + 56/35. Answer as a simple fraction.

Gemma 2B:

    To calculate 10/65 + 56/35, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 65 and 35.

    LCM(65, 35) = 455

    Now, we convert both fractions to equivalent fractions with the common denominator:

    10/65 = (10 × 7) / (65 × 7) = 70/455
    56/35 = (56 × 13) / (35 × 13) = 728/455

    Add the numerators and keep the common denominator:

    70/455 + 728/455 = (70 + 728) / 455 = 798/455

    Simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF):

    GCF(798, 455) = 7

    (798 ÷ 7) / (455 ÷ 7) = 114/65

    ### Answer: 114/65

Expected answer: 114/65

Correct? Yes

🔗 Follow-up

Problem: Following the result of the previous calculation (10/65 + 56/35), subtract your answer from 34. What's the resultant value? Answer as a simple fraction.

Gemma 2B:

    In the previous calculation, we found that 10/65 + 56/35 = 114/65.

    Now, we need to subtract 114/65 from 34.

    First, convert 34 to an improper fraction with the denominator 65:

    34 = (34 × 65) / 65 = 2210/65

    Now, subtract 114/65 from 2210/65:

    2210/65 - 114/65 = (2210 - 114) / 65 = 2096/65

    Simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF):

    GCF(2096, 65) = 1

    Since the GCF is 1, the fraction 2096/65 is already in its simplest form.

    ### Answer: 2096/65

Expected answer: 2096/65

Correct? Yes

🔗 Follow-up

Problem: Given your previous calculation with the 10/65 + 56/35, imagine instead that you started with 25 instead of 10 in the first fraction. What would be the outcome of 25/65 + 56/35? Answer as a simplified fraction.

Gemma 2B:

    Let's follow the same steps as before, but with 25/65 instead of 10/65.

    First, find the common denominator, which is still the least common multiple (LCM) of 65 and 35:

    LCM(65, 35) = 455

    Convert both fractions to equivalent fractions with the common denominator:

    25/65 = (25 × 7) / (65 × 7) = 175/455
    56/35 = (56 × 13) / (35 × 13) = 728/455

    Add the numerators and keep the common denominator:

    175/455 + 728/455 = (175 + 728) / 455 = 903/455

    Simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF):

    GCF(903, 455) = 7

    (903 ÷ 7) / (455 ÷ 7) = 129/65

    ### Answer: 129/65

Expected answer: 129/65

Correct? Yes

🔗 Problem

Problem: What is the result of adding 75/81 and 97/47? Leave your answer as an unsimplified fraction.

Gemma 2B:

    To add fractions with different denominators, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of the denominators.

    The LCM of 81 and 47 is: 81 * 47 = 3807

    Now, we need to convert each fraction to an equivalent fraction with the common denominator:

    75/81 = (75 * 47) / (81 * 47) = 3525/3807
    97/47 = (97 * 81) / (47 * 81) = 7857/3807

    Adding the fractions:
    (3525/3807) + (7857/3807) = (3525 + 7857) / 3807 = 11382/3807

    Therefore, 75/81 + 97/47 = 11382/3807

    ### Answer: 11382/3807

Expected answer: 3794/1269

Correct? Yes

🔗 Follow-up

Problem: After calculating the result of adding 75/81 and 97/47, what do you get when you add that result to 52/71? Provide your answer as an unsimplified fraction.

Gemma 2B:

    From the previous question, we found that 75/81 + 97/47 = 11382/3807.

    Now, we need to add 11382/3807 and 52/71.

    First, let's find the LCM of 3807 and 71.
    3807 = 3 * 7 * 181
    71 = 71
    LCM(3807, 71) = 3 * 7 * 71 * 181 = 270297

    Convert the fractions to equivalent fractions with the common denominator:

    11382/3807 = (11382 * 71) / (3807 * 71) = 808122/270297
    52/71 = (52 * 3807) / (71 * 3807) = 197964/270297

    Adding the fractions:
    (808122/270297) + (197964/270297) = (808122 + 197964) / 270297 = 1006086/270297

    Therefore, (75/81 + 97/47) + 52/71 = 1006086/270297

    ### Answer: 1006086/270297

Expected answer: 335362/90099

Correct? Yes

🔗 Problem

Problem: What is 88/1 - 38/53? Give your answer as a simplified fraction.

Gemma 2B:

    To solve 88/1 - 38/53, we need to find a common denominator for the fractions, then subtract the numerators and simplify the result.

    The common denominator is the least common multiple (LCM) of 1 and 53, which is 53.

    88/1 = (88 × 53) / (1 × 53) = 4664/53
    38/53 remains as it is.

    Now, we can subtract the numerators:
    4664/53 - 38/53 = (4664 - 38) / 53 = 4626/53

    To simplify the fraction, we find the greatest common divisor (GCD) of 4626 and 53.
    The GCD of 4626 and 53 is 1, so the fraction is already in its simplest form.

    ### Answer: 4626/53

Expected answer: 4626/53

Correct? Yes

🔗 Follow-up

Problem: After calculating the result of 88/1 - 38/53, add it to 25/79. What is the final value, and answer as a simplified fraction?

Gemma 2B:

    We already know that 88/1 - 38/53 = 4626/53.

    Now, we need to add 4626/53 and 25/79.

    To add these fractions, we need to find the least common multiple (LCM) of 53 and 79, which is 4187.

    4626/53 = (4626 × 79) / (53 × 79) = 365454/4187
    25/79 = (25 × 53) / (79 × 53) = 1325/4187

    Now, we can add the numerators:
    365454/4187 + 1325/4187 = (365454 + 1325) / 4187 = 366779/4187

    To simplify the fraction, we find the greatest common divisor (GCD) of 366779 and 4187.
    The GCD of 366779 and 4187 is 1, so the fraction is already in its simplest form.

    ### Answer: 366779/4187

Expected answer: 366779/4187

Correct? Yes

🔗 Follow-up

Problem: Previous problem: What is 88/1 - 38/53? Now consider if the second fraction (38/53) was changed to 38/93 instead. So, what is 88/1 - 38/93? Answer as a simplified fraction.

Gemma 2B:

    To solve 88/1 - 38/93, we need to find a common denominator for the fractions, then subtract the numerators and simplify the result.

    The common denominator is the least common multiple (LCM) of 1 and 93, which is 93.

    88/1 = (88 × 93) / (1 × 93) = 8184/93
    38/93 remains as it is.

    Now, we can subtract the numerators:
    8184/93 - 38/93 = (8184 - 38) / 93 = 8146/93

    To simplify the fraction, we find the greatest common divisor (GCD) of 8146 and 93.
    The GCD of 8146 and 93 is 1, so the fraction is already in its simplest form.

    ### Answer: 8146/93

Expected answer: 8146/93

Correct? Yes

🔗 Problem

Problem: Evaluate the expression ((80 / 94) + (78 / 59)). What is the answer in simplified form?

Gemma 2B:

    To evaluate the expression ((80 / 94) + (78 / 59)), we need to perform the division operations and then add the results.

    Step 1: Simplify 80 / 94
    80 / 94 ≈ 0.8511 (rounded to 4 decimal places)

    Step 2: Simplify 78 / 59
    78 / 59 ≈ 1.3220 (rounded to 4 decimal places)

    Step 3: Add the results from Step 1 and Step 2
    0.8511 + 1.3220 ≈ 2.1731

    To simplify this further, we can convert the decimal to a fraction:
    2.1731 = 21731 / 10000

    Simplifying the fraction:
    21731 / 10000 = 2 1731/10000

    ### Answer: 2 1731/10000

Expected answer: 6026/2773

Correct? No

🔗 Problem

Problem: What is the sum of 89/56 and 48/50? Answer as a simplified fraction.

Gemma 2B:

    To find the sum of 89/56 and 48/50, we need to find a common denominator. The least common multiple of 56 and 50 is 1400.

    89/56 = (89 × 25) / (56 × 25) = 2225/1400
    48/50 = (48 × 28) / (50 × 28) = 1344/1400

    Now we can add the fractions:

    2225/1400 + 1344/1400 = (2225 + 1344) / 1400 = 3569/1400

    To simplify this fraction, we divide both the numerator and denominator by their greatest common factor, which is 17.

    3569/1400 = (3569 ÷ 17) / (1400 ÷ 17) = 209/82

    Therefore, the sum of 89/56 and 48/50, expressed as a simplified fraction, is 209/82.

    ### Answer: 209/82

Expected answer: 3569/1400

Correct? No

🔗 Problem

Problem: What is the result when you subtract 38/87 from the sum of 96/11 and 12/5? Please leave your answer as a fraction.

Gemma 2B:

    To solve this problem, let's break it down into steps:

    1. Find the sum of 96/11 and 12/5.
       96/11 + 12/5 = (96 × 5 + 12 × 11) / (11 × 5)
                    = (480 + 132) / 55
                    = 612 / 55

    2. Subtract 38/87 from the result of step 1.
       612/55 - 38/87 = (612 × 87 - 38 × 55) / (55 × 87)
                      = (53244 - 2090) / 4785
                      = 51154 / 4785

    Therefore, the result is 51154/4785.

    ### Answer: 51154/4785

Expected answer: 51154/4785

Correct? Yes

🔗 Follow-up

Problem: After you find the result subtracting 38/87 from the sum of 96/11 and 12/5, add that result back to the initial sum of 96/11 and 12/5. What is the final result? Please leave your answer as a fraction.

Gemma 2B:

    Let's continue from the previous solution:

    1. The sum of 96/11 and 12/5 is 612/55.
    2. The result of subtracting 38/87 from 612/55 is 51154/4785.

    Now, let's add the result from step 2 back to the initial sum from step 1.

    3. Add 51154/4785 to 612/55.
       51154/4785 + 612/55 = (51154 × 55 + 612 × 4785) / (4785 × 55)
                            = (2813470 + 2928420) / 263175
                            = 5741890 / 263175
                            = 21820 / 1045

    Therefore, the final result is 21820/1045.

    ### Answer: 21820/1045

Expected answer: 104398/4785

Correct? No

🔗 Follow-up

Problem: After considering the fruit you have, suppose you actually started off with a fraction of the fruits, having 96/58 oranges, and still having 12/5 apples. If you subtracted 38/87 of your total fruits for charity, what fraction of fruits would you have left? Please leave your answer as a fraction.

Gemma 2B:

    Let's solve this problem step by step:

    1. Find the total number of fruits you started with:
       96/58 oranges + 12/5 apples = (96 × 5 + 12 × 58) / (58 × 5)
                                   = (480 + 696) / 290
                                   = 1176 / 290

    2. Calculate the fraction of fruits you are subtracting for charity:
       38/87 of the total fruits = (38 × 1176) / (87 × 290)
                                 = 44688 / 25230

    3. Subtract the fraction of fruits given to charity from the total fruits:
       1176/290 - 44688/25230 = (1176 × 25230 - 44688 × 290) / (290 × 25230)
                              = (29670480 - 12959520) / 7316700
                              = 16710960 / 7316700
                              = 2388709 / 1045243

    Therefore, after subtracting 38/87 of your total fruits for charity, you would have 2388709/1045243 of your fruits left.

    ### Answer: 2388709/1045243

Expected answer: 1574/435

Correct? No

🔗 Problem

Problem: If you have a number that's 82 divided by 9 and from this you subtract 82 divided by 63, what's the resulting value? Answer as a simplified fraction.

Gemma 2B:

    Let's solve this step by step:

    1) First, let's calculate 82 divided by 9:

       82 ÷ 9 = 9.111... (rounded to 3 decimal places)

    2) Next, let's calculate 82 divided by 63:

       82 ÷ 63 = 1.301... (rounded to 3 decimal places)

    3) Now, we subtract the second result from the first:

       9.111... - 1.301... = 7.810...

    4) To express this as a simplified fraction, we need to write these numbers as fractions:

       9.111... = 9 1/9
       1.301... = 1 19/63

    5) Now we can subtract these fractions:

       9 1/9 - 1 19/63 = (9 * 63 + 1 * 7) / 63 - (1 * 63 + 19 * 1) / 63
                       = (567 + 7) / 63 - (63 + 19) / 63
                       = 574 / 63 - 82 / 63
                       = 492 / 63

    6) Simplifying this fraction:

       492 ÷ 63 = 7 remainder 51
       51 ÷ 3 = 17

       So, 492 / 63 simplifies to 7 17/21

    ### Answer: 7 17/21

Expected answer: 164/21

Correct? Yes

🔗 Follow-up

Problem: In our previous question, we originally had a value of 82 divided by 9 and subtracted 82 divided by 63 from it. Now let's change it up. What would have been the result if, originally, the number we subtracted wasn't 82 divided by 63 but instead 37 divided by 63? What's the new result? Please provide your answer as a simplified fraction.

Gemma 2B:

    Okay, let's solve this new problem step by step:

    1) We already know from the previous question that 82 divided by 9 is equal to 9 1/9.

    2) Now, let's calculate 37 divided by 63:

       37 ÷ 63 = 0.587... (rounded to 3 decimal places)

    3) To express this as a fraction, we get:

       0.587... = 37/63

    4) Now, we subtract this fraction from 9 1/9:

       9 1/9 - 37/63 = (9 * 63 + 1 * 7) / 63 - 37 / 63
                     = (567 + 7) / 63 - 37 / 63
                     = 574 / 63 - 37 / 63
                     = 537 / 63

    5) Simplifying this fraction:

       537 ÷ 63 = 8 remainder 33
       33 ÷ 3 = 11

       So, 537 / 63 simplifies to 8 11/21

    ### Answer: 8 11/21

Expected answer: 179/21

Correct? Yes

🔗 Problem

Problem: Calculate the value of 23/3 minus the sum of 80/91 and 26/24. Answer as a simple fraction.

Gemma 2B:

    To calculate the value of 23/3 minus the sum of 80/91 and 26/24, we need to:
    1. Convert the mixed number 23/3 to an improper fraction.
    2. Add 80/91 and 26/24.
    3. Subtract the sum from the improper fraction.
    4. Simplify the result.

    Step 1: Convert 23/3 to an improper fraction
    23/3 = (2 × 3 + 3) / 3 = 9/3 = 3

    Step 2: Add 80/91 and 26/24
    To add fractions, we need a common denominator. The least common multiple of 91 and 24 is 728.
    80/91 = (80 × 8) / (91 × 8) = 640/728
    26/24 = (26 × 91) / (24 × 91) = 2366/2184
    640/728 + 2366/2184 = (640 × 3) / (728 × 3) + 2366/2184 = 1920/2184 + 2366/2184 = 4286/2184

    Step 3: Subtract the sum from the improper fraction
    3 - 4286/2184 = (3 × 2184 - 4286) / 2184 = (6552 - 4286) / 2184 = 2266/2184

    Step 4: Simplify the result
    2266/2184 = 1133/1092

    ### Answer: 1133/1092

Expected answer: 6229/1092

Correct? No

🔗 Problem

Problem: What is the sum of 37/18 and 24/60 when simplified to the lowest terms?

Gemma 2B:

    To find the sum of 37/18 and 24/60, we need to find a common denominator and then add the fractions. Let's solve this step by step.

    Step 1: Simplify 24/60 to the lowest terms.
    24/60 = 2/5 (divide both numerator and denominator by 12)

    Step 2: Find the common denominator for 37/18 and 2/5.
    The common denominator is the least common multiple (LCM) of 18 and 5.
    LCM(18, 5) = 90

    Step 3: Convert both fractions to equivalent fractions with the common denominator of 90.
    37/18 = (37 × 5)/(18 × 5) = 185/90
    2/5 = (2 × 18)/(5 × 18) = 36/90

    Step 4: Add the fractions with the common denominator.
    185/90 + 36/90 = (185 + 36)/90 = 221/90

    Step 5: Simplify the result to the lowest terms.
    221/90 = 17/90 (divide both numerator and denominator by 13)

    Therefore, the sum of 37/18 and 24/60, when simplified to the lowest terms, is 17/90.

    ### Answer: 17/90

Expected answer: 221/90

Correct? No

🔗 Problem

Problem: Determine the sum of 33/41 and 95/62. Write your answer as a simplified fraction.

Gemma 2B:

    To find the sum of 33/41 and 95/62, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 41 and 62.

    LCM(41, 62) = 2542

    Now, we convert both fractions to equivalent fractions with the common denominator:

    33/41 = (33 × 62) / (41 × 62) = 2046/2542
    95/62 = (95 × 41) / (62 × 41) = 3895/2542

    Add the numerators and keep the common denominator:

    2046/2542 + 3895/2542 = (2046 + 3895) / 2542 = 5941/2542

    Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF):

    GCF(5941, 2542) = 1

    Since the GCF is 1, the fraction 5941/2542 is already in its simplest form.

    ### Answer: 5941/2542

Expected answer: 5941/2542

Correct? Yes

🔗 Follow-up

Problem: After finding the sum of 33/41 and 95/62, add that sum to 95/62 once again. What is the final simplified fraction?

Gemma 2B:

    We already found the sum of 33/41 and 95/62 to be 5941/2542.

    Now, let's add 95/62 to this sum.

    First, convert 95/62 to an equivalent fraction with the denominator 2542:

    95/62 = (95 × 41) / (62 × 41) = 3895/2542

    Add 5941/2542 and 3895/2542:

    5941/2542 + 3895/2542 = (5941 + 3895) / 2542 = 9836/2542

    Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF):

    GCF(9836, 2542) = 2
    9836 ÷ 2 = 4918
    2542 ÷ 2 = 1271

    Therefore, the final simplified fraction is 4918/1271.

    ### Answer: 4918/1271

Expected answer: 4918/1271

Correct? Yes

🔗 Follow-up

Problem: After reconsidering the previous problem, suppose instead of 95/62, we now have 83/62. What would the sum of 33/41 and 83/62 be? Write your answer as a simplified fraction.

Gemma 2B:

    Let's follow the same steps as before to find the sum of 33/41 and 83/62.

    First, find the common denominator by calculating the least common multiple (LCM) of 41 and 62.

    LCM(41, 62) = 2542

    Convert both fractions to equivalent fractions with the common denominator:

    33/41 = (33 × 62) / (41 × 62) = 2046/2542
    83/62 = (83 × 41) / (62 × 41) = 3403/2542

    Add the numerators and keep the common denominator:

    2046/2542 + 3403/2542 = (2046 + 3403) / 2542 = 5449/2542

    Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF):

    GCF(5449, 2542) = 1

    Since the GCF is 1, the fraction 5449/2542 is already in its simplest form.

    ### Answer: 5449/2542

Expected answer: 5449/2542

Correct? Yes

🔗 Problem

Problem: Solve ((30 / 11) + (72 / 38)) and then add the result to (81 / 34). Answer as a simplified fraction.

Gemma 2B:

    Let's solve this problem step by step:

    1. First, let's solve ((30 / 11) + (72 / 38)):

       30 / 11 = 2.727272...
       72 / 38 = 1.894736...

       2.727272... + 1.894736... = 4.622008...

    2. Now, let's add the result to (81 / 34):

       81 / 34 = 2.382352...

       4.622008... + 2.382352... = 7.004360...

    3. To express the result as a simplified fraction, we need to find the ratio of the result to 1:

       7.004360... / 1 = 7.004360... / 1

       Simplifying the fraction:

       7.004360... / 1 = 7004360... / 1000000...

       Simplifying further:

       7004360... / 1000000... = 7004360 / 1000000 (approximately)

       Reducing the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD):

       GCD(7004360, 1000000) = 40

       (7004360 / 40) / (1000000 / 40) = 175109 / 25000

    ### Answer: 175109 / 25000

Expected answer: 49773/7106

Correct? No

🔗 Problem

Problem: What is the result of adding (64 / 34) + (3 / 24) and then adding the result to (41 / 96)? Answer as a simplified fraction.

Gemma 2B:

    Let's solve this problem step by step:

    1. First, let's add (64 / 34) and (3 / 24):

       To add fractions with different denominators, we need to find the least common denominator (LCD). The LCD of 34 and 24 is 408.

       (64 / 34) = (64 × 12) / (34 × 12) = 768 / 408
       (3 / 24) = (3 × 17) / (24 × 17) = 51 / 408

       Now we can add these fractions:
       (768 / 408) + (51 / 408) = 819 / 408

    2. Next, let's add the result (819 / 408) to (41 / 96):

       The LCD of 408 and 96 is 1224.

       (819 / 408) = (819 × 3) / (408 × 3) = 2457 / 1224
       (41 / 96) = (41 × 12) / (96 × 12) = 492 / 1224

       Adding these fractions:
       (2457 / 1224) + (492 / 1224) = 2949 / 1224

    3. Now, let's simplify the fraction 2949 / 1224:

       2949 and 1224 have a common factor of 3.
       2949 ÷ 3 = 983
       1224 ÷ 3 = 408

       The simplified fraction is 983 / 408.

    ### Answer: 983 / 408

Expected answer: 3973/1632

Correct? No

🔗 Problem

Problem: Daniel has to solve a math problem for his homework that includes fractions. Initially, he has been asked to add 83/73 and 53/77. The result of this step he saved as 'w'. Then, he needs to add 80/76 to the result 'w'. How would he calculate the final answer in simplified fraction form?

Gemma 2B:

    Let's solve this problem step by step:

    1. First, we need to find the value of 'w' by adding 83/73 and 53/77.
       To add fractions, we need to find the least common multiple (LCM) of the denominators.
       LCM(73, 77) = 5621
       Now, we can convert the fractions to equivalent fractions with the common denominator:
       83/73 = 83 × 77/73 × 77 = 6391/5621
       53/77 = 53 × 73/77 × 73 = 3869/5621
       Adding these fractions:
       w = 6391/5621 + 3869/5621 = 10260/5621

    2. Now, we need to add 80/76 to 'w'.
       Again, we need to find the LCM of the denominators:
       LCM(5621, 76) = 427196
       Converting the fractions to equivalent fractions with the common denominator:
       w = 10260/5621 = 10260 × 76/5621 × 76 = 779760/427196
       80/76 = 80 × 5621/76 × 5621 = 449680/427196
       Adding these fractions:
       779760/427196 + 449680/427196 = 1229440/427196

    3. Simplifying the final answer:
       1229440/427196 can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD).
       GCD(1229440, 427196) = 4
       1229440/427196 = (1229440 ÷ 4)/(427196 ÷ 4) = 307360/106799

    Therefore, the final answer in simplified fraction form is 307360/106799.

