Common Core Standard 5.NF.B.4
This standard covers the following:
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
Problem: Determine the product when you multiply the fraction 8/9 by the fraction 19/3. Please provide your answer as a simplified fraction.
Llama 3 8B:
To multiply the fractions, we multiply the numerators (8 and 19) and multiply the denominators (9 and 3), then simplify the resulting fraction. (8/9) ร (19/3) = (8 ร 19) / (9 ร 3) = 152/27 To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1. The simplified fraction is: 152/27 ### Answer: 152/27
Expected answer: 152/27
Correct? Yes
Problem: After determining the product when multiplying the fraction 8/9 by the fraction 19/3, take your result and then multiply it by 2. What does this new calculation result in when written as a simplified fraction?
Llama 3 8B:
We previously found that the product of multiplying the fractions 8/9 and 19/3 is: 152/27 To multiply this result by 2, we multiply the numerator and the denominator by 2: (152/27) ร 2 = (152 ร 2) / (27 ร 2) = 304/54 To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2. The simplified fraction is: 152/27 ### Answer: 304/54
Expected answer: 304/27
Correct? No
Problem: Imagine you made an error in the original multiplication calculation where you incorrectly used 8/9 instead of the correct fraction 8/15. Can you correct this mistake and find the new product if you multiply 8/15 by 19/3? Please provide your answer as a simplified fraction.
Llama 3 8B:
Let's redo the multiplication with the correct fraction 8/15. (8/15) ร (19/3) = (8 ร 19) / (15 ร 3) = 152/45 To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1. The simplified fraction is: 152/45 ### Answer: 152/45
Expected answer: 152/45
Correct? Yes
Problem: Julian is cutting sections of rope for a project. Each section is 13/2 feet long. He is only able to use 5/7 of each section. How many feet are in the usable part of each section of rope? Calculate this by multiplying 13/2 by 5/7.
Llama 3 8B:
Reasoning: To find the usable part of each section, we need to multiply the length of each section (13/2) by the fraction of the section that is usable (5/7). First, we can simplify the fraction 5/7 by dividing both the numerator and the denominator by their greatest common divisor, which is 1. This leaves us with the same fraction. Next, we can multiply the two fractions: (13/2) ร (5/7) = (13 ร 5) / (2 ร 7) = 65/14 To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1. This leaves us with the same fraction. Therefore, the usable part of each section of rope is 65/14 feet. ### Answer: 65/14
Expected answer: 65/14
Correct? Yes
Problem: Suppose Julian is considering replacing the rope sections with new ones. Each new section is 17/2 feet long and he is still able to use only 5/7 of each section. How many feet are in the usable part of each new section of rope? Calculate this by multiplying 17/2 by 5/7.
Llama 3 8B:
Reasoning: To find the usable part of each new section, we need to multiply the length of each new section (17/2) by the fraction of the section that is usable (5/7). First, we can simplify the fraction 5/7 by dividing both the numerator and the denominator by their greatest common divisor, which is 1. This leaves us with the same fraction. Next, we can multiply the two fractions: (17/2) ร (5/7) = (17 ร 5) / (2 ร 7) = 85/14 To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1. This leaves us with the same fraction. Therefore, the usable part of each new section of rope is 85/14 feet. ### Answer: 85/14
Expected answer: 85/14
Correct? Yes
Problem: What is the result when you multiply the whole number 12 by 1?
Llama 3 8B:
When you multiply the whole number 12 by 1, you are essentially multiplying it by its own identity. In other words, 12 multiplied by 1 is equal to 12 itself. ### Answer: 12
Expected answer: 12
Correct? Yes
Problem: If you take the product of 12 and 1, and then multiply that result by the fraction 7/16, what would be the final result? Write your answer as a simplified fraction or a whole number, if possible.
Llama 3 8B:
First, we multiply 12 by 1, which gives us 12. Then, we multiply 12 by the fraction 7/16. To do this, we multiply the numerator (7) by 12 and the denominator (16) by 1, and then simplify: (7 ร 12) / (16 ร 1) = 84 / 16 We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4: 84 รท 4 = 21 16 รท 4 = 4 So, the simplified result is: 21 / 4 ### Answer: 21/4
Expected answer: 21/4
Correct? Yes
Problem: Previously, you found the result of multiplying