    ### Answer: 307360/106799

Expected answer: 307360/106799

Correct? Yes

🔗 Follow-up

Problem: In reviewing Daniel's math homework, his teacher noticed he made a mistake. Instead of 26/73, he erroneously used 83/73 in his first calculation for 'w'. Now Daniel needs to correct his work. So initially, he has to add 26/73 and 53/77 to calculate 'w'. Then to find 'z', he needs to add 80/76 to 'w'. What will be his new final result for 'z' in simplified fraction form?

Gemma 2B:

    Let's solve this problem step by step with the corrected values:

    1. First, we need to find the value of 'w' by adding 26/73 and 53/77.
       To add fractions, we need to find the least common multiple (LCM) of the denominators.
       LCM(73, 77) = 5621
       Now, we can convert the fractions to equivalent fractions with the common denominator:
       26/73 = 26 × 77/73 × 77 = 2002/5621
       53/77 = 53 × 73/77 × 73 = 3869/5621
       Adding these fractions:
       w = 2002/5621 + 3869/5621 = 5871/5621

    2. Now, we need to add 80/76 to 'w' to find 'z'.
       Again, we need to find the LCM of the denominators:
       LCM(5621, 76) = 427196
       Converting the fractions to equivalent fractions with the common denominator:
       w = 5871/5621 = 5871 × 76/5621 × 76 = 446196/427196
       80/76 = 80 × 5621/76 × 5621 = 449680/427196
       Adding these fractions:
       z = 446196/427196 + 449680/427196 = 895876/427196

    3. Simplifying the final answer:
       895876/427196 can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD).
       GCD(895876, 427196) = 4
       895876/427196 = (895876 ÷ 4)/(427196 ÷ 4) = 223969/106799

    Therefore, the new final result for 'z' in simplified fraction form is 223969/106799.

    ### Answer: 223969/106799

Expected answer: 223969/106799

Correct? Yes

🔗 Problem

Problem: Add the following fractions and simplify your answer: 27/20 and 14/66.

Gemma 2B:

    To add fractions with different denominators, we first need to find the least common denominator (LCD). The LCD is the least common multiple of the denominators.

    Denominators: 20 and 66
    Factors of 20: 1, 2, 4, 5, 10, 20
    Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
    LCD: 2 × 3 × 5 × 11 = 330

    Now, we convert each fraction to an equivalent fraction with the LCD as the denominator:

    27/20 = 27 × 330/20 × 330 = 8910/6600
    14/66 = 14 × 330/66 × 330 = 4620/21780

    Add the fractions:
    8910/6600 + 4620/21780 = 8910/6600 + 1540/6600 = 10450/6600

    Simplify the result by dividing the numerator and denominator by their greatest common factor (GCF):
    Factors of 10450: 1, 2, 5, 10, 19, 22, 25, 38, 50, 95, 110, 190, 209, 418, 475, 550, 1045, 2090, 10450
    Factors of 6600: 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 25, 30, 33, 44, 50, 55, 60, 66, 75, 100, 110, 132, 150, 165, 200, 220, 264, 275, 300, 330, 440, 550, 600, 660, 825, 1100, 1320, 1650, 2200, 3300, 6600
    GCF: 550

    10450/6600 ÷ 550/550 = 19/12

    ### Answer: 19/12

Expected answer: 1031/660

Correct? No

🔗 Problem

Problem: What is the result of the expression ((32 / 14) - (22 / 47))? Write your answer as a simplified fraction.

Gemma 2B:

    To simplify the expression ((32 / 14) - (22 / 47)), let's solve it step by step:

    1. Simplify 32 / 14:
       32 / 14 = 16 / 7 = 2 2/7

    2. Simplify 22 / 47:
       22 / 47 cannot be simplified further

    3. Subtract the fractions:
       (2 2/7) - (22 / 47)

       To subtract fractions with different denominators, we need to find the least common denominator (LCD):
       LCD = 7 × 47 = 329

       Convert the fractions to equivalent fractions with the LCD:
       (2 2/7) = (16/7) = (16 × 47) / (7 × 47) = 752 / 329
       (22 / 47) = (22 × 7) / (47 × 7) = 154 / 329

       Now subtract the fractions:
       (752 / 329) - (154 / 329) = (752 - 154) / 329 = 598 / 329

    4. Simplify the result:
       598 / 329 = 2 × 13 × 23 / 7 × 47
       The numerator and denominator have no common factors other than 1, so the fraction is already in its simplest form.

    ### Answer: 598 / 329

Expected answer: 598/329

Correct? Yes

🔗 Follow-up

Problem: If you take the result of ((32 / 14) - (22 / 47)) you calculated earlier, what would be the value you get when you add this result to itself? Write your answer as a simplified fraction.

Gemma 2B:

    Let's call the result of ((32 / 14) - (22 / 47)) as 'x'.
    From the previous calculation, we found that x = 598 / 329.

    Now, we need to add x to itself, which means:
    x + x = (598 / 329) + (598 / 329)

    To add fractions with the same denominator, we simply add the numerators and keep the denominator the same:
    (598 / 329) + (598 / 329) = (598 + 598) / 329 = 1196 / 329

    Now, let's simplify the fraction 1196 / 329:
    1196 / 329 = 2 × 2 × 13 × 23 / 7 × 47
    The numerator and denominator have no common factors other than 1, so the fraction is already in its simplest form.

    ### Answer: 1196 / 329

Expected answer: 1196/329

Correct? Yes

🔗 Follow-up

Problem: Suppose instead of having 32/14 part of the original mixture, you actually had 71/14 part, and the same fraction (22/47) was subtracted from it. In that case, what would be the new result of the calculation: ((71 / 14) - (22 / 47))? Write your answer as a simplified fraction.

Gemma 2B:

    Let's solve the new expression ((71 / 14) - (22 / 47)) step by step:

    1. Simplify 71 / 14:
       71 / 14 = 5 1/14

    2. Simplify 22 / 47:
       22 / 47 cannot be simplified further

    3. Subtract the fractions:
       (5 1/14) - (22 / 47)

       To subtract fractions with different denominators, we need to find the least common denominator (LCD):
       LCD = 14 × 47 = 658

       Convert the fractions to equivalent fractions with the LCD:
       (5 1/14) = (71/14) = (71 × 47) / (14 × 47) = 3337 / 658
       (22 / 47) = (22 × 14) / (47 × 14) = 308 / 658

       Now subtract the fractions:
       (3337 / 658) - (308 / 658) = (3337 - 308) / 658 = 3029 / 658

    4. Simplify the result:
       3029 / 658 = 3029 / 658
       The numerator and denominator have no common factors other than 1, so the fraction is already in its simplest form.

    ### Answer: 3029 / 658

Expected answer: 3029/658

Correct? Yes

🔗 Problem

Problem: What is the sum of 74/61 and 41/53 expressed in fractions?

Gemma 2B:

    To find the sum of 74/61 and 41/53, we need to find a common denominator. The common denominator will be the product of the denominators: 61 * 53 = 3233.

    Now, we need to convert each fraction to an equivalent fraction with the common denominator:

    74/61 = 74 * 53 / (61 * 53) = 3922/3233
    41/53 = 41 * 61 / (53 * 61) = 2501/3233

    Now we can add the numerators:

    3922/3233 + 2501/3233 = (3922 + 2501)/3233 = 6423/3233

    Therefore, the sum of 74/61 and 41/53 is 6423/3233.

    ### Answer: 6423/3233

Expected answer: 6423/3233

Correct? Yes

🔗 Follow-up

Problem: Assuming you already calculated the sum of 74/61 and 41/53, what would be the total if you added 83/4 to the result? Answer as a simplified fraction.

Gemma 2B:

    We know from the previous calculation that the sum of 74/61 and 41/53 is 6423/3233.

    Now, we need to add 83/4 to this result. First, we need to convert 83/4 to an equivalent fraction with the common denominator of 3233:

    83/4 = 83 * 808.25 / (4 * 808.25) = 67085.75/3233 = 20753/3233 (rounded to the nearest whole number in the numerator)

    Now we can add 6423/3233 and 20753/3233:

    6423/3233 + 20753/3233 = (6423 + 20753)/3233 = 27176/3233

    To simplify this fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator. The GCD of 27176 and 3233 is 1.

    Since the GCD is 1, the fraction 27176/3233 is already in its simplest form.

    ### Answer: 27176/3233

Expected answer: 294031/12932

Correct? No

🔗 Follow-up

Problem: Previously you calculated the sum of 74/61 and 41/53. Now, let's consider if the second fraction was actually 41/88 instead of 41/53. What would be the new total of 74/61 and 41/88? Answer as a simplified fraction.

Gemma 2B:

    Apologies for the confusion. Let's calculate the sum of 74/61 and 41/88.

    To find the sum, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of the denominators: LCM(61, 88) = 1,708.

    Now, we need to convert each fraction to an equivalent fraction with the common denominator:

    74/61 = 74 * 28 / (61 * 28) = 2072/1708
    41/88 = 41 * 61 / (88 * 61) = 2501/5368

    Now we can add the numerators:

    2072/1708 + 2501/5368 = (2072 * 5368 + 2501 * 1708) / (1708 * 5368) = 15645644 / 9170944

    To simplify the fraction, we find the greatest common divisor (GCD) of the numerator and denominator:
    GCD(15645644, 9170944) = 4

    Dividing both the numerator and denominator by the GCD:

    (15645644 / 4) / (9170944 / 4) = 3911411 / 2292736

    Therefore, the sum of 74/61 and 41/88, expressed as a simplified fraction, is 3911411/2292736.

    ### Answer: 3911411/2292736

Expected answer: 9013/5368

Correct? No

🔗 Problem

Problem: First, find out the result of 94 / 2 - 74 / 57. Then add the result to 56 / 97. What fraction do you get?

Gemma 2B:

    Let's solve this problem step by step:

    1. First, let's calculate 94 / 2 - 74 / 57.

       94 / 2 = 47
       74 / 57 ≈ 1.2982 (rounded to 4 decimal places)

       47 - 1.2982 = 45.7018

    2. Now, let's add the result to 56 / 97.

       56 / 97 ≈ 0.5773 (rounded to 4 decimal places)

       45.7018 + 0.5773 = 46.2791

    3. The final result is a decimal, not a fraction. Let's convert it to a fraction.

       46.2791 = 462791 / 10000 (as a fraction)

       Simplifying the fraction:
       462791 / 10000 = 23139.55 / 500 ≈ 23139 / 500 (rounded down)

    ### Answer: 23139 / 500

Expected answer: 255877/5529

Correct? No

🔗 Problem

Problem: What is the sum of 14/89 and the sum of 24/34 and 44/87? Give your answer as a simplified fraction.

Gemma 2B:

    To find the sum of 14/89 and the sum of 24/34 and 44/87, we need to:
    1. Add 24/34 and 44/87
    2. Add the result to 14/89
    3. Simplify the final fraction

    Step 1: Adding 24/34 and 44/87
    To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators.
    LCM of 34 and 87 = 2958
    Now, we convert both fractions to equivalent fractions with the LCM as the denominator:
    24/34 = 24 × 87/34 × 87 = 2088/2958
    44/87 = 44 × 34/87 × 34 = 1496/2958
    2088/2958 + 1496/2958 = 3584/2958

    Step 2: Adding the result to 14/89
    Again, we need to find the LCM of the denominators (2958 and 89).
    LCM of 2958 and 89 = 263262
    Converting both fractions to equivalent fractions with the LCM as the denominator:
    3584/2958 = 3584 × 89/2958 × 89 = 319976/263262
    14/89 = 14 × 2958/89 × 2958 = 41412/263262
    319976/263262 + 41412/263262 = 361388/263262

    Step 3: Simplifying the final fraction
    The numerator and denominator have a common factor of 4.
    361388 ÷ 4 = 90347
    263262 ÷ 4 = 65817
    Simplified fraction = 90347/65817

    ### Answer: 90347/65817

Expected answer: 180194/131631

Correct? No

🔗 Problem

Problem: What would you get if you add 73/30 to 8/60?

Gemma 2B:

    To add fractions, we need to find a common denominator. In this case, the common denominator is 60, which is the least common multiple of 30 and 60.

    First, let's convert 73/30 to an equivalent fraction with a denominator of 60:
    73/30 = (73 * 2)/(30 * 2) = 146/60

    Now we can add 146/60 and 8/60:
    146/60 + 8/60 = (146 + 8)/60 = 154/60

    To simplify the fraction, we divide both the numerator and denominator by their greatest common factor, which is 2:
    154/60 = (154 ÷ 2)/(60 ÷ 2) = 77/30

    ### Answer: 77/30

Expected answer: 77/30

Correct? Yes

🔗 Follow-up

Problem: If you take the result of adding 73/30 to 8/60 and then add it to itself again, what fraction do you get?

Gemma 2B:

    From the previous question, we found that 73/30 + 8/60 = 77/30.

    Now, we need to add 77/30 to itself:
    77/30 + 77/30 = (77 + 77)/30 = 154/30

    To simplify the fraction, we divide both the numerator and denominator by their greatest common factor, which is 2:
    154/30 = (154 ÷ 2)/(30 ÷ 2) = 77/15

    ### Answer: 77/15

Expected answer: 77/15

Correct? Yes

🔗 Follow-up

Problem: Suppose you originally had a fraction of 73/30. Now, instead of adding 8/60 to it, you decide to add 49/60. What fraction will you get in this case?

Gemma 2B:

    Let's follow the same process as before. We'll convert 73/30 to an equivalent fraction with a denominator of 60, and then add 49/60 to it.

    Converting 73/30 to an equivalent fraction with a denominator of 60:
    73/30 = (73 * 2)/(30 * 2) = 146/60

    Now, adding 146/60 and 49/60:
    146/60 + 49/60 = (146 + 49)/60 = 195/60

    To simplify the fraction, we divide both the numerator and denominator by their greatest common factor, which is 15:
    195/60 = (195 ÷ 15)/(60 ÷ 15) = 13/4

    Therefore, if you add 49/60 to 73/30, you will get 13/4.

    ### Answer: 13/4

Expected answer: 13/4

Correct? Yes

🔗 Problem

Problem: Suppose you have the following three fractions: 82/49, 45/60, and 99/59. If you add the first fraction (82/49) with the second one (45/60), call this result 'd'. Then, add 'd' to the third fraction (99/59). What would be the resulting sum? Please provide your answer as a simplified fraction.

Gemma 2B:

    Let's solve this problem step by step:

    1. First, we need to add the fractions 82/49 and 45/60. To add fractions with different denominators, we need to find the least common denominator (LCD).

       The LCD of 49 and 60 is 1470 (49 * 30 = 1470, 60 * 30 = 1470).

       Now, we convert the fractions to equivalent fractions with the LCD:
       82/49 = (82 * 30) / (49 * 30) = 2460/1470
       45/60 = (45 * 30) / (60 * 30) = 1350/1470

       Adding these fractions:
       2460/1470 + 1350/1470 = 3810/1470

       This result is 'd'.

    2. Now, we add 'd' (3810/1470) to the third fraction, 99/59.

       The LCD of 1470 and 59 is 86730 (1470 * 59 = 86730).

       Converting the fractions to equivalent fractions with the LCD:
       3810/1470 = (3810 * 59) / (1470 * 59) = 224790/86730
       99/59 = (99 * 1470) / (59 * 1470) = 145530/86730

       Adding these fractions:
       224790/86730 + 145530/86730 = 370320/86730

    3. Simplifying the resulting fraction:
       370320/86730 = 4260/999

    Therefore, the resulting sum, simplified, is 4260/999.

    ### Answer: 4260/999

Expected answer: 47429/11564

Correct? No

🔗 Problem

Problem: Solve the following two steps: first, subtract 76/30 from 91/16 and second, add the answer to 18/44. Round the final answer to the nearest hundredth.

Gemma 2B:

    Step 1: Subtract 76/30 from 91/16

    To subtract fractions, we need to find a common denominator. The common denominator is the least common multiple (LCM) of 30 and 16.

    LCM(30, 16) = 240

    Now, we convert both fractions to equivalent fractions with the common denominator:

    91/16 = 1365/240
    76/30 = 608/240

    Subtracting the fractions:

    1365/240 - 608/240 = 757/240

    Step 2: Add the answer from Step 1 to 18/44

    First, let's simplify 757/240:

    757/240 = 3.154166...

    Now, we need to find the common denominator for 3.154166... and 18/44. The common denominator is 44.

    3.154166... = 138.783333.../44
    18/44 = 18/44

    Adding the fractions:

    138.783333.../44 + 18/44 = 156.783333.../44

    Rounding the final answer to the nearest hundredth:

    156.783333.../44 ≈ 3.56

    ### Answer: 3.56

Expected answer: 9407/2640

Correct? No

🔗 Problem

Problem: Calculate the result of ((8 / 91) + (49 / 5)) and subtract (32 / 76) from the result. Provide your answer as a simplified fraction.

Gemma 2B:

    Let's break this down step by step:

    1. First, let's calculate (8 / 91) + (49 / 5):

       8 / 91 = 8/91 (already in simplified form)
       49 / 5 = 9 4/5

       Now, add these fractions:
       8/91 + 9 4/5 = (8/91) + (484/91) = 492/91

    2. Next, we need to subtract (32 / 76) from the result:

       32 / 76 = 8/19 (simplified form)

       492/91 - 8/19 = (492/91) - (8/19)

       To subtract these fractions, we need a common denominator. The LCM of 91 and 19 is 1729.

       (492 * 19)/(91 * 19) - (8 * 91)/(19 * 91) = 9348/1729 - 728/1729 = 8620/1729

    3. Finally, simplify the fraction 8620/1729:

       Divide both the numerator and denominator by their GCD, which is 1.
       8620/1729 is already in its simplest form.

    ### Answer: 8620/1729

Expected answer: 81841/8645

Correct? No

🔗 Problem

Problem: Calculate the value of ((75 / 45) + (5 / 49)) first. Then add this value with 3 / 58. Provide the answer as a simple fraction.

Gemma 2B:

    Let's solve this problem step by step:

    1. First, let's calculate the value of ((75 / 45) + (5 / 49)):
       75 / 45 = 5 / 3
       5 / 49 = 5 / 49
       (5 / 3) + (5 / 49) = ((5 * 49) + (5 * 3)) / (3 * 49)
                         = (245 + 15) / 147
                         = 260 / 147

    2. Now, let's add (3 / 58) to the result from step 1:
       (260 / 147) + (3 / 58) = ((260 * 58) + (3 * 147)) / (147 * 58)
                              = (15080 + 441) / 8526
                              = 15521 / 8526

    3. Simplify the fraction:
       15521 and 8526 have a common factor of 7.
       15521 / 7 = 2217
       8526 / 7 = 1218

       So, the simplified fraction is 2217 / 1218.

    ### Answer: 2217 / 1218

Expected answer: 15521/8526

Correct? No

🔗 Problem

Problem: Calculate the answer to ((43 / 15) - (33 / 95)) and simplify it to its lowest terms.

Gemma 2B:

    To calculate ((43 / 15) - (33 / 95)), let's first perform the division operations:

    43 / 15 = 2.866666...
    33 / 95 = 0.347368...

    Now, subtract these values:

    2.866666... - 0.347368... = 2.519298...

    To simplify this fraction to its lowest terms, we need to convert it to a rational number (a fraction).

    2.519298... = 2 + 0.519298...

    0.519298... can be written as a fraction by setting up an equation:

    Let x = 0.519298...
    100x = 51.9298...
    100x - x = 51.9298... - 0.519298...
    99x = 51.41
    x = 51.41 / 99
    x = 5141 / 9900

    Therefore, 2.519298... = 2 + 5141 / 9900 = 19900 / 9900 + 5141 / 9900 = 25041 / 9900

    Simplifying this fraction:
    25041 and 9900 have a common factor of 99.
    25041 / 99 = 253
    9900 / 99 = 100

    Therefore, ((43 / 15) - (33 / 95)) simplified to its lowest terms is:
    253 / 100

    ### Answer: 253 / 100

Expected answer: 718/285

Correct? No

🔗 Problem

Problem: What is the sum of ((78 / 45) + (89 / 36)) added to itself? Answer as a simple fraction.

Gemma 2B:

    To find the sum of ((78 / 45) + (89 / 36)) added to itself, we need to:
    1. Calculate (78 / 45) + (89 / 36)
    2. Add the result to itself
    3. Simplify the fraction

    Step 1: Calculate (78 / 45) + (89 / 36)
    - Find a common denominator: 45 × 36 = 1620
    - Convert fractions to equivalent fractions with the common denominator:
      - 78 / 45 = (78 × 36) / 1620 = 2808 / 1620
      - 89 / 36 = (89 × 45) / 1620 = 4005 / 1620
    - Add the numerators: (2808 + 4005) / 1620 = 6813 / 1620

    Step 2: Add the result to itself
    - (6813 / 1620) + (6813 / 1620) = (6813 × 2) / 1620 = 13626 / 1620

    Step 3: Simplify the fraction
    - Divide the numerator and denominator by their greatest common factor (GCF)
    - GCF of 13626 and 1620 is 6
    - (13626 / 6) / (1620 / 6) = 2271 / 270

    ### Answer: 2271 / 270

Expected answer: 757/90

Correct? Yes

🔗 Follow-up

Problem: After finding the sum of ((78 / 45) + (89 / 36)) added to itself, what is the resultant value when that sum is added to the original ((78 / 45) + (89 / 36))? Answer as a simple fraction.

Gemma 2B:

    Let's break this down step by step:

    1. We already know that the sum of ((78 / 45) + (89 / 36)) added to itself is 2271 / 270.

    2. Now, we need to add this sum to the original ((78 / 45) + (89 / 36)).

    3. First, let's calculate ((78 / 45) + (89 / 36)):
       - Find a common denominator: 45 × 36 = 1620
       - Convert fractions to equivalent fractions with the common denominator:
         - 78 / 45 = (78 × 36) / 1620 = 2808 / 1620
         - 89 / 36 = (89 × 45) / 1620 = 4005 / 1620
       - Add the numerators: (2808 + 4005) / 1620 = 6813 / 1620

    4. Now, we add (2271 / 270) to (6813 / 1620):
       - Find a common denominator: 270 × 1620 = 437400
       - Convert fractions to equivalent fractions with the common denominator:
         - 2271 / 270 = (2271 × 1620) / 437400 = 3679020 / 437400
         - 6813 / 1620 = (6813 × 270) / 437400 = 1839510 / 437400
       - Add the numerators: (3679020 + 1839510) / 437400 = 5518530 / 437400

    5. Simplify the fraction:
       - Divide the numerator and denominator by their greatest common factor (GCF)
       - GCF of 5518530 and 437400 is 30
       - (5518530 / 30) / (437400 / 30) = 183951 / 14580

    ### Answer: 183951 / 14580

Expected answer: 757/60

Correct? Yes

🔗 Follow-up

Problem: Previously, you calculated the sum of ((78 / 45) + (89 / 36)) added to itself. But what if the first fraction was instead (78 / 93)? In that case, what would be the new result of ((78 / 93) + (89 / 36)) added to itself? Please give your answer as a simple fraction.

Gemma 2B:

    Let's solve this problem step by step:

    1. Calculate (78 / 93) + (89 / 36)
    2. Add the result to itself
    3. Simplify the fraction

    Step 1: Calculate (78 / 93) + (89 / 36)
    - Find a common denominator: 93 × 36 = 3348
    - Convert fractions to equivalent fractions with the common denominator:
      - 78 / 93 = (78 × 36) / 3348 = 2808 / 3348
      - 89 / 36 = (89 × 93) / 3348 = 8277 / 3348
    - Add the numerators: (2808 + 8277) / 3348 = 11085 / 3348

    Step 2: Add the result to itself
    - (11085 / 3348) + (11085 / 3348) = (11085 × 2) / 3348 = 22170 / 3348

    Step 3: Simplify the fraction
    - Divide the numerator and denominator by their greatest common factor (GCF)
    - GCF of 22170 and 3348 is 6
    - (22170 / 6) / (3348 / 6) = 3695 / 558

    ### Answer: 3695 / 558

Expected answer: 3695/558

Correct? Yes

🔗 Problem

Problem: Let's consider that 93 is divided by 34 to get a fraction value, from which is subtracted another fraction 77/74. What would be the result as a simplified fraction?

Gemma 2B:

    Okay, let's solve this problem step by step:

    1. First, let's divide 93 by 34 to get a fraction:
       93 ÷ 34 = 93/34

    2. Now, we have to subtract 77/74 from 93/34:
       93/34 - 77/74

    3. To subtract fractions, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 34 and 74.
       LCM(34, 74) = 1258

    4. Now, we convert both fractions to equivalent fractions with the common denominator:
       93/34 = (93 × 37) / (34 × 37) = 3441/1258
       77/74 = (77 × 17) / (74 × 17) = 1309/1258

    5. Subtract the fractions:
       3441/1258 - 1309/1258 = (3441 - 1309) / 1258 = 2132/1258

    6. Simplify the resulting fraction by dividing both the numerator and denominator by their greatest common divisor (GCD):
       GCD(2132, 1258) = 2
       (2132 ÷ 2) / (1258 ÷ 2) = 1066/629

    Therefore, the simplified fraction is 1066/629.

    ### Answer: 1066/629

Expected answer: 1066/629

Correct? Yes

🔗 Follow-up

Problem: Continuing from our previous problem, let's now take our previous result and add it to the fraction 64/70. What would we get as a simplified fraction as the final answer?

Gemma 2B:

    Great! Let's continue from the previous problem and add the fraction 64/70 to our result, 1066/629.

    1. We have to add 1066/629 and 64/70:
       1066/629 + 64/70

    2. To add fractions, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 629 and 70.
       LCM(629, 70) = 44030

    3. Now, we convert both fractions to equivalent fractions with the common denominator:
       1066/629 = (1066 × 70) / (629 × 70) = 74620/44030
       64/70 = (64 × 629) / (70 × 629) = 40256/44030

    4. Add the fractions:
       74620/44030 + 40256/44030 = (74620 + 40256) / 44030 = 114876/44030

    5. Simplify the resulting fraction by dividing both the numerator and denominator by their greatest common divisor (GCD):
       GCD(114876, 44030) = 2
       (114876 ÷ 2) / (44030 ÷ 2) = 57438/22015

    Therefore, the simplified fraction after adding 64/70 to the previous result is 57438/22015.

    ### Answer: 57438/22015

Expected answer: 57438/22015

Correct? Yes

🔗 Follow-up

Problem: Recall the previous problem where we had 93 divided by 34 and subtracted the fraction 77/74 from it. Now, let's slightly adjust the scenario. Suppose instead of subtracting 77/74, we subtract 77/51 from the result of 93 divided by 34. What would be the result as a simplified fraction under this new circumstance?

Gemma 2B:

    Great! Let's solve this problem step by step, similar to the previous one:

    1. First, let's divide 93 by 34 to get a fraction:
       93 ÷ 34 = 93/34

    2. Now, we have to subtract 77/51 from 93/34:
       93/34 - 77/51

    3. To subtract fractions, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 34 and 51.
       LCM(34, 51) = 1734

    4. Now, we convert both fractions to equivalent fractions with the common denominator:
       93/34 = (93 × 51) / (34 × 51) = 4743/1734
       77/51 = (77 × 34) / (51 × 34) = 2618/1734

    5. Subtract the fractions:
       4743/1734 - 2618/1734 = (4743 - 2618) / 1734 = 2125/1734

    6. Simplify the resulting fraction by dividing both the numerator and denominator by their greatest common divisor (GCD):
       GCD(2125, 1734) = 17
       (2125 ÷ 17) / (1734 ÷ 17) = 125/102

    Therefore, under the new circumstance, the simplified fraction is 125/102.

    ### Answer: 125/102

Expected answer: 125/102

Correct? Yes

🔗 Problem

Problem: Find the sum of 86/35 and 68/85. Express your answer as a simplified fraction.

Gemma 2B:

    To find the sum of 86/35 and 68/85, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 35 and 85.

    LCM(35, 85) = 595

    Now, we convert both fractions to equivalent fractions with the common denominator:

    86/35 = (86 × 17) / (35 × 17) = 1462/595
    68/85 = (68 × 7) / (85 × 7) = 476/595

    Add the numerators:

    1462/595 + 476/595 = (1462 + 476) / 595 = 1938/595

    Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF):

    GCF(1938, 595) = 17

    (1938/17) / (595/17) = 114/35

    ### Answer: 114/35

Expected answer: 114/35

Correct? Yes

🔗 Follow-up

Problem: After finding the sum of 86/35 and 68/85, add the result to 86/35 again. Express your answer as a simplified fraction.

Gemma 2B:

    We already found the sum of 86/35 and 68/85 to be 114/35.

    Now, we need to add 114/35 and 86/35:

    114/35 + 86/35 = (114 + 86) / 35 = 200/35

    Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF):

    GCF(200, 35) = 5

    (200/5) / (35/5) = 40/7

    ### Answer: 40/7

Expected answer: 40/7

Correct? Yes

🔗 Follow-up

Problem: Reconsider the previous problem where you found the sum of 86/35 and 68/85. What if there were a mistake and the original fraction was actually 86/75, not 86/35? Find the sum of the revised fraction, 86/75, with 68/85. Express your answer as a simplified fraction.

Gemma 2B:

    Apologies for the confusion. Let's solve the problem with the revised fraction, 86/75, and find its sum with 68/85.

    To find the sum of 86/75 and 68/85, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 75 and 85.

    LCM(75, 85) = 1275

    Now, we convert both fractions to equivalent fractions with the common denominator:

    86/75 = (86 × 17) / (75 × 17) = 1462/1275
    68/85 = (68 × 15) / (85 × 15) = 1020/1275

    Add the numerators:

    1462/1275 + 1020/1275 = (1462 + 1020) / 1275 = 2482/1275

    Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF):

    GCF(2482, 1275) = 1

    Since the GCF is 1, the fraction 2482/1275 is already in its simplest form.

    ### Answer: 2482/1275

Expected answer: 146/75

Correct? Yes

🔗 Problem

Problem: What is the sum of 99/53 and 67/94 in simplest form?

Gemma 2B:

    To find the sum of 99/53 and 67/94 in simplest form, we need to find a common denominator, add the fractions, and then simplify the result.

    Step 1: Find the least common multiple (LCM) of the denominators 53 and 94.
    LCM(53, 94) = 4982

    Step 2: Convert both fractions to equivalent fractions with the common denominator of 4982.
    99/53 = 99 × (4982/53) / (4982/53) = 9306/4982
    67/94 = 67 × (4982/94) / (4982/94) = 3551/4982

    Step 3: Add the numerators of the equivalent fractions.
    9306/4982 + 3551/4982 = (9306 + 3551)/4982 = 12857/4982

    Step 4: Simplify the resulting fraction by dividing the numerator and denominator by their greatest common factor (GCF).
    GCF(12857, 4982) = 1
    The fraction 12857/4982 is already in its simplest form.

    ### Answer: 12857/4982

Expected answer: 12857/4982

Correct? Yes

🔗 Follow-up

Problem: What if you were to add the fraction 50/56 to the sum you previously found (of 99/53 and 67/94)? What is the resulting value in its simplest form?

Gemma 2B:

    To add 50/56 to the sum of 99/53 and 67/94, we will use the sum found in the previous question (12857/4982) and find a common denominator with 50/56.

    Step 1: Find the least common multiple (LCM) of the denominators 4982 and 56.
    LCM(4982, 56) = 278992

    Step 2: Convert both fractions to equivalent fractions with the common denominator of 278992.
    12857/4982 = 12857 × (278992/4982) / (278992/4982) = 719984/278992
    50/56 = 50 × (278992/56) / (278992/56) = 249200/278992

    Step 3: Add the numerators of the equivalent fractions.
    719984/278992 + 249200/278992 = (719984 + 249200)/278992 = 969184/278992

    Step 4: Simplify the resulting fraction by dividing the numerator and denominator by their greatest common factor (GCF).
    GCF(969184, 278992) = 64
    969184/64 = 15143
    278992/64 = 4359

    The simplified fraction is 15143/4359.

    ### Answer: 15143/4359

Expected answer: 242273/69748

Correct? No

🔗 Problem

Problem: What is the simplified form of the fraction that results from 74/27 minus 56/33?

Gemma 2B:

    To simplify the fraction that results from 74/27 minus 56/33, we need to:
    1. Find a common denominator for the fractions
    2. Subtract the numerators
    3. Simplify the resulting fraction

    Step 1: Find the common denominator
    - The common denominator is the least common multiple (LCM) of 27 and 33.
    - 27 = 3 × 3 × 3
    - 33 = 3 × 11
    - LCM(27, 33) = 3 × 3 × 3 × 11 = 891

    Step 2: Subtract the numerators
    - 74/27 = (74 × 33) / 891 = 2442 / 891
    - 56/33 = (56 × 27) / 891 = 1512 / 891
    - (2442 / 891) - (1512 / 891) = (2442 - 1512) / 891 = 930 / 891

    Step 3: Simplify the resulting fraction
    - Divide the numerator and denominator by their greatest common factor (GCF).
    - GCF(930, 891) = 3
    - (930 / 891) ÷ 3 = (310 / 297)

    ### Answer: 310/297

Expected answer: 310/297

Correct? Yes

🔗 Follow-up

Problem: If you then add 92/70 to the result of 74/27 minus 56/33, what fraction do you now have? Please answer as a simplified fraction.

Gemma 2B:

    Let's continue from the previous result:
    74/27 - 56/33 = 310/297

    Now, we need to add 92/70 to 310/297.

    Step 1: Find the common denominator
    - The common denominator is the least common multiple (LCM) of 297 and 70.
    - 297 = 3 × 3 × 3 × 11
    - 70 = 2 × 5 × 7
    - LCM(297, 70) = 2 × 3 × 3 × 3 × 5 × 7 × 11 = 20790

    Step 2: Add the numerators
    - 310/297 = (310 × 70) / 20790 = 21700 / 20790
    - 92/70 = (92 × 297) / 20790 = 27324 / 20790
    - (21700 / 20790) + (27324 / 20790) = (21700 + 27324) / 20790 = 49024 / 20790

    Step 3: Simplify the resulting fraction
    - Divide the numerator and denominator by their greatest common factor (GCF).
    - GCF(49024, 20790) = 2
    - (49024 / 20790) ÷ 2 = 24512 / 10395

    ### Answer: 24512/10395

Expected answer: 24512/10395

Correct? Yes

🔗 Follow-up

Problem: What if we had 77/27 instead of 74/27 in the beginning? What would the fraction be if you subtracted 56/33 from this? Please answer as a simplified fraction.

Gemma 2B:

    Let's solve this problem step by step, following the same process as before.

    Step 1: Find the common denominator
    - The common denominator is the least common multiple (LCM) of 27 and 33.
    - 27 = 3 × 3 × 3
    - 33 = 3 × 11
    - LCM(27, 33) = 3 × 3 × 3 × 11 = 891

    Step 2: Subtract the numerators
    - 77/27 = (77 × 33) / 891 = 2541 / 891
    - 56/33 = (56 × 27) / 891 = 1512 / 891
    - (2541 / 891) - (1512 / 891) = (2541 - 1512) / 891 = 1029 / 891

    Step 3: Simplify the resulting fraction
    - Divide the numerator and denominator by their greatest common factor (GCF).
    - GCF(1029, 891) = 3
    - (1029 / 891) ÷ 3 = (343 / 297)

    ### Answer: 343/297

Expected answer: 343/297

Correct? Yes

🔗 Problem

Problem: Find the result when you subtract 91/65 from the sum of 96/40 and 11/99. Leave your answer as a simplified fraction.

Gemma 2B:

    To solve this problem, let's break it down into steps:

    1. Find the sum of 96/40 and 11/99.
    2. Subtract 91/65 from the result of step 1.
    3. Simplify the resulting fraction.

    Step 1: Find the sum of 96/40 and 11/99.
    To add fractions, we need a common denominator. The least common multiple of 40 and 99 is 3960.

    96/40 = 96 × 99 / 40 × 99 = 9504/3960
    11/99 = 11 × 40 / 99 × 40 = 440/3960

    Now, we can add the fractions:
    9504/3960 + 440/3960 = 9944/3960

    Step 2: Subtract 91/65 from the result of step 1.
    To subtract fractions, we need a common denominator. The least common multiple of 3960 and 65 is 257400.

    9944/3960 = 9944 × 65 / 3960 × 65 = 646360/257400
    91/65 = 91 × 3960 / 65 × 3960 = 360360/257400

    Now, we can subtract the fractions:
    646360/257400 - 360360/257400 = 286000/257400

    Step 3: Simplify the resulting fraction.
    Divide the numerator and denominator by their greatest common factor, which is 28600.

    286000/257400 = 10/9

    ### Answer: 10/9

Expected answer: 10/9

Correct? Yes

🔗 Follow-up

Problem: After finding the result from the previous problem, add that result to 86/73. What is the new total? Leave your answer as a simplified fraction.

Gemma 2B:

    In the previous problem, we found that the result was 10/9.

    Now, we need to add 10/9 to 86/73.

    To add fractions, we need a common denominator. The least common multiple of 9 and 73 is 657.

    10/9 = 10 × 73 / 9 × 73 = 730/657
    86/73 = 86 × 9 / 73 × 9 = 774/657

    Now, we can add the fractions:
    730/657 + 774/657 = 1504/657

    Simplify the resulting fraction by dividing the numerator and denominator by their greatest common factor, which is 73.

    1504/657 = 16/7

    ### Answer: 16/7

Expected answer: 1504/657

Correct? No

🔗 Follow-up

Problem: In the previous problem, you may have made a mistake. You accidentally added 63/99 instead of 11/99 to 96/40. Now, subtract 91/65 from this new sum. What result do you get in this case? Please leave your answer as a simplified fraction.

Gemma 2B:

    You're right, I apologize for the mistake. Let's solve the problem with the correct fraction, 11/99.

    Step 1: Find the sum of 96/40 and 11/99.
    The least common multiple of 40 and 99 is 3960.

    96/40 = 96 × 99 / 40 × 99 = 9504/3960
    11/99 = 11 × 40 / 99 × 40 = 440/3960

    Now, we can add the fractions:
    9504/3960 + 440/3960 = 9944/3960

    Step 2: Subtract 91/65 from the result of step 1.
    The least common multiple of 3960 and 65 is 257400.

    9944/3960 = 9944 × 65 / 3960 × 65 = 646360/257400
    91/65 = 91 × 3960 / 65 × 3960 = 360360/257400

    Now, we can subtract the fractions:
    646360/257400 - 360360/257400 = 286000/257400

    Step 3: Simplify the resulting fraction.
    Divide the numerator and denominator by their greatest common factor, which is 2000.

    286000/257400 = 143/1287

    ### Answer: 143/1287

Expected answer: 18/11

Correct? No

🔗 Problem

Problem: Calculate the sum of the following expressions: 1) Divide 10 by 5 and add that result to 35 divided by 27. This will give you a value h. 2) Then, add 47 divided by 99 to h. This will give you a value p. What is the value of p?

Gemma 2B:

    Let's solve this problem step by step:

    1) First, we need to calculate the value of h.
       - Divide 10 by 5: 10 ÷ 5 = 2
       - Divide 35 by 27: 35 ÷ 27 ≈ 1.2963 (rounded to 4 decimal places)
       - Add the results: 2 + 1.2963 = 3.2963
       So, h = 3.2963

    2) Now, we need to calculate the value of p by adding 47 divided by 99 to h.
       - Divide 47 by 99: 47 ÷ 99 ≈ 0.4747 (rounded to 4 decimal places)
       - Add this result to h: 3.2963 + 0.4747 = 3.7710
       So, p = 3.7710

    ### Answer: 3.7710

Expected answer: 1120/297

Correct? No

🔗 Problem

Problem: Consider the fraction 90/81. Add it to 2/66 and simplify your answer to the simplest form. What is the result?

Gemma 2B:

    To add 90/81 and 2/66, we need to find a common denominator. The least common multiple of 81 and 66 is 594.

    90/81 = 90/81 * 11/11 = 990/891
    2/66 = 2/66 * 9/9 = 18/594

    Now we can add the fractions:
    990/891 + 18/594 = (990*1 + 18*1)/(594*1) = 1008/594

    Simplifying the fraction:
    1008/594 = 504/297 = 168/99 = 56/33

    Therefore, 90/81 + 2/66 = 56/33.

    ### Answer: 56/33

Expected answer: 113/99

Correct? No

🔗 Problem

Problem: If Oliver has a piece of ribbon that is 56/41 yards long and he gets another piece of the same length, how long would both pieces of ribbon be together?

Gemma 2B:

    Let's solve this step by step:

    1. Oliver has a piece of ribbon that is 56/41 yards long.
    2. He gets another piece of the same length. This means he now has 2 pieces of ribbon, each 56/41 yards long.
    3. To find the total length of both pieces together, we need to add the lengths:

       56/41 + 56/41 = (56 + 56) / 41
                    = 112 / 41
                    = <<112/41=2.731707317073171>>2 28/41 yards (or 2.731707317073171 yards as a decimal)

    Therefore, both pieces of ribbon together would be 2 28/41 yards long.

    ### Answer: 2 28/41 yards

Expected answer: 112/41

Correct? No

🔗 Problem

Problem: What is the result of 92/75 + 66/92? Please give your answer as a simplified fraction.

Gemma 2B:

    To solve 92/75 + 66/92, we need to find a common denominator. The least common multiple of 75 and 92 is 6900.

    92/75 = (92 * 92) / (75 * 92) = 8464/6900
    66/92 = (66 * 75) / (92 * 75) = 4950/6900

    Now we can add the fractions:

    8464/6900 + 4950/6900 = (8464 + 4950) / 6900 = 13414/6900

    Simplifying the fraction:

    13414/6900 = 1341/690 = 447/230

    Therefore, 92/75 + 66/92 = 447/230.

    ### Answer: 447/230

Expected answer: 6707/3450

Correct? No

🔗 Problem

Problem: What is the sum of 32/65 and 73/22? Leave your answer as an unsimplified fraction.

Gemma 2B:

    To find the sum of 32/65 and 73/22, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 65 and 22.

    LCM(65, 22) = 1430

    Now, we convert both fractions to equivalent fractions with the common denominator:

    32/65 = (32 × 22) / (65 × 22) = 704 / 1430
    73/22 = (73 × 65) / (22 × 65) = 4745 / 1430

    Add the numerators and keep the common denominator:

    (704 + 4745) / 1430 = 5449 / 1430

    Therefore, the sum of 32/65 and 73/22 is 5449/1430.

    ### Answer: 5449/1430

Expected answer: 5449/1430

Correct? Yes

🔗 Follow-up

Problem: Following up on the previous question, what is the sum of your answer from that problem and 24/71? Leave your answer as an unsimplified fraction.

Gemma 2B:

    In the previous question, we found that the sum of 32/65 and 73/22 is 5449/1430.

    Now, we need to add 5449/1430 and 24/71. Again, we need to find a common denominator, which will be the LCM of 1430 and 71.

    LCM(1430, 71) = 101530

    Convert both fractions to equivalent fractions with the common denominator:

    5449/1430 = (5449 × 71) / (1430 × 71) = 386879 / 101530
    24/71 = (24 × 1430) / (71 × 1430) = 34320 / 101530

    Add the numerators and keep the common denominator:

    (386879 + 34320) / 101530 = 421199 / 101530

    Therefore, the sum of 5449/1430 (the answer from the previous question) and 24/71 is 421199/101530.

    ### Answer: 421199/101530

Expected answer: 421199/101530

Correct? Yes

🔗 Follow-up

Problem: In the earlier problem, we considered the sum of 32/65 and 73/22. But what if the fraction was 53/65 instead of 32/65? What would the new sum be? Please leave your answer as an unsimplified fraction.

Gemma 2B:

    In this case, we will find the sum of 53/65 and 73/22. As we found earlier, the common denominator is the least common multiple (LCM) of 65 and 22, which is 1430.

    Let's convert both fractions to equivalent fractions with the common denominator:

    53/65 = (53 × 22) / (65 × 22) = 1166 / 1430
    73/22 = (73 × 65) / (22 × 65) = 4745 / 1430

    Now, add the numerators and keep the common denominator:

    (1166 + 4745) / 1430 = 5911 / 1430

    Therefore, the sum of 53/65 and 73/22 is 5911/1430.

    ### Answer: 5911/1430

Expected answer: 5911/1430

Correct? Yes

🔗 Problem

Problem: What is the difference between 51/34 and 12/86? Express your answer in its simplest form.

Gemma 2B:

    To find the difference between 51/34 and 12/86, we need to subtract these fractions. However, we can only subtract fractions with the same denominator. So, we first need to find the least common denominator (LCD) of 34 and 86.

    The LCD of 34 and 86 is 1462 because 1462 = 2 × 17 × 43, and 34 = 2 × 17, 86 = 2 × 43.

    Now, we can express both fractions with the denominator 1462:

    51/34 = (51 × 43) / (34 × 43) = 2193/1462
    12/86 = (12 × 17) / (86 × 17) = 204/1462

    Next, we subtract:

    2193/1462 - 204/1462 = (2193 - 204)/1462 = 1989/1462

    To simplify this fraction, we find the greatest common factor (GCF) of 1989 and 1462.

    The GCF of 1989 and 1462 is 17 because 1989 = 17 × 117 and 1462 = 2 × 17 × 43.

    Dividing both the numerator and denominator by 17:

    (1989/17) / (1462/17) = 117/86

    Therefore, the difference between 51/34 and 12/86 in its simplest form is 117/86.

    ### Answer: 117/86

Expected answer: 117/86

Correct? Yes

🔗 Follow-up

Problem: After finding the difference between 51/34 and 12/86, subtract 30/91 from this result. What fraction do you get when expressed in its simplest form?

Gemma 2B:

    In the previous question, we found that the difference between 51/34 and 12/86 is 117/86.

    Now, we need to subtract 30/91 from 117/86.

    First, let's find the LCD of 86 and 91. The LCD is 7826 because 7826 = 2 × 7 × 13 × 43, and 86 = 2 × 43, 91 = 7 × 13.

    Express both fractions with the denominator 7826:

    117/86 = (117 × 91) / (86 × 91) = 10647/7826
    30/91 = (30 × 86) / (91 × 86) = 2580/7826

    Now, subtract:

    10647/7826 - 2580/7826 = (10647 - 2580)/7826 = 8067/7826

    To simplify this fraction, find the GCF of 8067 and 7826.

    The GCF of 8067 and 7826 is 1 because 8067 and 7826 have no common factors other than 1.

    Therefore, 8067/7826 is already in its simplest form.

    ### Answer: 8067/7826

Expected answer: 8067/7826

Correct? Yes

🔗 Follow-up

Problem: Previously, you found the difference between 51/34 and 12/86. Now, let's change the second fraction to 18/86. What is the resulting difference if you subtract 18/86 from 51/34? Write your answer in simplest form.

Gemma 2B:

    Okay, let's solve this problem step by step. We need to find the difference between 51/34 and 18/86.

    As before, we need to find the least common denominator (LCD) of 34 and 86.

    The LCD of 34 and 86 is still 1462 because 1462 = 2 × 17 × 43, and 34 = 2 × 17, 86 = 2 × 43.

    Now, we express both fractions with the denominator 1462:

    51/34 = (51 × 43) / (34 × 43) = 2193/1462
    18/86 = (18 × 17) / (86 × 17) = 306/1462

    Next, we subtract:

    2193/1462 - 306/1462 = (2193 - 306)/1462 = 1887/1462

    To simplify this fraction, we find the greatest common factor (GCF) of 1887 and 1462.

    The GCF of 1887 and 1462 is 37 because 1887 = 3 × 17 × 37 and 1462 = 2 × 17 × 43.

    Dividing both the numerator and denominator by 37:

    (1887/37) / (1462/37) = 51/86

    Therefore, the difference between 51/34 and 18/86 in its simplest form is 51/86.

    ### Answer: 51/86

Expected answer: 111/86

Correct? No

🔗 Problem

Problem: First take the whole number 51 and add it to the fraction 93/8. Take that sum and add it to the fraction 58/44. What is the final result as a simplified fraction?

Gemma 2B:

    Let's solve this problem step by step:

    1. Add 51 to 93/8:
       51 + 93/8 = 408/8 + 93/8 = 501/8

    2. Add the result from step 1 to 58/44:
       501/8 + 58/44 = 5508/88 + 116/88 = 5624/88

    3. Simplify the fraction 5624/88:
       Divide both the numerator and denominator by their greatest common factor (GCF).
       The GCF of 5624 and 88 is 8.
       5624 ÷ 8 = 703
       88 ÷ 8 = 11

       So, 5624/88 simplifies to 703/11.

    ### Answer: 703/11

Expected answer: 5627/88

Correct? No

🔗 Problem

Problem: Calculate the result of the following fraction subtraction: 82/5 - 98/25. Write the answer in the simplest form.

Gemma 2B:

    To subtract fractions, we need to find a common denominator. The common denominator is the least common multiple (LCM) of the denominators.

    LCM of 5 and 25 is 25. So, we will convert both fractions to equivalent fractions with a denominator of 25.

    82/5 = (82 × 5) / (5 × 5) = 410/25
    98/25 remains as it is.

    Now, we can subtract the fractions:

    410/25 - 98/25 = (410 - 98) / 25 = 312/25

    To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator.

    GCD of 312 and 25 is 1. So, the fraction 312/25 is already in its simplest form.

    ### Answer: 312/25

Expected answer: 312/25

Correct? Yes

🔗 Follow-up

Problem: Given the result you obtained previously from calculating 82/5 - 98/25, what would you get if you added this result to itself?

Gemma 2B:

    In the previous problem, we found that 82/5 - 98/25 = 312/25.

    Now, we need to add this result to itself:

    312/25 + 312/25 = (312 + 312) / 25 = 624/25

    To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator.

    GCD of 624 and 25 is 1. So, the fraction 624/25 is already in its simplest form.

    ### Answer: 624/25

Expected answer: 624/25

Correct? Yes

🔗 Follow-up

Problem: If you originally had 82/5 oranges and instead of taking away 98/25 of them, you took away 98/90 oranges, how many oranges would you have left? Write the answer in the simplest form.

Gemma 2B:

    Let's solve this problem step by step:

    1. Convert 82/5 to an improper fraction:
       82/5 = (16 × 5 + 2) / 5 = 82/5

    2. Find the common denominator for 82/5 and 98/90:
       LCM of 5 and 90 is 90. So, we will convert 82/5 to an equivalent fraction with a denominator of 90.

       82/5 = (82 × 18) / (5 × 18) = 1476/90

    3. Subtract 98/90 from 1476/90:
       1476/90 - 98/90 = (1476 - 98) / 90 = 1378/90

    4. Simplify the fraction 1378/90:
       Divide both the numerator and denominator by their GCD, which is 2.

       1378/90 = (1378 ÷ 2) / (90 ÷ 2) = 689/45

    5. Convert 689/45 to a mixed number:
       689/45 = 15 + 14/45 = 15 14/45

    Therefore, if you originally had 82/5 oranges and took away 98/90 oranges, you would have 15 14/45 oranges left.

    ### Answer: 15 14/45

Expected answer: 689/45

Correct? Yes

🔗 Problem

Problem: Calculate (64 / 50) + (70 / 22) and provide your answer as an unsimplified fraction.

Gemma 2B:

    To calculate (64 / 50) + (70 / 22), we need to find a common denominator for the fractions and then add the numerators.

    The common denominator is the least common multiple (LCM) of 50 and 22.
    50 = 2 × 5^2
    22 = 2 × 11
    LCM(50, 22) = 2 × 5^2 × 11 = 550

    Now, we convert both fractions to equivalent fractions with the common denominator:

    64 / 50 = (64 × 11) / (50 × 11) = 704 / 550
    70 / 22 = (70 × 25) / (22 × 25) = 1750 / 550

    Adding the numerators:
    (64 / 50) + (70 / 22) = (704 / 550) + (1750 / 550) = (704 + 1750) / 550 = 2454 / 550

    ### Answer: 2454 / 550

Expected answer: 1227/275

Correct? Yes

🔗 Follow-up

Problem: In the previous question, we considered a situation where we added the fractions (64 / 50) and (70 / 22). Now imagine we made a slight error in our calculations, and the initial fraction was actually (64 / 49), not (64 / 50). How would that affect our total sum? Calculate (64 / 49) + (70 / 22) and provide your answer as an unsimplified fraction.

Gemma 2B:

    To calculate (64 / 49) + (70 / 22), we need to find a common denominator for the fractions and then add the numerators.

    The common denominator is the least common multiple (LCM) of 49 and 22.
    49 = 7^2
    22 = 2 × 11
    LCM(49, 22) = 2 × 7^2 × 11 = 1078

    Now, we convert both fractions to equivalent fractions with the common denominator:

    64 / 49 = (64 × 22) / (49 × 22) = 1408 / 1078
    70 / 22 = (70 × 49) / (22 × 49) = 3430 / 1078

    Adding the numerators:
    (64 / 49) + (70 / 22) = (1408 / 1078) + (3430 / 1078) = (1408 + 3430) / 1078 = 4838 / 1078

    ### Answer: 4838 / 1078

Expected answer: 2419/539

Correct? Yes

🔗 Problem

Problem: John calculated s by adding 24 divided by 6 to 40 divided by 53. He then added s to itself to get b. Can you find the value of b?

Gemma 2B:

    Let's solve this problem step by step:

    1. Calculate the value of 24 divided by 6:
       24 ÷ 6 = 4

    2. Calculate the value of 40 divided by 53:
       40 ÷ 53 ≈ 0.7547

    3. Add the results from steps 1 and 2 to get the value of s:
       s = 4 + 0.7547
       s ≈ 4.7547

    4. To get the value of b, add s to itself:
       b = s + s
       b ≈ 4.7547 + 4.7547
       b ≈ 9.5094

    ### Answer: 9.5094

Expected answer: 504/53

Correct? No

🔗 Problem

Problem: Calculate ((80 / 90) + (52 / 11)) and express your answer as a mixed number.

Gemma 2B:

    To calculate ((80 / 90) + (52 / 11)), let's break it down into steps:

    1. Simplify 80 / 90:
       80 / 90 = 8 / 9 (divide both numerator and denominator by 10)

    2. Simplify 52 / 11:
       52 / 11 = 4 8/11 (divide 52 by 11; the quotient is 4 with a remainder of 8)

    3. Add the fractions:
       8/9 + 4 8/11
       = (8/9) + ((4 * 11 + 8) / 11) (convert the mixed number to an improper fraction)
       = (8/9) + (52/11) (simplify the numerator)
       = ((8 * 11) / (9 * 11)) + (52 / 11) (find a common denominator by multiplying both denominators)
       = (88 / 99) + (52 / 11) (simplify the first fraction)
       = ((88 * 1) / (99 * 1)) + ((52 * 9) / (11 * 9)) (multiply the numerators and denominators by the reciprocal of the second denominator)
       = (88 / 99) + (468 / 99) (simplify the second fraction)
       = (88 + 468) / 99 (add the numerators)
       = 556 / 99 (simplify the numerator)
       = 5 59/99 (convert the improper fraction to a mixed number)

    Therefore, ((80 / 90) + (52 / 11)) = 5 59/99.

    ### Answer: 5 59/99

Expected answer: 556/99

Correct? No

🔗 Problem

Problem: Calculate the sum of 12/18 and 91/74. Express your answer as a simplified fraction.

Gemma 2B:

    To calculate the sum of 12/18 and 91/74, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 18 and 74.

    LCM(18, 74) = 2 × 3 × 3 × 37 = 666

    Now, we convert both fractions to equivalent fractions with the common denominator:

    12/18 = (12 × 37) / (18 × 37) = 444/666
    91/74 = (91 × 9) / (74 × 9) = 819/666

    Adding the fractions:
    444/666 + 819/666 = (444 + 819) / 666 = 1263/666

    Simplifying the fraction:
    1263/666 = 1 263/666 = 1 + 597/666 = 1 + (3 × 199)/(3 × 222) = 1 + 199/222 = 1 + (199/3) / (222/3) = 1 + 199/222

    Therefore, 12/18 + 91/74 = 1 + 199/222 = 421/222

    ### Answer: 421/222

Expected answer: 421/222

Correct? Yes

🔗 Follow-up

Problem: You previously calculated the sum of 12/18 and 91/74. Now, double that result. What is the new sum? Answer as a simplified fraction.

Gemma 2B:

    In the previous problem, we found that 12/18 + 91/74 = 421/222.

    To double this result, we multiply the fraction by 2:

    (421/222) × 2 = 842/222

    Simplifying the fraction:
    842/222 = 2 × 421 / 2 × 111 = 421/111

    Therefore, doubling the sum of 12/18 and 91/74 results in 421/111.

    ### Answer: 421/111

Expected answer: 421/111

Correct? Yes

🔗 Follow-up

Problem: You originally added 12/18 and 91/74. Instead, what if we added 78/18 and 91/74? What is the new sum? Answer as a simplified fraction.

Gemma 2B:

    Let's calculate the sum of 78/18 and 91/74. We'll follow the same steps as before, finding the common denominator and then adding the fractions.

    The common denominator is still LCM(18, 74) = 666.

    Converting the fractions to equivalent fractions with the common denominator:

    78/18 = (78 × 37) / (18 × 37) = 2886/666
    91/74 = (91 × 9) / (74 × 9) = 819/666

    Adding the fractions:
    2886/666 + 819/666 = (2886 + 819) / 666 = 3705/666

    Simplifying the fraction:
    3705/666 = 5 111/222 = 5 + 111/222

    Therefore, 78/18 + 91/74 = 5 + 111/222 = 1333/222

    ### Answer: 1333/222

Expected answer: 1235/222

Correct? No

🔗 Problem

Problem: Find the sum of the fractions 7/2 and 51/25. Write your answer as a simple fraction.

Gemma 2B:

    To find the sum of 7/2 and 51/25, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 2 and 25.

    LCM(2, 25) = 2 × 25 = 50

    Now, we convert each fraction to an equivalent fraction with the denominator 50:

    7/2 = (7 × 25) / (2 × 25) = 175/50
    51/25 = (51 × 2) / (25 × 2) = 102/50

    Add the numerators:
    175/50 + 102/50 = (175 + 102) / 50 = 277/50

    Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF):

    GCF(277, 50) = 1

    Since the GCF is 1, the fraction 277/50 is already in its simplest form.

    ### Answer: 277/50

Expected answer: 277/50

Correct? Yes

🔗 Follow-up

Problem: Following up on the previous question, add the fraction 86/39 to the sum of 7/2 and 51/25. Express your answer as a simple fraction.

Gemma 2B:

    From the previous question, we found that the sum of 7/2 and 51/25 is 277/50.

    Now, we need to add 86/39 to 277/50. To do this, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 50 and 39.

    LCM(50, 39) = 1950

    Convert each fraction to an equivalent fraction with the denominator 1950:

    277/50 = (277 × 39) / (50 × 39) = 10803/1950
    86/39 = (86 × 50) / (39 × 50) = 4300/1950

    Add the numerators:
    10803/1950 + 4300/1950 = (10803 + 4300) / 1950 = 15103/1950

    Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF):

    GCF(15103, 1950) = 1

    Since the GCF is 1, the fraction 15103/1950 is already in its simplest form.

    ### Answer: 15103/1950

Expected answer: 15103/1950

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, you were asked to find the sum of 7/2 and 51/25. Now suppose that instead of 7/2, the fraction was 7/22. How would this change the result? Calculate 7/22 + 51/25 as a simplified fraction.

Gemma 2B:

    Let's solve this problem step by step.

    To find the sum of 7/22 and 51/25, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 22 and 25.

    LCM(22, 25) = 550

    Now, we convert each fraction to an equivalent fraction with the denominator 550:

    7/22 = (7 × 25) / (22 × 25) = 175/550
    51/25 = (51 × 22) / (25 × 22) = 1122/550

    Add the numerators:
    175/550 + 1122/550 = (175 + 1122) / 550 = 1297/550

    Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF):

    GCF(1297, 550) = 1

    Since the GCF is 1, the fraction 1297/550 is already in its simplest form.

    ### Answer: 1297/550

Expected answer: 1297/550

Correct? Yes

🔗 Problem

Problem: Calculate the following expression: ((68 / 69) + (93 / 7)) is a monomial. Add this to (3 / 46). Provide the resulting value as a simple fraction.

Gemma 2B:

    Let's break this down step by step:

    1. First, let's evaluate ((68 / 69) + (93 / 7)).

       68 / 69 = 0.9855... (rounded)
       93 / 7 = 13.2857... (rounded)

       0.9855... + 13.2857... = 14.2712...

    2. Now, we need to determine if 14.2712... is a monomial. A monomial is a single term that can be a number, a variable, or a product of numbers and variables with whole number exponents. In this case, 14.2712... is a number, so it is a monomial.

    3. Next, we add this monomial to (3 / 46).

       14.2712... + (3 / 46) = 14.2712... + 0.0652... = 14.3364...

    4. To provide the resulting value as a simple fraction, we need to convert 14.3364... to a fraction.

       14.3364... = 14 + 0.3364...
                  = 14 + (0.3364... * 10000) / 10000
                  = 14 + 3364 / 10000
                  = 140000 / 10000 + 3364 / 10000
                  = 143364 / 10000
                  = 14591 / 1020 (after simplifying)

    ### Answer: 14591 / 1020

Expected answer: 13849/966

Correct? No

🔗 Problem

Problem: What is the result of adding 31/98 to 60/4? Answer as a simplified fraction.

Gemma 2B:

    To add 31/98 and 60/4, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 98 and 4.

    LCM(98, 4) = 196

    Now, we convert both fractions to equivalent fractions with the common denominator:

    31/98 = (31 × 2)/(98 × 2) = 62/196
    60/4 = (60 × 49)/(4 × 49) = 2940/196

    Adding the fractions:

    62/196 + 2940/196 = (62 + 2940)/196 = 3002/196

    Simplifying the fraction:

    3002/196 = 1501/98

    Therefore, 31/98 + 60/4 = 1501/98.

    ### Answer: 1501/98

Expected answer: 1501/98

Correct? Yes

🔗 Follow-up

Problem: Following the previous problem, what's the result when you subtract 41/52 from the sum of 31/98 and 60/4? Answer as a simplified fraction.

Gemma 2B:

    From the previous problem, we found that 31/98 + 60/4 = 1501/98.

    Now, we need to subtract 41/52 from 1501/98.

    First, let's find the common denominator of 98 and 52.

    LCM(98, 52) = 2548

    Converting the fractions to equivalent fractions with the common denominator:

    1501/98 = (1501 × 26)/(98 × 26) = 39026/2548
    41/52 = (41 × 49)/(52 × 49) = 2009/2548

    Subtracting the fractions:

    39026/2548 - 2009/2548 = (39026 - 2009)/2548 = 37017/2548

    Simplifying the fraction:

    37017/2548 cannot be simplified further as the numerator and denominator have no common factors other than 1.

    Therefore, (31/98 + 60/4) - 41/52 = 37017/2548.

    ### Answer: 37017/2548

Expected answer: 37017/2548

Correct? Yes

🔗 Follow-up

Problem: In the previous situation, instead of adding 31/98 to 60/4, what would happen if you added 31/98 to 83/4? What would the new sum be, in simplified fraction form?

Gemma 2B:

    Let's add 31/98 and 83/4 and simplify the resulting fraction.

    First, find the common denominator, which is the LCM of 98 and 4.

    LCM(98, 4) = 196

    Convert both fractions to equivalent fractions with the common denominator:

    31/98 = (31 × 2)/(98 × 2) = 62/196
    83/4 = (83 × 49)/(4 × 49) = 4067/196

    Add the fractions:

    62/196 + 4067/196 = (62 + 4067)/196 = 4129/196

    Simplify the fraction:

    4129/196 = 21 + 1/196 = 21 1/196

    Therefore, 31/98 + 83/4 = 21 1/196.

    ### Answer: 21 1/196

Expected answer: 4129/196

Correct? No

🔗 Problem

Problem: Calculate ((3 / 2) + (24 / 36)) and state your answer as a simplified fraction.

Gemma 2B:

    To calculate ((3 / 2) + (24 / 36)), let's simplify the fractions and then add them together.

    1. Simplify 3 / 2:
       3 / 2 is already in its simplest form.

    2. Simplify 24 / 36:
       24 and 36 have a common factor of 12.
       24 ÷ 12 = 2
       36 ÷ 12 = 3
       So, 24 / 36 simplifies to 2 / 3.

    3. Add the simplified fractions:
       (3 / 2) + (2 / 3)

       To add fractions with different denominators, we need to find a common denominator. The least common multiple of 2 and 3 is 6.

       Multiply the first fraction by 3/3 and the second fraction by 2/2 to get equivalent fractions with a common denominator of 6:

       (3 / 2) × (3 / 3) = 9 / 6
       (2 / 3) × (2 / 2) = 4 / 6

       Now add the fractions:
       (9 / 6) + (4 / 6) = 13 / 6

    4. Simplify the result:
       13 and 6 have no common factors other than 1, so 13 / 6 is already in its simplest form.

    ### Answer: 13 / 6

Expected answer: 13/6

Correct? Yes

🔗 Follow-up

Problem: After completing the calculation for ((3 / 2) + (24 / 36)), add the result to 7/2 and give your answer as a simplified fraction.

Gemma 2B:

    The result of ((3 / 2) + (24 / 36)) is 13 / 6, as calculated in the previous step.

    Now, let's add 13 / 6 to 7 / 2.

    1. Find a common denominator for 13 / 6 and 7 / 2:
       The least common multiple of 6 and 2 is 6.

    2. Convert 7 / 2 to an equivalent fraction with a denominator of 6:
       (7 / 2) × (3 / 3) = 21 / 6

    3. Add the fractions:
       (13 / 6) + (21 / 6) = 34 / 6

    4. Simplify the result:
       34 and 6 have a common factor of 2.
       34 ÷ 2 = 17
       6 ÷ 2 = 3
       So, 34 / 6 simplifies to 17 / 3.

    ### Answer: 17 / 3

Expected answer: 17/3

Correct? Yes

🔗 Follow-up

Problem: Suppose instead of having 3/2, we had (32/36) as part of the calculation along with what you previously calculated. Can you determine the new total if you calculate ((3 / 2) + (32 / 36))? Answer as a simplified fraction.

Gemma 2B:

    Sure! Let's calculate ((3 / 2) + (32 / 36)) and simplify the result.

    1. Simplify 3 / 2:
       3 / 2 is already in its simplest form.

    2. Simplify 32 / 36:
       32 and 36 have a common factor of 4.
       32 ÷ 4 = 8
       36 ÷ 4 = 9
       So, 32 / 36 simplifies to 8 / 9.

    3. Add the simplified fractions:
       (3 / 2) + (8 / 9)

       To add fractions with different denominators, we need to find a common denominator. The least common multiple of 2 and 9 is 18.

       Multiply the first fraction by 9/9 and the second fraction by 2/2 to get equivalent fractions with a common denominator of 18:

       (3 / 2) × (9 / 9) = 27 / 18
       (8 / 9) × (2 / 2) = 16 / 18

       Now add the fractions:
       (27 / 18) + (16 / 18) = 43 / 18

    4. Simplify the result:
       43 and 18 have no common factors other than 1, so 43 / 18 is already in its simplest form.

    ### Answer: 43 / 18

Expected answer: 43/18

Correct? Yes

🔗 Problem

Problem: Firstly, calculate the sum of 92/54 and 90/13, then from the result take away 46/41. What's the result as a simplified fraction?

Gemma 2B:

    To solve this problem, let's break it down into steps:

    1. Calculate the sum of 92/54 and 90/13:
       92/54 + 90/13 = (92 × 13 + 90 × 54) / (54 × 13)
                     = (1196 + 4860) / 702
                     = 6056 / 702
                     = <<6056/702=8 62/702>>8 62/702

    2. Subtract 46/41 from the result:
       8 62/702 - 46/41 = (8 62/702 × 41 - 46 × 702) / (702 × 41)
                        = (8 × 41 + 62 × 41 - 46 × 702) / (702 × 41)
                        = (328 + 2542 - 32292) / 28782
                        = -29422 / 28782
                        = <<-29422/28782=-1 640/28782>>-1 640/28782

    3. Simplify the fraction:
       -1 640/28782 = <<-1 640/28782=-1 20/1693>>-1 20/1693

    ### Answer: -1 20/1693

Expected answer: 108002/14391

Correct? No

🔗 Problem

Problem: What is twice the value of 29/23? Simplify your answer to the simplest form.

Gemma 2B:

    To find twice the value of 29/23, we need to multiply the fraction by 2.

    (29/23) × 2 = (29 × 2)/(23 × 1) = 58/23

    Now, let's simplify 58/23 to its simplest form by dividing both the numerator and denominator by their greatest common factor (GCF).

    The factors of 58 are 1, 2, 29, and 58.
    The factors of 23 are 1 and 23.

    The GCF of 58 and 23 is 1. Since the GCF is 1, 58/23 is already in its simplest form.

    ### Answer: 58/23

Expected answer: 58/23

Correct? Yes

🔗 Follow-up

Problem: After calculating the value of 2*(29/23), subtract this result from 32/5. What is the resulting fraction in simplest form?

Gemma 2B:

    First, let's calculate the value of 2 × (29/23):

    2 × (29/23) = 58/23

    Now, we need to subtract 58/23 from 32/5.

    To subtract fractions with different denominators, we need to find the least common multiple (LCM) of the denominators.

    The LCM of 23 and 5 is 115.

    Now, let's convert both fractions to equivalent fractions with the denominator 115:

    32/5 = (32 × 23)/(5 × 23) = 736/115
    58/23 = (58 × 5)/(23 × 5) = 290/115

    Subtracting the fractions:

    (736/115) - (290/115) = (736 - 290)/115 = 446/115

    To simplify 446/115, let's find the GCF of 446 and 115.

    The factors of 446 are 1, 2, 223, and 446.
    The factors of 115 are 1, 5, 23, and 115.

    The GCF of 446 and 115 is 1. Since the GCF is 1, 446/115 is already in its simplest form.

    ### Answer: 446/115

Expected answer: 446/115

Correct? Yes

🔗 Follow-up

Problem: If the initial number was 36/23 instead of 29/23 in our previous problem, what would now be the value of two times this new fraction? Simplify your answer to the simplest form.

Gemma 2B:

    In this new problem, we need to find twice the value of 36/23 and simplify the result to its simplest form.

    To find twice the value of 36/23, we multiply the fraction by 2:

    (36/23) × 2 = (36 × 2)/(23 × 1) = 72/23

    Now, let's simplify 72/23 to its simplest form by dividing both the numerator and denominator by their greatest common factor (GCF).

    The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
    The factors of 23 are 1 and 23.

    The GCF of 72 and 23 is 1. Since the GCF is 1, 72/23 is already in its simplest form.

    ### Answer: 72/23

Expected answer: 72/23

Correct? Yes

🔗 Problem

Problem: What is the sum of 29/20 and 17/72? Answer as a simplified fraction.

Gemma 2B:

    To find the sum of 29/20 and 17/72, we need to find a common denominator. The least common multiple of 20 and 72 is 360.

    29/20 = (29 * 18) / (20 * 18) = 522/360
    17/72 = (17 * 5) / (72 * 5) = 85/360

    Now we can add the fractions:

    522/360 + 85/360 = (522 + 85) / 360 = 607/360

    To simplify this fraction, we divide both the numerator and denominator by their greatest common factor. The greatest common factor of 607 and 360 is 1.

    607/360 = 607/360

    Therefore, the sum of 29/20 and 17/72 as a simplified fraction is:

    ### Answer: 607/360

Expected answer: 607/360

Correct? Yes

🔗 Follow-up

Problem: After finding the sum of 29/20 and 17/72 in the previous question, now subtract 9/68 from that sum to obtain a new value. What is the simplified fraction of this new answer?

Gemma 2B:

    From the previous question, we found that the sum of 29/20 and 17/72 is 607/360.

    Now, we need to subtract 9/68 from 607/360.

    First, let's find the common denominator of 360 and 68. The least common multiple of 360 and 68 is 1360.

    607/360 = (607 * 20) / (360 * 20) = 12140/7200
    9/68 = (9 * 20) / (68 * 20) = 180/1360

    Now we can subtract the fractions:

    12140/7200 - 180/1360 = (12140 * 17 - 180 * 90) / (7200 * 17)
                           = (206380 - 16200) / 122400
                           = 190180 / 122400

    To simplify this fraction, we divide both the numerator and denominator by their greatest common factor. The greatest common factor of 190180 and 122400 is 20.

    190180 / 122400 = (190180 / 20) / (122400 / 20) = 9509 / 6120

    Therefore, the simplified fraction of the new answer is:

    ### Answer: 9509/6120

Expected answer: 9509/6120

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, you found the sum of 29/20 and 17/72. Now, imagine that instead of having 29/20 of a quantity, you only had 29/5. What would be the sum of 29/5 and 17/72? Keep your answer as a simplified fraction.

Gemma 2B:

    In this case, we are finding the sum of 29/5 and 17/72. Again, we need to find a common denominator. The least common multiple of 5 and 72 is 360.

    29/5 = (29 * 72) / (5 * 72) = 2088/360
    17/72 = (17 * 5) / (72 * 5) = 85/360

    Now we can add the fractions:

    2088/360 + 85/360 = (2088 + 85) / 360 = 2173/360

    To simplify this fraction, we divide both the numerator and denominator by their greatest common factor. The greatest common factor of 2173 and 360 is 1.

    2173/360 = 2173/360

    Therefore, the sum of 29/5 and 17/72 as a simplified fraction is:

    ### Answer: 2173/360

Expected answer: 2173/360

Correct? Yes

🔗 Problem

Problem: Calculate the value of this expression: ((36 / 27) + (80 / 10)) - (73 / 79). Simplify your answer as much as possible.

Gemma 2B:

    Let's solve this problem step by step:

    1. First, let's simplify the fractions within the parentheses:
       (36 / 27) = 1.3333...
       (80 / 10) = 8
       (73 / 79) = 0.9240...

    2. Now, let's add the first two terms:
       (36 / 27) + (80 / 10) = 1.3333... + 8 = 9.3333...

    3. Finally, let's subtract the third term from the sum:
       9.3333... - (73 / 79) = 9.3333... - 0.9240... = 8.4093...

    4. The simplified answer is a repeating decimal, which can be approximated as:
       8.41 (rounded to two decimal places)

    ### Answer: 8.41

Expected answer: 1993/237

Correct? No

🔗 Problem

Problem: What is the answer to (86 / 71) + (91 / 75)? Answer as a decimal to the nearest hundredth.

Gemma 2B:

    To solve (86 / 71) + (91 / 75), let's break it down into steps:

    1. Divide 86 by 71:
       86 ÷ 71 ≈ 1.211267605633803

    2. Divide 91 by 75:
       91 ÷ 75 = 1.213333333333333

    3. Add the results from steps 1 and 2:
       1.211267605633803 + 1.213333333333333 = 2.424600938967136

    4. Round the result to the nearest hundredth:
       2.424600938967136 rounded to the nearest hundredth is 2.42

    ### Answer: 2.42

Expected answer: 12911/5325

Correct? No

🔗 Problem

Problem: Calculate the following, and express the result as a simplified fraction: ((21 / 75) + (74 / 43)) + (10 / 62)

Gemma 2B:

    Let's solve this problem step by step:

    1. First, let's add (21 / 75) and (74 / 43):
       (21 / 75) + (74 / 43) = (21 * 43) / (75 * 43) + (74 * 75) / (43 * 75)
                              = 903 / 3225 + 5550 / 3225
                              = (903 + 5550) / 3225
                              = 6453 / 3225

    2. Now, let's add (10 / 62) to the result from step 1:
       (6453 / 3225) + (10 / 62) = (6453 * 62) / (3225 * 62) + (10 * 3225) / (62 * 3225)
                                 = 400086 / 200150 + 32250 / 200150
                                 = (400086 + 32250) / 200150
                                 = 432336 / 200150

    3. To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator:
       GCD(432336, 200150) = 2

    4. Divide both the numerator and denominator by the GCD:
       (432336 / 2) / (200150 / 2) = 216168 / 100075

    Therefore, the simplified fraction is:
    ### Answer: 216168 / 100075

Expected answer: 72056/33325

Correct? No

🔗 Problem

Problem: Compute ((75 / 66) + (81 / 61)), and give your answer as a fraction reduced to its lowest term.

Gemma 2B:

    To compute ((75 / 66) + (81 / 61)), we need to find a common denominator for the fractions, add the numerators, and then reduce the resulting fraction to its lowest term.

    Step 1: Find the least common multiple (LCM) of the denominators 66 and 61.
    LCM(66, 61) = 4,026

    Step 2: Convert both fractions to equivalent fractions with the common denominator of 4,026.
    (75 / 66) = (75 × 61) / (66 × 61) = 4,575 / 4,026
    (81 / 61) = (81 × 66) / (61 × 66) = 5,346 / 4,026

    Step 3: Add the numerators of the equivalent fractions.
    (4,575 / 4,026) + (5,346 / 4,026) = (4,575 + 5,346) / 4,026 = 9,921 / 4,026

    Step 4: Reduce the resulting fraction to its lowest term by dividing the numerator and denominator by their greatest common factor (GCF).
    GCF(9,921, 4,026) = 3
    (9,921 / 4,026) = (9,921 ÷ 3) / (4,026 ÷ 3) = 3,307 / 1,342

    ### Answer: 3,307 / 1,342

Expected answer: 3307/1342

Correct? Yes

🔗 Follow-up

Problem: After you have computed ((75 / 66) + (81 / 61)), what is the result if you additionally add (47 / 19) to that sum? Give your response as a simplified fraction.

Gemma 2B:

    To add (47 / 19) to the previous sum of ((75 / 66) + (81 / 61)), we need to find a common denominator for the fractions (3,307 / 1,342) and (47 / 19), add the numerators, and then reduce the resulting fraction to its lowest term.

    Step 1: Find the least common multiple (LCM) of the denominators 1,342 and 19.
    LCM(1,342, 19) = 25,498

    Step 2: Convert both fractions to equivalent fractions with the common denominator of 25,498.
    (3,307 / 1,342) = (3,307 × 19) / (1,342 × 19) = 62,833 / 25,498
    (47 / 19) = (47 × 1,342) / (19 × 1,342) = 63,074 / 25,498

    Step 3: Add the numerators of the equivalent fractions.
    (62,833 / 25,498) + (63,074 / 25,498) = (62,833 + 63,074) / 25,498 = 125,907 / 25,498

    Step 4: Reduce the resulting fraction to its lowest term by dividing the numerator and denominator by their greatest common factor (GCF).
    GCF(125,907, 25,498) = 1
    The fraction (125,907 / 25,498) is already in its lowest term.

    ### Answer: 125,907 / 25,498

Expected answer: 125907/25498

Correct? Yes

🔗 Problem

Problem: Consider two identical fractions, t, each equal to sum of 53/18 and 21/99. Find the total sum, l, of these fractions and present your answer as a simple fraction.

Gemma 2B:

    To find the total sum, l, of two identical fractions, t, we first need to calculate the value of t.

    Given:
    - t = 53/18 + 21/99
    - We need to find l, where l = t + t

    Step 1: Calculate the value of t by adding 53/18 and 21/99.
    To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators.
    LCM(18, 99) = 198

    Now, we can convert the fractions to equivalent fractions with the common denominator of 198:
    53/18 = 583/198 (multiply both numerator and denominator by 11)
    21/99 = 42/198 (multiply both numerator and denominator by 2)

    t = 583/198 + 42/198
    t = 625/198
    t = 25/6 (divide both numerator and denominator by 33)

    Step 2: Calculate the total sum, l, by adding t to itself.
    l = t + t
    l = 25/6 + 25/6
    l = 50/6
    l = 25/3 (divide both numerator and denominator by 2)

    Therefore, the total sum, l, of two identical fractions, t, is 25/3.

    ### Answer: 25/3

Expected answer: 625/99

Correct? No

🔗 Problem

Problem: First, calculate the result of 58/49 + 31/34. Then, add that result to the fraction 74/38. What is the final result as a simple fraction?

Gemma 2B:

    Okay, let's solve this problem step by step:

    1. Calculate 58/49 + 31/34
       To add fractions, we need a common denominator. The common denominator is 49 × 34 = 1666.

       58/49 = 1972/1666 (multiply numerator and denominator by 34)
       31/34 = 1519/1666 (multiply numerator and denominator by 49)

       1972/1666 + 1519/1666 = 3491/1666

    2. Add the result of step 1 to 74/38
       Again, we need a common denominator. The common denominator is 1666 × 38 = 63308.

       3491/1666 = 132658/63308 (multiply numerator and denominator by 38)
       74/38 = 123902/63308 (multiply numerator and denominator by 1666)

       132658/63308 + 123902/63308 = 256560/63308

    3. Simplify the fraction 256560/63308
       Divide the numerator and denominator by their greatest common divisor (GCD).
       The GCD of 256560 and 63308 is 4.

       256560/4 = 64140
       63308/4 = 15827

       The simplified fraction is 64140/15827.

    ### Answer: 64140/15827

Expected answer: 127971/31654

Correct? No

🔗 Problem

Problem: Calculate the sum of 100 divided by 76 and 29 divided by 14. Please provide your answer as a simplified fraction or decimal.

Gemma 2B:

    To calculate the sum of 100 divided by 76 and 29 divided by 14, we can follow these steps:

    1. Calculate 100 divided by 76:
    100 ÷ 76 ≈ 1.3157894736842106

    2. Calculate 29 divided by 14:
    29 ÷ 14 ≈ 2.0714285714285716

    3. Add the results from steps 1 and 2:
    1.3157894736842106 + 2.0714285714285716 ≈ 3.387218045112782

    Simplified fraction:
    100/76 + 29/14 = 700/532 + 406/532 = 1106/532

    ### Answer: 3.387218045112782 or 1106/532

Expected answer: 901/266

Correct? No

🔗 Problem

Problem: Given that Evan has read 51/18 of his novel, and Olivia has read (8/42) after reading the same amount of novel as Evan, how much of the novel has Olivia read in total? Answer as a simplified fraction.

Gemma 2B:

    Let's solve this step by step:

    1) First, let's simplify the fraction of the novel that Evan has read:
       51/18 = 17/6 <<51/18 = 17/6>>

    2) Now, Olivia has read the same amount as Evan, plus an additional 8/42.
       To add fractions, we need a common denominator. The common denominator of 6 and 42 is 42.

    3) Convert 17/6 to an equivalent fraction with denominator 42:
       17/6 = 17/6 * 7/7 = 119/42 <<17/6 = 17/6 * 7/7 = 119/42>>

    4) Now we can add the fractions:
       119/42 + 8/42 = 127/42 <<119/42 + 8/42 = 127/42>>

    5) Simplify the fraction:
       127/42 = 3 1/42 <<127/42 = 3 1/42>>

    Therefore, Olivia has read 3 1/42 of the novel in total.

    ### Answer: 3 1/42

Expected answer: 127/42

Correct? Yes

🔗 Follow-up

Problem: Building off of the previous question and given that Evan then continues to read and finishes the same amount of his novel as Olivia had read in total, how much of the novel has Evan read now? Answer as a simplified fraction.

Gemma 2B:

    Continuing from the previous question:

    1) We know that Olivia has read 3 1/42 of the novel in total.

    2) Evan has already read 17/6 of the novel. Now, he reads an additional amount equal to what Olivia has read in total, which is 3 1/42.

    3) To add these fractions, we need a common denominator. The common denominator of 6 and 42 is 42.

    4) Convert 17/6 to an equivalent fraction with denominator 42:
       17/6 = 17/6 * 7/7 = 119/42 <<17/6 = 17/6 * 7/7 = 119/42>>

    5) Now we can add the fractions:
       119/42 + 3 1/42 = 119/42 + 43/42 = 162/42 <<119/42 + 3 1/42 = 119/42 + 43/42 = 162/42>>

    6) Simplify the fraction:
       162/42 = 3 6/7 <<162/42 = 3 6/7>>

    Therefore, Evan has now read 3 6/7 of the novel.

    ### Answer: 3 6/7

Expected answer: 41/7

Correct? No

🔗 Follow-up

Problem: In the previous scenario, let's now instead assume that Olivia initially read 3/42 of her novel, instead of 8/42, before reading the same amount as Evan. Now how much of the novel has Olivia read altogether? Answer as a simplified fraction.

Gemma 2B:

    Okay, let's solve this new scenario step by step:

    1) Evan has read 51/18 of his novel, which simplifies to:
       51/18 = 17/6 <<51/18 = 17/6>>

    2) Olivia initially read 3/42 of her novel, and then read the same amount as Evan.
       To add these fractions, we need a common denominator. The common denominator of 6 and 42 is 42.

    3) Convert 17/6 to an equivalent fraction with denominator 42:
       17/6 = 17/6 * 7/7 = 119/42 <<17/6 = 17/6 * 7/7 = 119/42>>

    4) Now we can add the fractions:
       119/42 + 3/42 = 122/42 <<119/42 + 3/42 = 122/42>>

    5) Simplify the fraction:
       122/42 = 61/21 <<122/42 = 61/21>>

    Therefore, in this new scenario, Olivia has read 61/21 of the novel in total.

    ### Answer: 61/21

Expected answer: 61/21

Correct? Yes

🔗 Problem

Problem: What is the sum of 48 divided by 13 and 31 divided by 22? Answer as a fraction or a decimal.

Gemma 2B:

    To find the sum of 48 divided by 13 and 31 divided by 22, we need to perform the divisions and then add the results together.

    48 ÷ 13 = 3.692307692... (rounded to 9 decimal places)
    31 ÷ 22 = 1.409090909... (rounded to 9 decimal places)

    3.692307692... + 1.409090909... = 5.101398601... (rounded to 9 decimal places)

    To express the result as a fraction, we need to find a common denominator. The least common multiple of 13 and 22 is 286.

    48 ÷ 13 = 48 × (22/286) = 1056/286
    31 ÷ 22 = 31 × (13/286) = 403/286

    1056/286 + 403/286 = 1459/286

    Therefore, the sum of 48 divided by 13 and 31 divided by 22 can be expressed as:

    Decimal: 5.101398601 (rounded to 9 decimal places)
    Fraction: 1459/286

    ### Answer: 5.101398601 or 1459/286

Expected answer: 1459/286

Correct? Yes

🔗 Problem

Problem: First, find the value of 24/86 + 76/77. Subtract your answer from 27/6. Write out your process and show your work.

Gemma 2B:

    To find the value of 24/86 + 76/77, we need to find a common denominator. The least common multiple of 86 and 77 is 6,622.

    24/86 = 24 * (6,622/6,622) = 1,848/6,622
    76/77 = 76 * (6,622/6,622) = 6,534/6,622

    Now, we can add the fractions:
    1,848/6,622 + 6,534/6,622 = (1,848 + 6,534)/6,622 = 8,382/6,622

    To subtract this result from 27/6, we need to convert 27/6 to an equivalent fraction with a denominator of 6,622:
    27/6 = 27 * (1,103/1,103) = 29,781/6,622

    Now, we can subtract:
    29,781/6,622 - 8,382/6,622 = (29,781 - 8,382)/6,622 = 21,399/6,622

    To simplify this fraction, we can divide both the numerator and denominator by their greatest common factor, which is 17:
    21,399/6,622 = (21,399/17) / (6,622/17) = 1,259/389

    Therefore, the final answer is 1,259/389.

    ### Answer: 1,259/389

Expected answer: 21415/6622

Correct? No

🔗 Problem

Problem: Find the sum of 73/39 and 49/14, and express your answer as a simplified fraction.

Gemma 2B:

    To find the sum of 73/39 and 49/14, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 39 and 14.

    LCM(39, 14) = 546

    Now, we convert each fraction to an equivalent fraction with the common denominator:

    73/39 = (73 × 14) / (39 × 14) = 1022/546
    49/14 = (49 × 39) / (14 × 39) = 1911/546

    Add the fractions:

    1022/546 + 1911/546 = (1022 + 1911) / 546 = 2933/546

    Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF):

    GCF(2933, 546) = 91

    (2933/91) / (546/91) = 2933/546

    Therefore, the sum of 73/39 and 49/14 is 2933/546.

    ### Answer: 2933/546

Expected answer: 419/78

Correct? Yes

🔗 Follow-up

Problem: After finding the sum of 73/39 and 49/14 (the last problem), now add the result to 21/80. What is the new total? Express your answer as a simplified fraction.

Gemma 2B:

    From the previous problem, we found that the sum of 73/39 and 49/14 is 2933/546.

    Now, we need to add 2933/546 and 21/80.

    First, find the common denominator by calculating the LCM of 546 and 80.

    LCM(546, 80) = 10920

    Convert each fraction to an equivalent fraction with the common denominator:

    2933/546 = (2933 × 20) / (546 × 20) = 58660/10920
    21/80 = (21 × 136.5) / (80 × 136.5) = 2866.5/10920

    Add the fractions:

    58660/10920 + 2866.5/10920 = (58660 + 2866.5) / 10920 = 61526.5/10920

    Simplify the fraction by dividing the numerator and denominator by their GCF:

    GCF(61526.5, 10920) = 1.5

    (61526.5/1.5) / (10920/1.5) = 41017/7280

    Therefore, the new total after adding the sum of 73/39 and 49/14 to 21/80 is 41017/7280.

    ### Answer: 41017/7280

Expected answer: 17579/3120

Correct? No

🔗 Follow-up

Problem: After finding the sum of 73/6 and 49/14 (instead of 73/39 as in the previous question), what would be the new total? Please express it as a simplified fraction.

Gemma 2B:

    I apologize for the confusion in the previous question. Let's solve the problem with the correct fractions: 73/6 and 49/14.

    To find the sum of 73/6 and 49/14, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 6 and 14.

    LCM(6, 14) = 42

    Now, we convert each fraction to an equivalent fraction with the common denominator:

    73/6 = (73 × 7) / (6 × 7) = 511/42
    49/14 = (49 × 3) / (14 × 3) = 147/42

    Add the fractions:

    511/42 + 147/42 = (511 + 147) / 42 = 658/42

    Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF):

    GCF(658, 42) = 14

    (658/14) / (42/14) = 47/3

    Therefore, the sum of 73/6 and 49/14 is 47/3.

    ### Answer: 47/3

Expected answer: 47/3

Correct? Yes

🔗 Problem

Problem: What is the sum of 75/65 and 7/39? Simplify your answer.

Gemma 2B:

    To find the sum of 75/65 and 7/39, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 65 and 39.

    LCM(65, 39) = 65 × 39 ÷ GCD(65, 39)
    GCD(65, 39) = 13 (using the Euclidean algorithm)
    LCM(65, 39) = 65 × 39 ÷ 13 = 195

    Now, we can convert both fractions to equivalent fractions with the common denominator of 195:

    75/65 = (75 × 3)/(65 × 3) = 225/195
    7/39 = (7 × 5)/(39 × 5) = 35/195

    Adding the fractions:
    225/195 + 35/195 = (225 + 35)/195 = 260/195

    Simplifying the result:
    260/195 = 4/3 (dividing both numerator and denominator by their GCD, which is 65)

    ### Answer: 4/3

Expected answer: 4/3

Correct? Yes

🔗 Follow-up

Problem: You previously calculated the sum of 75/65 and 7/39. Now, add the fraction 65/97 to your result. What is your new total?

Gemma 2B:

    In the previous problem, we found that the sum of 75/65 and 7/39 is 4/3.

    Now, we need to add 65/97 to 4/3.

    First, let's find the common denominator for 4/3 and 65/97. The LCM of 3 and 97 is 3 × 97 = 291.

    Converting 4/3 to an equivalent fraction with a denominator of 291:
    4/3 = (4 × 97)/(3 × 97) = 388/291

    Converting 65/97 to an equivalent fraction with a denominator of 291:
    65/97 = (65 × 3)/(97 × 3) = 195/291

    Adding the fractions:
    388/291 + 195/291 = (388 + 195)/291 = 583/291

    Simplifying the result:
    583/291 cannot be simplified further as the GCD of 583 and 291 is 1.

    ### Answer: 583/291

Expected answer: 583/291

Correct? Yes

🔗 Follow-up

Problem: In a previous calculation, you found the sum of 75/65 and 7/39. Now, suppose we had originally used 75/65 and 7/47 instead. What would be the sum of these two fractions?

Gemma 2B:

    Let's follow the same steps as before to find the sum of 75/65 and 7/47.

    First, find the common denominator by calculating the LCM of 65 and 47.

    LCM(65, 47) = 65 × 47 ÷ GCD(65, 47)
    GCD(65, 47) = 1 (using the Euclidean algorithm)
    LCM(65, 47) = 65 × 47 ÷ 1 = 3055

    Convert both fractions to equivalent fractions with the common denominator of 3055:

    75/65 = (75 × 47)/(65 × 47) = 3525/3055
    7/47 = (7 × 65)/(47 × 65) = 455/3055

    Add the fractions:
    3525/3055 + 455/3055 = (3525 + 455)/3055 = 3980/3055

    Simplify the result:
    3980/3055 = 1306/1001 (dividing both numerator and denominator by their GCD, which is 2)

    ### Answer: 1306/1001

Expected answer: 796/611

Correct? No

🔗 Problem

Problem: First, calculate 79/1 - 30/92. Then, subtract 61/63 from the result. What value do you get?

Gemma 2B:

    Let's solve this problem step by step:

    1. Calculate 79/1 - 30/92
       79/1 = 79
       30/92 ≈ 0.326 (rounded to 3 decimal places)
       79 - 0.326 = 78.674

    2. Subtract 61/63 from the result (78.674)
       61/63 ≈ 0.968 (rounded to 3 decimal places)
       78.674 - 0.968 = 77.706

    Therefore, the final result is approximately 77.706.

    ### Answer: 77.706

Expected answer: 225191/2898

Correct? No

🔗 Problem

Problem: Calculate (58 / 26) + (58 / 26), and express your answer in simplest form.

Gemma 2B:

    To calculate (58 / 26) + (58 / 26), we can follow these steps:

    1. Simplify 58 / 26:
       58 ÷ 26 = 2 remainder 6
       58 / 26 = 2 6/26
       Simplify 6/26 by dividing both the numerator and denominator by 2:
       6 ÷ 2 = 3
       26 ÷ 2 = 13
       So, 58 / 26 = 2 3/13

    2. Now, we can rewrite the expression as:
       (58 / 26) + (58 / 26) = (2 3/13) + (2 3/13)

    3. To add fractions with the same denominator, we simply add the numerators:
       (2 3/13) + (2 3/13) = (2 + 2) + (3/13 + 3/13)
                          = 4 + 6/13
                          = 4 6/13

    Therefore, (58 / 26) + (58 / 26) = 4 6/13

    ### Answer: 4 6/13

Expected answer: 58/13

Correct? Yes

🔗 Follow-up

Problem: After you have calculated twice the fraction (58 / 26), what would be the result if you then added (49 / 66) to that sum? Express your final answer as a simplified fraction.

Gemma 2B:

    Let's continue from the previous calculation:

    1. We found that (58 / 26) + (58 / 26) = 4 6/13

    2. Now, we need to add (49 / 66) to 4 6/13

    3. First, let's simplify 49 / 66:
       49 ÷ 1 = 49
       66 ÷ 1 = 66
       Simplify 49/66 by dividing both the numerator and denominator by 1:
       49 ÷ 1 = 49
       66 ÷ 1 = 66
       So, 49 / 66 = 49/66

    4. To add 4 6/13 and 49/66, we need to find a common denominator. The least common multiple of 13 and 66 is 858.

    5. Convert 4 6/13 to an equivalent fraction with a denominator of 858:
       4 6/13 = (4 × 66) + (6 × 66) / (13 × 66)
              = 264 + 396 / 858
              = 660 / 858

    6. Convert 49/66 to an equivalent fraction with a denominator of 858:
       49/66 = 49 × 13 / 66 × 13
             = 637 / 858

    7. Now, we can add the fractions:
       660/858 + 637/858 = (660 + 637) / 858
                         = 1297 / 858

    8. Simplify 1297 / 858 by dividing both the numerator and denominator by their greatest common factor, which is 1:
       1297 ÷ 1 = 1297
       858 ÷ 1 = 858

    Therefore, the final result is 1297/858.

    ### Answer: 1297/858

Expected answer: 4465/858

Correct? No

🔗 Follow-up

Problem: If originally instead of 58 parts, there were 54 parts in every batch of 26, and two such fractions were added, what would be the sum? Express your answer in simplest form.

Gemma 2B:

    In this case, we are adding (54 / 26) + (54 / 26). Let's follow the same steps as before:

    1. Simplify 54 / 26:
       54 ÷ 26 = 2 remainder 2
       54 / 26 = 2 2/26
       Simplify 2/26 by dividing both the numerator and denominator by 2:
       2 ÷ 2 = 1
       26 ÷ 2 = 13
       So, 54 / 26 = 2 1/13

    2. Now, we can rewrite the expression as:
       (54 / 26) + (54 / 26) = (2 1/13) + (2 1/13)

    3. To add fractions with the same denominator, we simply add the numerators:
       (2 1/13) + (2 1/13) = (2 + 2) + (1/13 + 1/13)
                          = 4 + 2/13
                          = 4 2/13

    Therefore, if originally there were 54 parts in every batch of 26, and two such fractions were added, the sum would be 4 2/13.

    ### Answer: 4 2/13

Expected answer: 54/13

Correct? Yes

🔗 Problem

Problem: If Alex has 69/63 gallons of orange juice and he bought additional 77/5 gallons, giving him a total of 'k' gallons. Later, he received another 47/71 gallons of orange juice from Sally. How many gallons did Alex have in total?

Gemma 2B:

    Let's solve this problem step by step:

    1. Alex initially has 69/63 gallons of orange juice.
    2. He buys an additional 77/5 gallons.
    3. After buying, he has a total of 'k' gallons.
    4. Later, he receives another 47/71 gallons from Sally.

    To find the total gallons Alex has, we need to add the initial amount, the bought amount, and the received amount.

    Initial amount: 69/63 gallons
    Bought amount: 77/5 gallons
    Received amount: 47/71 gallons

    Now, let's add these fractions:
    69/63 + 77/5 + 47/71

    First, we need to find the least common multiple (LCM) of the denominators:
    LCM(63, 5, 71) = 22365

    Next, we convert each fraction to have the common denominator:
    (69 × 355)/22365 + (77 × 4473)/22365 + (47 × 315)/22365

    Simplifying:
    24495/22365 + 344421/22365 + 14805/22365

    Adding the numerators:
    (24495 + 344421 + 14805)/22365 = 383721/22365

    Simplifying the fraction:
    383721/22365 ≈ 17.16 gallons

    ### Answer: Alex had approximately 17.16 gallons of orange juice in total.

Expected answer: 127907/7455

Correct? No

🔗 Problem

Problem: What is the result of ((100 / 61) + ((39 / 6) + (67 / 49)))? Answer as a simplified fraction.

Gemma 2B:

    Let's solve this problem step by step:

    1. First, let's simplify the innermost parentheses (67 / 49):
       67 / 49 = 1 19/49

    2. Now, let's simplify (39 / 6) + (1 19/49):
       39 / 6 = 6 3/6 = 6 1/2
       6 1/2 + 1 19/49 = 13/2 + 68/49 = (13 * 49)/(2 * 49) + 68/(2 * 49) = (637 + 68)/(2 * 49) = 705/(2 * 49) = 705/98

    3. Finally, let's simplify (100 / 61) + (705/98):
       100 / 61 = 1 39/61
       1 39/61 + 705/98 = (1 * 98 + 39 * 98)/(61 * 98) + (705 * 61)/(98 * 61) = (98 + 3822)/(61 * 98) + 42005/(61 * 98) = 3920/(61 * 98) + 42005/(61 * 98) = (3920 + 42005)/(61 * 98) = 45925/(61 * 98)

    Simplifying the fraction:
    45925/(61 * 98) = 45925/5978 = 165/22

    ### Answer: 165/22

Expected answer: 56831/5978

Correct? No

🔗 Problem

Problem: What is the sum of 85/1 and 83/69? Simplify your answer as much as possible.

Gemma 2B:

    To find the sum of 85/1 and 83/69, we need to find a common denominator. The common denominator is the least common multiple (LCM) of 1 and 69, which is 69.

    85/1 = (85 × 69) / (1 × 69) = 5865/69

    Now, we can add the fractions:

    5865/69 + 83/69 = (5865 + 83) / 69 = 5948/69

    To simplify the fraction, we need to find the greatest common divisor (GCD) of 5948 and 69.

    The GCD of 5948 and 69 is 1.

    Since the GCD is 1, the fraction 5948/69 is already in its simplest form.

    ### Answer: 5948/69

Expected answer: 5948/69

Correct? Yes

🔗 Follow-up

Problem: After calculating the sum of 85/1 and 83/69, what is the result if you then add 21/86 to that sum?

Gemma 2B:

    In the previous problem, we found that the sum of 85/1 and 83/69 is 5948/69.

    Now, we need to add 21/86 to 5948/69.

    First, let's find the common denominator of 69 and 86. The LCM of 69 and 86 is 5934.

    5948/69 = (5948 × 86) / (69 × 86) = 511528/5934
    21/86 = (21 × 69) / (86 × 69) = 1449/5934

    Now, we can add the fractions:

    511528/5934 + 1449/5934 = (511528 + 1449) / 5934 = 512977/5934

    To simplify the fraction, we need to find the GCD of 512977 and 5934.

    The GCD of 512977 and 5934 is 1.

    Since the GCD is 1, the fraction 512977/5934 is already in its simplest form.

    ### Answer: 512977/5934

Expected answer: 512977/5934

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, instead of adding 83/69, what would be the result if you added 83/52 to 85/1 instead?

Gemma 2B:

    To find the sum of 85/1 and 83/52, we need to find a common denominator. The common denominator is the least common multiple (LCM) of 1 and 52, which is 52.

    85/1 = (85 × 52) / (1 × 52) = 4420/52

    Now, we can add the fractions:

    4420/52 + 83/52 = (4420 + 83) / 52 = 4503/52

    To simplify the fraction, we need to find the greatest common divisor (GCD) of 4503 and 52.

    The GCD of 4503 and 52 is 1.

    Since the GCD is 1, the fraction 4503/52 is already in its simplest form.

    ### Answer: 4503/52

Expected answer: 4503/52

Correct? Yes

🔗 Problem

Problem: What is the sum of 92/13 and 43/86 as a simplified fraction?

Gemma 2B:

    To find the sum of 92/13 and 43/86, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 13 and 86.

    LCM(13, 86) = 13 × 86 = 1118 (since 13 and 86 are relatively prime)

    Now, we convert both fractions to equivalent fractions with the common denominator:

    92/13 = 92 × (86/86) = 7912/1118
    43/86 = 43 × (13/13) = 559/1118

    Adding the fractions:

    7912/1118 + 559/1118 = (7912 + 559)/1118 = 8471/1118

    Simplifying the fraction:
    The greatest common divisor (GCD) of 8471 and 1118 is 1 (using the Euclidean algorithm or prime factorization).

    Since the GCD is 1, the fraction 8471/1118 is already in its simplest form.

    ### Answer: 8471/1118

Expected answer: 197/26

Correct? Yes

🔗 Follow-up

Problem: You solved the sum of 92/13 and 43/86 in the previous problem. Now, additional 36/72 to that sum. What is the total as a simplified fraction?

Gemma 2B:

    In the previous problem, we found that the sum of 92/13 and 43/86 is 8471/1118.

    Now, we need to add 36/72 to 8471/1118.

    First, let's simplify 36/72:
    36/72 = (36 ÷ 36)/(72 ÷ 36) = 1/2

    Next, we need to find a common denominator between 8471/1118 and 1/2.
    LCM(1118, 2) = 2236

    Converting the fractions to equivalent fractions with the common denominator:
    8471/1118 = 8471 × (2/2) = 16942/2236
    1/2 = 1 × (1118/1118) = 1118/2236

    Adding the fractions:
    16942/2236 + 1118/2236 = (16942 + 1118)/2236 = 18060/2236

    Simplifying the fraction:
    The GCD of 18060 and 2236 is 4 (using the Euclidean algorithm or prime factorization).

    Dividing both the numerator and denominator by 4:
    (18060 ÷ 4)/(2236 ÷ 4) = 4515/559

    Therefore, the sum of 92/13, 43/86, and 36/72 as a simplified fraction is 4515/559.

    ### Answer: 4515/559

Expected answer: 105/13

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, you found the sum of 92/13 and 43/86. Now suppose the original problem actually was about adding 61/13, not 92/13, to 43/86. What would be the new sum as a simplified fraction?

Gemma 2B:

    In this new problem, we need to find the sum of 61/13 and 43/86. We will follow the same steps as before, using the common denominator of 1118.

    61/13 = 61 × (86/86) = 5246/1118
    43/86 = 43 × (13/13) = 559/1118

    Adding the fractions:

    5246/1118 + 559/1118 = (5246 + 559)/1118 = 5805/1118

    Simplifying the fraction:
    The greatest common divisor (GCD) of 5805 and 1118 can be found using the Euclidean algorithm or prime factorization.

    5805 = 5 × 1161
    1118 = 2 × 13 × 43

    The GCD of 5805 and 1118 is 1.

    Since the GCD is 1, the fraction 5805/1118 is already in its simplest form.

    ### Answer: 5805/1118

Expected answer: 135/26

Correct? Yes

🔗 Problem

Problem: What is the sum of 67/32 and 10/98, expressed as a simplified fraction?

Gemma 2B:

    To find the sum of 67/32 and 10/98, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 32 and 98.

    LCM(32, 98) = 2 × 7 × 2 × 7 = 196

    Now, we convert both fractions to equivalent fractions with the common denominator:

    67/32 = (67 × 6)/(32 × 6) = 402/192
    10/98 = (10 × 2)/(98 × 2) = 20/196

    Adding the fractions:
    402/192 + 20/196 = (402 + 20)/196 = 422/196

    Simplifying the fraction:
    422/196 = 211/98

    ### Answer: 211/98

Expected answer: 3443/1568

Correct? No

🔗 Problem

Problem: What is the sum of 59/52 and 70/32? Please provide your answer as a simplified fraction.

Gemma 2B:

    To find the sum of 59/52 and 70/32, we need to find a common denominator. The least common multiple of 52 and 32 is 416.

    1. Convert 59/52 to an equivalent fraction with a denominator of 416:
       59/52 × 8/8 = 472/416

    2. Convert 70/32 to an equivalent fraction with a denominator of 416:
       70/32 × 13/13 = 910/416

    3. Add the numerators of the equivalent fractions:
       472/416 + 910/416 = 1382/416

    4. Simplify the resulting fraction by dividing the numerator and denominator by their greatest common factor (GCF). The GCF of 1382 and 416 is 2.
       1382/416 ÷ 2/2 = 691/208

    Therefore, the sum of 59/52 and 70/32 is 691/208.

    ### Answer: 691/208

Expected answer: 691/208

Correct? Yes

🔗 Follow-up

Problem: After finding the sum of 59/52 and 70/32, add this to 42/41. What is the final sum as a simplified fraction?

Gemma 2B:

    We already know that the sum of 59/52 and 70/32 is 691/208. Now, let's add 42/41 to this sum.

    1. Find the least common multiple of 208 and 41, which is 8528.

    2. Convert 691/208 to an equivalent fraction with a denominator of 8528:
       691/208 × 41/41 = 28371/8528

    3. Convert 42/41 to an equivalent fraction with a denominator of 8528:
       42/41 × 208/208 = 8736/8528

    4. Add the numerators of the equivalent fractions:
       28371/8528 + 8736/8528 = 37107/8528

    5. Simplify the resulting fraction by dividing the numerator and denominator by their greatest common factor (GCF). The GCF of 37107 and 8528 is 1.
       37107/8528 ÷ 1/1 = 37107/8528

    Therefore, the final sum of 59/52, 70/32, and 42/41 is 37107/8528.

    ### Answer: 37107/8528

Expected answer: 37067/8528

Correct? No

🔗 Follow-up

Problem: After recalculating the original problem with 74/52 instead of 59/52 and still adding this to 70/32, what is the new sum as a simplified fraction?

Gemma 2B:

    Let's solve the problem with the updated fraction 74/52 and add it to 70/32.

    1. Convert 74/52 to an equivalent fraction with a denominator of 416 (the least common multiple of 52 and 32):
       74/52 × 8/8 = 592/416

    2. Convert 70/32 to an equivalent fraction with a denominator of 416:
       70/32 × 13/13 = 910/416

    3. Add the numerators of the equivalent fractions:
       592/416 + 910/416 = 1502/416

    4. Simplify the resulting fraction by dividing the numerator and denominator by their greatest common factor (GCF). The GCF of 1502 and 416 is 2.
       1502/416 ÷ 2/2 = 751/208

    Therefore, the sum of 74/52 and 70/32 is 751/208.

    ### Answer: 751/208

Expected answer: 751/208

Correct? Yes

🔗 Problem

Problem: Let's first perform this operation: 48 divided by 5 subtracted from 11 divided by 65. Then, add the result to 28 divided by 2. What is the answer?

Gemma 2B:

    Okay, let's break this down step by step:

    1. First, we need to calculate 48 divided by 5:
       48 ÷ 5 = 9.6

    2. Next, we calculate 11 divided by 65:
       11 ÷ 65 ≈ 0.1692

    3. Now, we subtract the result of step 1 from the result of step 2:
       0.1692 - 9.6 = -9.4308

    4. Then, we calculate 28 divided by 2:
       28 ÷ 2 = 14

    5. Finally, we add the result of step 3 to the result of step 4:
       -9.4308 + 14 = 4.5692

    ### Answer: 4.5692

Expected answer: 1523/65

Correct? No

🔗 Problem

Problem: What is the result when you add 20/52 to 75/82? Simplify your answer to the smallest possible fraction.

Gemma 2B:

    To add 20/52 and 75/82, we need to find a common denominator. The least common multiple of 52 and 82 is 2,706.

    20/52 = (20 * 41) / (52 * 41) = 820/2,706
    75/82 = (75 * 33) / (82 * 33) = 2,475/2,706

    Now we can add the fractions:
    820/2,706 + 2,475/2,706 = 3,295/2,706

    To simplify this fraction, we find the greatest common factor of the numerator and denominator:
    3,295 = 5 * 659
    2,706 = 2 * 1,353
    The greatest common factor is 1.

    Therefore, the simplified fraction is 3,295/2,706.

    ### Answer: 3,295/2,706

Expected answer: 1385/1066

Correct? No

🔗 Problem

Problem: What is the result of subtracting 92/84 from 31/5? Answer as a simplified fraction.

Gemma 2B:

    To subtract 92/84 from 31/5, we need to find a common denominator. The least common multiple of 84 and 5 is 420.

    31/5 = (31 × 84) / (5 × 84) = 2604/420
    92/84 = (92 × 5) / (84 × 5) = 460/420

    Now we can subtract:

    2604/420 - 460/420 = (2604 - 460) / 420 = 2144/420

    Simplifying the fraction:
    2144/420 = 1072/210 = 536/105 = 268/52 = 134/26 = 67/13

    ### Answer: 67/13

Expected answer: 536/105

Correct? No

🔗 Problem

Problem: Calculate the following: Double the sum of 81/90 and 94/49.

Gemma 2B:

    To calculate the given expression, let's break it down into steps:

    1. Calculate the sum of 81/90 and 94/49.
       81/90 + 94/49 = (81 × 49 + 94 × 90) / (90 × 49)
                     = (3969 + 8460) / 4410
                     = 12429 / 4410
                     = <<12429/4410=141/50>>141/50

    2. Double the sum obtained in step 1.
       2 × 141/50 = 282/50
                  = <<282/50=141/25>>141/25

    Therefore, double the sum of 81/90 and 94/49 is 141/25.

    ### Answer: 141/25

Expected answer: 1381/245

Correct? No

🔗 Problem

Problem: Find the difference between 69/21 and 10/92. Write your answer as a simple fraction.

Gemma 2B:

    To find the difference between 69/21 and 10/92, we need to subtract these fractions. However, we can only subtract fractions with the same denominator. So, we first need to find the least common denominator (LCD) of 21 and 92.

    The LCD of 21 and 92 is 21 × 92 = 1932.

    Now, let's convert both fractions to equivalent fractions with the LCD as the denominator:

    69/21 = (69 × 92) / (21 × 92) = 6348/1932
    10/92 = (10 × 21) / (92 × 21) = 210/1932

    Now we can subtract:

    6348/1932 - 210/1932 = (6348 - 210)/1932 = 6138/1932

    Simplifying the fraction:
    6138/1932 = 3069/966 = 3069/966

    Therefore, the difference between 69/21 and 10/92 is 3069/966.

    ### Answer: 3069/966

Expected answer: 1023/322

Correct? Yes

🔗 Follow-up

Problem: Given that the difference between 69/21 and 10/92 is noted as a certain value, what will be the new value if you add 24/46 to it? Write your answer as a simplified fraction.

Gemma 2B:

    Let's call the difference between 69/21 and 10/92 as 'x'.

    x = 3069/966 (from the previous answer)

    Now, we need to add 24/46 to this value.

    To add fractions, we need to find the least common denominator (LCD) of 966 and 46.

    The LCD of 966 and 46 is 966 × 2 = 1932.

    Let's convert 24/46 to an equivalent fraction with the LCD as the denominator:

    24/46 = (24 × 21) / (46 × 21) = 504/966

    Now we can add:

    3069/966 + 504/966 = (3069 + 504)/966 = 3573/966

    Simplifying the fraction:
    3573/966 = 3573/966

    Therefore, if we add 24/46 to the difference between 69/21 and 10/92, the new value will be 3573/966.

    ### Answer: 3573/966

Expected answer: 1191/322

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, you found the difference between certain fractions. Now, consider a slight change. If the first fraction was 63/21 instead of 69/21, what would the new difference be? Calculate 63/21 - 10/92, and write your answer as a simplified fraction.

Gemma 2B:

    Let's follow the same steps as before, but with 63/21 instead of 69/21.

    The LCD of 21 and 92 is still 21 × 92 = 1932.

    Converting the fractions to equivalent fractions with the LCD as the denominator:

    63/21 = (63 × 92) / (21 × 92) = 5796/1932
    10/92 = (10 × 21) / (92 × 21) = 210/1932

    Subtracting:

    5796/1932 - 210/1932 = (5796 - 210)/1932 = 5586/1932

    Simplifying the fraction:
    5586/1932 = 2793/966

    Therefore, the difference between 63/21 and 10/92 is 2793/966.

    ### Answer: 2793/966

Expected answer: 133/46

Correct? Yes

🔗 Problem

Problem: First, find the result of (26 / 87) + (92 / 88). Then add the result to (26 / 57). What's the answer?

Gemma 2B:

    Let's solve this problem step by step:

    1. Find the result of (26 / 87) + (92 / 88):
       (26 / 87) + (92 / 88) = 0.2988505747126437 + 1.0454545454545454
                             = 1.3443051201671891

    2. Add the result from step 1 to (26 / 57):
       1.3443051201671891 + (26 / 57) = 1.3443051201671891 + 0.45614035087719296
                                       = 1.8004454710443821

    Therefore, the final result is 1.8004454710443821.

    ### Answer: 1.8004454710443821

Expected answer: 21825/12122

Correct? No

🔗 Problem

Problem: What is the result if you add 78/66, 28/6, and 90/34 together? Please provide your answer as a simplified fraction.

Gemma 2B:

    To add fractions, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of the denominators 66, 6, and 34.

    LCM(66, 6, 34) = 1122

    Now, we convert each fraction to an equivalent fraction with the denominator 1122:

    78/66 = (78 × 17) / (66 × 17) = 1326/1122
    28/6 = (28 × 187) / (6 × 187) = 5236/1122
    90/34 = (90 × 33) / (34 × 33) = 2970/1122

    Adding the numerators:
    1326/1122 + 5236/1122 + 2970/1122 = (1326 + 5236 + 2970)/1122 = 9532/1122

    Simplifying the fraction:
    9532/1122 = 4766/561

    ### Answer: 4766/561

Expected answer: 4766/561

Correct? Yes

🔗 Follow-up

Problem: For the result you obtained from adding 78/66, 28/6, and 90/34 together, what would be the new result if you now subtract 56/61 from it? Please provide your answer as a simplified fraction.

Gemma 2B:

    In the previous question, we found that 78/66 + 28/6 + 90/34 = 4766/561.

    Now, we need to subtract 56/61 from 4766/561.

    First, let's find the common denominator of 561 and 61, which is their LCM.
    LCM(561, 61) = 34221

    Converting the fractions to equivalent fractions with the denominator 34221:
    4766/561 = (4766 × 61) / (561 × 61) = 290726/34221
    56/61 = (56 × 561) / (61 × 561) = 31416/34221

    Subtracting the numerators:
    (290726 - 31416)/34221 = 259310/34221

    Simplifying the fraction:
    259310/34221 = 7590/1001

    ### Answer: 7590/1001

Expected answer: 259310/34221

Correct? No

🔗 Follow-up

Problem: Previously you added 78/66, 28/6, and 90/34 together. Now consider what would the result be if you instead added 78/66, 53/6, and 90/34 together? Please provide your answer as a simplified fraction.

Gemma 2B:

    To add fractions, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of the denominators 66, 6, and 34.

    LCM(66, 6, 34) = 1122

    Now, we convert each fraction to an equivalent fraction with the denominator 1122:

    78/66 = (78 × 17) / (66 × 17) = 1326/1122
    53/6 = (53 × 187) / (6 × 187) = 9911/1122
    90/34 = (90 × 33) / (34 × 33) = 2970/1122

    Adding the numerators:
    1326/1122 + 9911/1122 + 2970/1122 = (1326 + 9911 + 2970)/1122 = 14207/1122

    Simplifying the fraction:
    14207/1122 = 14207/1122

    The fraction 14207/1122 cannot be simplified further as the greatest common divisor (GCD) of 14207 and 1122 is 1.

    ### Answer: 14207/1122

Expected answer: 14207/1122

Correct? Yes

🔗 Problem

Problem: Calculate: (12 / 7) - (9 / 23). Please simplify your answer to the lowest terms.

Gemma 2B:

    To calculate (12 / 7) - (9 / 23), we need to find a common denominator for the fractions.

    The least common multiple (LCM) of 7 and 23 is 7 × 23 = 161.

    Now, we can rewrite the fractions with the common denominator:

    (12 / 7) = (12 × 23) / (7 × 23) = 276 / 161
    (9 / 23) = (9 × 7) / (23 × 7) = 63 / 161

    Subtracting the fractions:

    (276 / 161) - (63 / 161) = (276 - 63) / 161 = 213 / 161

    Simplifying the fraction to the lowest terms:

    213 and 161 have a common factor of 3.
    (213 / 3) / (161 / 3) = 71 / 53

    ### Answer: 71 / 53

Expected answer: 213/161

Correct? No

🔗 Problem

Problem: Calculate the sum of 95/18 and 51/61, and represent your answer as a simplified fraction.

Gemma 2B:

    To calculate the sum of 95/18 and 51/61, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 18 and 61.

    LCM(18, 61) = 1098

    Now, we convert both fractions to equivalent fractions with the common denominator:

    95/18 = 95 × 61/18 × 61 = 5795/1098
    51/61 = 51 × 18/61 × 18 = 918/1098

    Adding the fractions:
    5795/1098 + 918/1098 = 6713/1098

    Simplifying the fraction:
    6713/1098 = 6713/1098 ÷ 1 = 6713/1098

    The fraction 6713/1098 cannot be simplified further as the greatest common divisor (GCD) of 6713 and 1098 is 1.

    ### Answer: 6713/1098

Expected answer: 6713/1098

Correct? Yes

🔗 Follow-up

Problem: Following the last question, find the sum of the answer to the previous problem and 45/27, represented as a simplified fraction.

Gemma 2B:

    From the previous problem, we found that the sum of 95/18 and 51/61 is 6713/1098.

    Now, we need to add 6713/1098 and 45/27.

    First, let's find the common denominator by calculating the LCM of 1098 and 27.

    LCM(1098, 27) = 29646

    Converting the fractions to equivalent fractions with the common denominator:

    6713/1098 = 6713 × 27/1098 × 27 = 181251/29646
    45/27 = 45 × 1098/27 × 1098 = 49410/29646

    Adding the fractions:
    181251/29646 + 49410/29646 = 230661/29646

    Simplifying the fraction:
    230661/29646 = 230661/29646 ÷ 3 = 76887/9882

    The fraction 76887/9882 cannot be simplified further as the GCD of 76887 and 9882 is 1.

    ### Answer: 76887/9882

Expected answer: 8543/1098

Correct? Yes

🔗 Follow-up

Problem: Suppose instead of 95/18 in the previous problem, we had 59/18. Now compute the sum of 59/18 and 51/61, and represent your answer as a simplified fraction.

Gemma 2B:

    To calculate the sum of 59/18 and 51/61, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 18 and 61.

    LCM(18, 61) = 1098

    Now, we convert both fractions to equivalent fractions with the common denominator:

    59/18 = 59 × 61/18 × 61 = 3599/1098
    51/61 = 51 × 18/61 × 18 = 918/1098

    Adding the fractions:
    3599/1098 + 918/1098 = 4517/1098

    Simplifying the fraction:
    4517/1098 = 4517/1098 ÷ 1 = 4517/1098

    The fraction 4517/1098 cannot be simplified further as the greatest common divisor (GCD) of 4517 and 1098 is 1.

    ### Answer: 4517/1098

Expected answer: 4517/1098

Correct? Yes

🔗 Problem

Problem: Calculate the following subtraction of fractions: (93 / 46) - (51 / 84). Answer as a simplified fraction.

Gemma 2B:

    To subtract fractions, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of the denominators 46 and 84.

    LCM(46, 84) = 2 × 46 = 92 (since 84 is divisible by 46)

    Now, we convert both fractions to equivalent fractions with the common denominator:

    (93 / 46) = (93 × 2) / (46 × 2) = 186 / 92
    (51 / 84) = (51 × 1) / (84 × 1) = 51 / 92

    Subtracting the fractions:

    (186 / 92) - (51 / 92) = (186 - 51) / 92 = 135 / 92

    Simplifying the fraction:

    135 / 92 = 45 / 46 (dividing both numerator and denominator by their GCD, which is 3)

    ### Answer: 45 / 46

Expected answer: 911/644

Correct? No

🔗 Problem

Problem: Calculate the sum of the fractions 12/70 and 84/9. Please provide your answer in simplified form.

Gemma 2B:

    To calculate the sum of 12/70 and 84/9, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 70 and 9.

    LCM(70, 9) = 630

    Now, we convert each fraction to an equivalent fraction with the common denominator:

    12/70 = (12 × 9)/(70 × 9) = 108/630
    84/9 = (84 × 70)/(9 × 70) = 5880/630

    Add the numerators and keep the common denominator:

    108/630 + 5880/630 = 5988/630

    Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD):

    GCD(5988, 630) = 126

    (5988/126)/(630/126) = 47.5/5 = 9.5

    ### Answer: 9.5

Expected answer: 998/105

Correct? No

🔗 Problem

Problem: If you subtract 40/92 from 32/3 and double the result, what would you get?

Gemma 2B:

    Let's solve this problem step by step:

    1. First, we need to subtract 40/92 from 32/3.
       32/3 - 40/92 = (32 × 92 - 40 × 3) / (3 × 92)
                    = (2944 - 120) / 276
                    = 2824 / 276
                    = 141/138

    2. Now, we need to double the result.
       141/138 × 2 = 282/138
                  = 141/69

    Therefore, if you subtract 40/92 from 32/3 and double the result, you would get 141/69.

    ### Answer: 141/69

Expected answer: 1412/69

Correct? No

🔗 Problem

Problem: What is the sum of 79/24 and 79/24? Keep your answer as a simplified fraction.

Gemma 2B:

    To find the sum of 79/24 and 79/24, we can follow these steps:

    1. Since the fractions have the same denominator, we can simply add the numerators and keep the denominator the same.

       79/24 + 79/24 = (79 + 79) / 24

    2. Add the numerators:

       (79 + 79) / 24 = 158 / 24

    3. Simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF). The GCF of 158 and 24 is 2.

       (158 ÷ 2) / (24 ÷ 2) = 79 / 12

    Therefore, the sum of 79/24 and 79/24 is 79/12.

    ### Answer: 79/12

Expected answer: 79/12

Correct? Yes

🔗 Follow-up

Problem: In continuation to the previous problem, now find out what is the sum of two times the previously found sum. In other words, calculate (79/24 + 79/24) + (79/24 + 79/24). Please answer as a simplified fraction.

Gemma 2B:

    In the previous problem, we found that 79/24 + 79/24 = 79/12.

    Now, we need to find the sum of two times this result:

    (79/24 + 79/24) + (79/24 + 79/24) = 79/12 + 79/12

    To find the sum of 79/12 and 79/12, we can follow these steps:

    1. Since the fractions have the same denominator, we can simply add the numerators and keep the denominator the same.

       79/12 + 79/12 = (79 + 79) / 12

    2. Add the numerators:

       (79 + 79) / 12 = 158 / 12

    3. Simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF). The GCF of 158 and 12 is 2.

       (158 ÷ 2) / (12 ÷ 2) = 79 / 6

    Therefore, the sum of (79/24 + 79/24) and (79/24 + 79/24) is 79/6.

    ### Answer: 79/6

Expected answer: 79/6

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, you added together two fractions of 79/24. Now, consider if those were fractions of 79/20 instead. What would be the total if you added together two fractions of 79/20? Please express your answer as a simplified fraction.

Gemma 2B:

    Certainly! Let's solve this problem step by step.

    Given: We are adding two fractions of 79/20.

    Step 1: Add the fractions by adding the numerators and keeping the denominator the same.
    79/20 + 79/20 = (79 + 79) / 20 = 158 / 20

    Step 2: Simplify the resulting fraction by dividing both the numerator and denominator by their greatest common factor (GCF). To find the GCF of 158 and 20, let's factor each number:
    158 = 2 × 79
    20 = 2 × 2 × 5

    The GCF of 158 and 20 is 2.

    Step 3: Divide both the numerator and denominator by the GCF (2).
    (158 ÷ 2) / (20 ÷ 2) = 79 / 10

    Therefore, the sum of two fractions of 79/20 is 79/10.

    ### Answer: 79/10

Expected answer: 79/10

Correct? Yes

🔗 Problem

Problem: What is the sum of 91/76 and 12/22? Please simplify your fraction.

Gemma 2B:

    To find the sum of 91/76 and 12/22, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 76 and 22.

    LCM(76, 22) = 1672

    Now, we convert both fractions to equivalent fractions with the common denominator:

    91/76 = 91 × 22 / 76 × 22 = 2002/1672
    12/22 = 12 × 76 / 22 × 76 = 912/1672

    Adding the fractions:

    2002/1672 + 912/1672 = 2914/1672

    Simplifying the fraction:

    2914/1672 = 1457/836

    Therefore, the sum of 91/76 and 12/22 is 1457/836.

    ### Answer: 1457/836

Expected answer: 1457/836

Correct? Yes

🔗 Follow-up

Problem: The previous problem asked to calculate the sum of 91/76 and 12/22. Now, what would be the sum if you added 94/59 to the result of the previous problem? Please give your answer as a simplified fraction.

Gemma 2B:

    In the previous problem, we found that the sum of 91/76 and 12/22 is 1457/836.

    Now, we need to add 94/59 to 1457/836.

    First, let's find the common denominator for 1457/836 and 94/59. The LCM of 836 and 59 is 49324.

    Converting the fractions to equivalent fractions with the common denominator:

    1457/836 = 1457 × 59 / 836 × 59 = 85963/49324
    94/59 = 94 × 836 / 59 × 836 = 78584/49324

    Adding the fractions:

    85963/49324 + 78584/49324 = 164547/49324

    Simplifying the fraction:

    164547/49324 = 10283/3083

    Therefore, the sum of 1457/836 and 94/59 is 10283/3083.

    ### Answer: 10283/3083

Expected answer: 164547/49324

Correct? No

🔗 Problem

Problem: First, add 88/93 to 6/47. Then, add the result to 92/4. What do you get?

Gemma 2B:

    Let's solve this problem step by step:

    1. Add 88/93 to 6/47:
       To add fractions, we need to find a common denominator. The common denominator is 93 * 47 = 4371.

       88/93 = 88 * 47 / 4371 = 4136/4371
       6/47 = 6 * 93 / 4371 = 558/4371

       4136/4371 + 558/4371 = 4694/4371

    2. Add the result (4694/4371) to 92/4:
       Again, we need to find a common denominator. The common denominator is 4 * 4371 = 17484.

       4694/4371 = 4694 * 4 / 17484 = 18776/17484
       92/4 = 92 * 4371 / 17484 = 401132/17484

       18776/17484 + 401132/17484 = 419908/17484

    3. Simplify the result:
       419908/17484 = 24 + 908/17484 = 24 + (227/4371) = 24 227/4371

    ### Answer: 24 227/4371

Expected answer: 105227/4371

Correct? No

🔗 Problem

Problem: Calculate the sum of 95/83 and the result of 52/21 + 75/67. Write your answer as a simplified fraction.

Gemma 2B:

    To calculate the sum of 95/83 and the result of 52/21 + 75/67, let's break it down into steps:

    Step 1: Calculate 52/21 + 75/67
    52/21 = 52 ÷ 21 = 52 × 1/21 = 52/21
    75/67 = 75 ÷ 67 = 75 × 1/67 = 75/67
    To add fractions, we need a common denominator. The least common multiple of 21 and 67 is 21 × 67 = 1407.
    (52/21) × (67/67) = 3484/1407
    (75/67) × (21/21) = 1575/1407
    3484/1407 + 1575/1407 = 5059/1407

    Step 2: Add 95/83 to the result from Step 1
    95/83 = 95 ÷ 83 = 95 × 1/83 = 95/83
    The least common multiple of 1407 and 83 is 1407 × 83 = 116781.
    (5059/1407) × (83/83) = 419897/116781
    (95/83) × (1407/1407) = 133665/116781
    419897/116781 + 133665/116781 = 553562/116781

    Step 3: Simplify the fraction
    553562/116781 can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 7.
    553562 ÷ 7 = 79080
    116781 ÷ 7 = 16683
    79080/16683 is the simplified fraction.

    ### Answer: 79080/16683

Expected answer: 553562/116781

Correct? No

🔗 Problem

Problem: What is the value of the expression ((73 / 27) - (23 / 48))? Answer as a simplified fraction.

Gemma 2B:

    To find the value of the expression ((73 / 27) - (23 / 48)), we need to perform the division operations and then subtract the results. Let's solve this step by step.

    Step 1: Simplify 73 / 27
    73 / 27 = 2 19/27 (divide 73 by 27 to get the mixed number)

    Step 2: Simplify 23 / 48
    23 / 48 = 23/48 (this fraction cannot be simplified further)

    Step 3: Convert 2 19/27 to an improper fraction
    2 19/27 = (2 × 27 + 19) / 27 = 73/27

    Step 4: Subtract the fractions
    (73/27) - (23/48) = (73 × 48 - 23 × 27) / (27 × 48) = (3504 - 621) / 1296 = 2883/1296

    Step 5: Simplify the resulting fraction
    2883/1296 = 37/16 (divide both the numerator and denominator by 37)

    Therefore, the value of the expression ((73 / 27) - (23 / 48)) is 37/16.

    ### Answer: 37/16

Expected answer: 961/432

Correct? No

🔗 Problem

Problem: Solve the expression (78 / 2) - (70 / 23). Answer as a simplified decimal or fraction.

Gemma 2B:

    To solve the expression (78 / 2) - (70 / 23), let's break it down into steps:

    1. First, calculate 78 / 2:
       78 / 2 = 39

    2. Next, calculate 70 / 23:
       70 / 23 ≈ 3.0434782608695652 (as a decimal)
       or
       70 / 23 = 3 2/23 (as a mixed fraction)

    3. Now, subtract the result of step 2 from the result of step 1:
       39 - 3.0434782608695652 ≈ 35.9565217391304348 (as a decimal)
       or
       39 - 3 2/23 = 35 21/23 (as a mixed fraction)

    Therefore, the simplified result is:
    (78 / 2) - (70 / 23) ≈ 35.9565217391304348 (as a decimal)
    or
    (78 / 2) - (70 / 23) = 35 21/23 (as a mixed fraction)

    ### Answer: 35 21/23

Expected answer: 827/23

Correct? No

🔗 Problem

Problem: What is the result when you add 34/1 to 53/4? Express your answer as a mixed number.

Gemma 2B:

    To add 34/1 and 53/4, we first need to convert 34/1 to an improper fraction.

    34/1 = 34

    Now, we can add 34 and 53/4:

    34 + 53/4 = (34 × 4 + 53) / 4
             = (136 + 53) / 4
             = 189 / 4

    To convert 189/4 to a mixed number, we divide 189 by 4:

    189 ÷ 4 = 47 remainder 1

    This means that 189/4 = 47 1/4

    ### Answer: 47 1/4

Expected answer: 189/4

Correct? Yes

🔗 Follow-up

Problem: Following the result of the previous problem, what is the sum of 24/67 and the result you got from adding 34/1 to 53/4? Express your answer as a mixed number.

Gemma 2B:

    From the previous problem, we found that 34/1 + 53/4 = 47 1/4.

    Now, we need to add 24/67 to 47 1/4.

    First, let's convert 47 1/4 to an improper fraction:

    47 1/4 = (47 × 4 + 1) / 4 = 189/4

    Next, we need to find a common denominator for 189/4 and 24/67. The least common multiple of 4 and 67 is 268.

    189/4 = 189 × 67 / 4 × 67 = 12663/268
    24/67 = 24 × 4 / 67 × 4 = 96/268

    Now we can add the fractions:

    12663/268 + 96/268 = 12759/268

    To convert 12759/268 to a mixed number, we divide 12759 by 268:

    12759 ÷ 268 = 47 remainder 163

    This means that 12759/268 = 47 163/268

    ### Answer: 47 163/268

Expected answer: 12759/268

Correct? Yes

🔗 Follow-up

Problem: Let's reconsider the problem where you were adding fractions. Previously, it was asked to add 34/1 to 53/4. Now consider whether it may have been 34/97 instead of 34/1. What will be the result if you add 34/97 to 53/4? Write your answer as a mixed number.

Gemma 2B:

    I apologize for the confusion. Let's solve the problem with the correct fractions: 34/97 and 53/4.

    To add fractions with different denominators, we need to find the least common denominator (LCD). The LCD of 97 and 4 is 388.

    Now, let's convert both fractions to equivalent fractions with the LCD:

    34/97 = (34 × 4) / (97 × 4) = 136/388
    53/4 = (53 × 97) / (4 × 97) = 5141/388

    Adding the fractions:

    136/388 + 5141/388 = 5277/388

    To convert 5277/388 to a mixed number, we divide 5277 by 388:

    5277 ÷ 388 = 13 remainder 193

    This means that 5277/388 = 13 193/388

    Simplifying the fraction 193/388 by dividing both the numerator and denominator by their greatest common factor (GCF):

    GCF of 193 and 388 is 1 (they are coprime).

    Therefore, 193/388 cannot be simplified further.

    ### Answer: 13 193/388

Expected answer: 5277/388

Correct? No

🔗 Problem

Problem: What is the sum of 3/36 and 97/96? Answer as a simplified fraction.

Gemma 2B:

    To find the sum of 3/36 and 97/96, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 36 and 96.

    LCM(36, 96) = 2^3 × 3^2 = 288

    Now, we convert both fractions to equivalent fractions with the common denominator:

    3/36 = (3 × 8)/(36 × 8) = 24/288
    97/96 = (97 × 3)/(96 × 3) = 291/288

    Adding the fractions:
    24/288 + 291/288 = (24 + 291)/288 = 315/288

    Simplifying the fraction:
    315/288 = (315 ÷ 9)/(288 ÷ 9) = 35/32

    ### Answer: 35/32

Expected answer: 35/32

Correct? Yes

🔗 Follow-up

Problem: After finding the sum of 3/36 and 97/96, add your answer to 55/69. What is your result reduced to its simplest form?

Gemma 2B:

    From the previous question, we found that the sum of 3/36 and 97/96 is 35/32.

    Now, we need to add 35/32 and 55/69. First, let's find the common denominator, which is the LCM of 32 and 69.

    LCM(32, 69) = 32 × 69 = 2208

    Converting the fractions to equivalent fractions with the common denominator:

    35/32 = (35 × 69)/(32 × 69) = 2415/2208
    55/69 = (55 × 32)/(69 × 32) = 1760/2208

    Adding the fractions:
    2415/2208 + 1760/2208 = (2415 + 1760)/2208 = 4175/2208

    Simplifying the fraction:
    4175/2208 = (4175 ÷ 17)/(2208 ÷ 17) = 245/128

    ### Answer: 245/128

Expected answer: 4175/2208

Correct? No

🔗 Follow-up

Problem: After the initial calculation with 3/36 and 97/96, now consider you made an error and the actual fraction was 3/38 not 3/36. Recalculate the sum of 3/38 and 97/96. What is the new sum as a simplified fraction?

Gemma 2B:

    I apologize for the confusion. Let's recalculate the sum of 3/38 and 97/96.

    First, we need to find the least common multiple (LCM) of 38 and 96 to determine the common denominator.

    LCM(38, 96) = 2^5 × 3 × 19 = 1824

    Now, we convert both fractions to equivalent fractions with the common denominator:

    3/38 = (3 × 48)/(38 × 48) = 144/1824
    97/96 = (97 × 19)/(96 × 19) = 1843/1824

    Adding the fractions:
    144/1824 + 1843/1824 = (144 + 1843)/1824 = 1987/1824

    Simplifying the fraction:
    1987/1824 = (1987 ÷ 7)/(1824 ÷ 7) = 284/261

    ### Answer: 284/261

Expected answer: 1987/1824

Correct? No

🔗 Problem

Problem: Calculate ((92 / 95) + (4 / 74)). Answer as a simplified fraction.

Gemma 2B:

    To calculate ((92 / 95) + (4 / 74)), let's first perform the division operations and then add the resulting fractions.

    Step 1: Simplify 92 / 95
    92 and 95 have no common factors other than 1, so this fraction cannot be simplified further.

    Step 2: Simplify 4 / 74
    4 and 74 have a common factor of 2.
    4 ÷ 2 = 2
    74 ÷ 2 = 37
    So, 4 / 74 = 2 / 37

    Step 3: Add the fractions 92 / 95 and 2 / 37
    To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators.
    LCM of 95 and 37 is 3515.

    Multiply the numerator and denominator of each fraction by the factor that makes the denominator equal to the LCM:
    92 / 95 = (92 × 37) / (95 × 37) = 3404 / 3515
    2 / 37 = (2 × 95) / (37 × 95) = 190 / 3515

    Now add the numerators and keep the denominator the same:
    (3404 / 3515) + (190 / 3515) = (3404 + 190) / 3515 = 3594 / 3515

    Step 4: Simplify the resulting fraction
    3594 and 3515 have no common factors other than 1, so this fraction cannot be simplified further.

    ### Answer: 3594 / 3515

Expected answer: 3594/3515

Correct? Yes

🔗 Problem

Problem: If the value of a variable 'v' is 69/47, what is the value of 'd' if 'd' equals 88/72 + 'v'? Please write your answer as a fraction.

Gemma 2B:

    To find the value of 'd', we need to add 88/72 and 69/47.

    First, let's convert both fractions to a common denominator. The common denominator will be the least common multiple (LCM) of 72 and 47.

    LCM(72, 47) = 3384

    Now, let's convert each fraction to an equivalent fraction with the denominator 3384:

    88/72 = 88 * (3384/72) / 3384 = 4136/3384
    69/47 = 69 * (3384/47) / 3384 = 4968/3384

    Adding the fractions:

    d = 4136/3384 + 4968/3384
    d = (4136 + 4968) / 3384
    d = 9104/3384

    Simplifying the fraction:

    9104/3384 = 2276/846 = 1138/423

    ### Answer: 1138/423

Expected answer: 1138/423

Correct? Yes

🔗 Follow-up

Problem: Following from the last question, if we now have a new variable 'r' which is defined as 92/22 + 'd', what is the value of 'r'? Please write your answer as a fraction.

Gemma 2B:

    In the previous question, we found that the value of 'd' is 1138/423.

    To find the value of 'r', we need to add 92/22 and 1138/423.

    First, let's convert both fractions to a common denominator. The common denominator will be the least common multiple (LCM) of 22 and 423.

    LCM(22, 423) = 9306

    Now, let's convert each fraction to an equivalent fraction with the denominator 9306:

    92/22 = 92 * (9306/22) / 9306 = 38896/9306
    1138/423 = 1138 * (9306/423) / 9306 = 25024/9306

    Adding the fractions:

    r = 38896/9306 + 25024/9306
    r = (38896 + 25024) / 9306
    r = 63920/9306

    Simplifying the fraction:

    63920/9306 = 6880/1002 = 3440/501

    ### Answer: 3440/501

Expected answer: 31976/4653

Correct? No

🔗 Follow-up

Problem: In the problem from before, let's consider that variable 'v' no longer represents 69/47, but is now represented by 69/8. Given that change, what is the new value for 'd' if 'd' continues to be defined as the sum of 88/72 and 'v'? Write your answer as a fraction.

Gemma 2B:

    Now that the value of 'v' has changed to 69/8, let's recalculate the value of 'd' using the same method as before.

    Given:
    - 'd' equals 88/72 + 'v'
    - 'v' equals 69/8

    Step 1: Find the common denominator of 88/72 and 69/8.
    The common denominator is the least common multiple (LCM) of 72 and 8.
    LCM(72, 8) = 72

    Step 2: Convert 88/72 and 69/8 to equivalent fractions with the common denominator of 72.

    88/72 is already in the correct form.
    69/8 = 69 × (72/8) / 72 = 621/72

    Step 3: Add the fractions.

    d = 88/72 + 621/72
    d = (88 + 621) / 72
    d = 709/72

    Step 4: Simplify the fraction.

    709/72 cannot be simplified further as there are no common factors between 709 and 72.

    ### Answer: 709/72

Expected answer: 709/72

Correct? Yes

🔗 Problem

Problem: Let's say there is a wholesaler who has 41/26 barrels of olive oil in their warehouse. They sell a portion of the oil which is equivalent to 41/72 barrels. How much olive oil do they have now? Express your answer as a simple fraction.

Gemma 2B:

    Okay, let's solve this problem step by step:

    1. The wholesaler initially has 41/26 barrels of olive oil.
    2. They sell a portion equivalent to 41/72 barrels.
    3. To find out how much olive oil they have now, we need to subtract the amount sold from the initial amount.

    41/26 - 41/72

    4. To subtract fractions, we need to find a common denominator. The common denominator is the least common multiple (LCM) of 26 and 72.
       LCM(26, 72) = 936

    5. Now, we convert both fractions to equivalent fractions with the common denominator:

    41/26 = (41 × 36)/(26 × 36) = 1476/936
    41/72 = (41 × 13)/(72 × 13) = 533/936

    6. Subtract the fractions:

    1476/936 - 533/936 = (1476 - 533)/936 = 943/936

    7. Simplify the fraction:

    943/936 = 41/39

    Therefore, the wholesaler now has 41/39 barrels of olive oil.

    ### Answer: 41/39

Expected answer: 943/936

Correct? No

🔗 Problem

Problem: What is the sum of 85/75 and 88/56? Write your answer in decimal form.

Gemma 2B:

    To find the sum of 85/75 and 88/56, we need to convert the fractions to a common denominator, add them together, and then convert the result to decimal form.

    Converting 85/75 and 88/56 to a common denominator:
    85/75 = (85 * 56) / (75 * 56) = 4760/4200
    88/56 = (88 * 75) / (56 * 75) = 6600/4200

    Adding the fractions:
    4760/4200 + 6600/4200 = (4760 + 6600) / 4200 = 11360/4200

    Simplifying the result:
    11360/4200 = 568/210

    Converting 568/210 to decimal form:
    568 ÷ 210 ≈ 2.704761904761905

    ### Answer: 2.704761904761905

Expected answer: 284/105

Correct? No

🔗 Problem

Problem: What is the result of adding 12 over 33 to 49 over 2? Write your answer as a mixed fraction.

Gemma 2B:

    To add 12/33 and 49/2, we first need to find a common denominator. The least common multiple of 33 and 2 is 66.

    12/33 = (12 × 2)/(33 × 2) = 24/66
    49/2 = (49 × 33)/(2 × 33) = 1617/66

    Now we can add the fractions:
    24/66 + 1617/66 = 1641/66

    To convert 1641/66 to a mixed fraction, we divide 1641 by 66:
    1641 ÷ 66 = 24 remainder 57

    So, 1641/66 = 24 57/66

    Simplifying the fraction 57/66 by dividing both the numerator and denominator by 3:
    57 ÷ 3 = 19
    66 ÷ 3 = 22

    Therefore, 57/66 = 19/22

    The final answer as a mixed fraction is:
    24 19/22

    ### Answer: 24 19/22

Expected answer: 547/22

Correct? Yes

🔗 Follow-up

Problem: What is the result when you add the fraction 17 over 94 to the solution obtained from the previous calculation (i.e., the sum of 12 over 33 and 49 over 2)? Write your answer as a mixed fraction.

Gemma 2B:

    From the previous calculation, we found that the sum of 12/33 and 49/2 is 24 19/22.

    Now, we need to add 17/94 to 24 19/22.

    First, convert 24 19/22 to an improper fraction:
    24 19/22 = (24 × 22 + 19)/22 = 547/22

    Next, find the common denominator of 547/22 and 17/94. The least common multiple of 22 and 94 is 2068.

    547/22 = (547 × 94)/(22 × 94) = 51418/2068
    17/94 = (17 × 22)/(94 × 22) = 374/2068

    Now, add the fractions:
    51418/2068 + 374/2068 = 51792/2068

    To convert 51792/2068 to a mixed fraction, divide 51792 by 2068:
    51792 ÷ 2068 = 25 remainder 92

    So, 51792/2068 = 25 92/2068

    Simplifying the fraction 92/2068 by dividing both the numerator and denominator by 4:
    92 ÷ 4 = 23
    2068 ÷ 4 = 517

    Therefore, 92/2068 = 23/517

    The final answer as a mixed fraction is:
    25 23/517

    ### Answer: 25 23/517

Expected answer: 12948/517

Correct? Yes

🔗 Follow-up

Problem: What if we originally started with 12 out of 84 parts instead of 33 parts, as in the first scenario? What would the sum of this fraction and 49 over 2 be? State your answer as a mixed fraction.

Gemma 2B:

    Let's solve this problem step by step.

    Given:
    - First fraction: 12/84
    - Second fraction: 49/2

    Step 1: Find the common denominator of 84 and 2.
    The least common multiple of 84 and 2 is 84.

    Step 2: Convert 49/2 to an equivalent fraction with a denominator of 84.
    49/2 = (49 × 42)/(2 × 42) = 2058/84

    Step 3: Add the fractions 12/84 and 2058/84.
    12/84 + 2058/84 = 2070/84

    Step 4: Convert 2070/84 to a mixed fraction.
    2070 ÷ 84 = 24 remainder 54
    2070/84 = 24 54/84

    Step 5: Simplify the fraction 54/84 by dividing both the numerator and denominator by their greatest common factor, which is 6.
    54 ÷ 6 = 9
    84 ÷ 6 = 14

    Therefore, 54/84 = 9/14

    The sum of 12/84 and 49/2 as a mixed fraction is:
    24 9/14

    ### Answer: 24 9/14

Expected answer: 345/14

Correct? Yes

🔗 Problem

Problem: What is the result of adding two fractions, where each fraction is 78/65?

Gemma 2B:

    To add two fractions with the same denominator, we simply add the numerators and keep the denominator the same.

    Given fractions: 78/65 and 78/65

    Step 1: Add the numerators
    78 + 78 = 156

    Step 2: Keep the denominator the same
    The denominator remains 65

    Step 3: Simplify the resulting fraction, if possible
    156/65 cannot be simplified further as the numerator and denominator have no common factors other than 1.

    Therefore, the sum of the two fractions is 156/65.

    ### Answer: 156/65

Expected answer: 12/5

Correct? Yes

🔗 Follow-up

Problem: After obtaining the result from the previous problem, where you added two fractions both equal to 78/65, what would you get if you add the result to 71/32?

Gemma 2B:

    In the previous problem, we found that the sum of two fractions, each equal to 78/65, is 156/65.

    Now, we need to add 156/65 and 71/32.

    To add fractions with different denominators, we first need to find the least common denominator (LCD) and then convert the fractions to equivalent fractions with the LCD.

    Step 1: Find the LCD
    The LCD of 65 and 32 is 65 × 32 = 2080

    Step 2: Convert the fractions to equivalent fractions with the LCD
    156/65 = 156 × (32/32) = 4992/2080
    71/32 = 71 × (65/65) = 4615/2080

    Step 3: Add the numerators of the equivalent fractions
    4992/2080 + 4615/2080 = (4992 + 4615)/2080 = 9607/2080

    Step 4: Simplify the resulting fraction, if possible
    9607/2080 cannot be simplified further as the numerator and denominator have no common factors other than 1.

    Therefore, the sum of 156/65 and 71/32 is 9607/2080.

    ### Answer: 9607/2080

Expected answer: 739/160

Correct? Yes

🔗 Follow-up

Problem: Suppose that instead of having two fractions both equal to 78/65 like in the previous problem, they were both equal to 78/78. What would be the result of adding these two fractions together?

Gemma 2B:

    In this case, both fractions are equal to 78/78, which simplifies to 1.

    Given fractions: 78/78 and 78/78

    Step 1: Simplify each fraction
    78/78 = 1
    78/78 = 1

    Step 2: Add the simplified fractions
    1 + 1 = 2

    Therefore, the sum of the two fractions 78/78 and 78/78 is 2.

    ### Answer: 2

Expected answer: 2

Correct? Yes

🔗 Problem

Problem: Calculate the sum of 16/7 and 11/90. Answer as a simplified fraction.

Gemma 2B:

    To calculate the sum of 16/7 and 11/90, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 7 and 90.

    LCM(7, 90) = 630

    Now, we convert both fractions to equivalent fractions with the common denominator:

    16/7 = (16 × 90) / (7 × 90) = 1440/630
    11/90 = (11 × 7) / (90 × 7) = 77/630

    Add the numerators:

    1440/630 + 77/630 = 1517/630

    Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD):

    GCD(1517, 630) = 1

    Since the GCD is 1, the fraction 1517/630 is already in its simplest form.

    ### Answer: 1517/630

Expected answer: 1517/630

Correct? Yes

🔗 Follow-up

Problem: After finding the sum of 16/7 and 11/90, add your answer to 38/69. What is this new sum, expressed as a simplified fraction?

Gemma 2B:

    From the previous calculation, we found that the sum of 16/7 and 11/90 is 1517/630.

    Now, we need to add 1517/630 and 38/69.

    First, find the common denominator by calculating the LCM of 630 and 69.

    LCM(630, 69) = 43470

    Convert both fractions to equivalent fractions with the common denominator:

    1517/630 = (1517 × 69) / (630 × 69) = 104673/43470
    38/69 = (38 × 630) / (69 × 630) = 23940/43470

    Add the numerators:

    104673/43470 + 23940/43470 = 128613/43470

    Simplify the fraction by dividing the numerator and denominator by their GCD:

    GCD(128613, 43470) = 3

    128613/43470 ÷ 3/3 = 42871/14490

    ### Answer: 42871/14490

Expected answer: 42871/14490

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, you calculated the sum of 16/7 and 11/90. Now, let's consider if there were actually 99 parts out of 90 (as strange as that might sound) instead of 11 parts out of 90. What would be the sum of 16/7 and 99/90, expressed as a simplified fraction?

Gemma 2B:

    Interesting question! Let's solve this problem step by step.

    Given:
    - First fraction: 16/7
    - Second fraction: 99/90

    Step 1: Find the common denominator by calculating the LCM of 7 and 90.
    LCM(7, 90) = 630

    Step 2: Convert both fractions to equivalent fractions with the common denominator.
    16/7 = (16 × 90) / (7 × 90) = 1440/630
    99/90 = (99 × 7) / (90 × 7) = 693/630

    Step 3: Add the numerators of the equivalent fractions.
    1440/630 + 693/630 = 2133/630

    Step 4: Simplify the resulting fraction by dividing the numerator and denominator by their GCD.
    Numerator: 2133
    Denominator: 630
    GCD(2133, 630) = 3

    Simplified fraction: (2133 ÷ 3) / (630 ÷ 3) = 711/210

    ### Answer: 711/210

Expected answer: 237/70

Correct? Yes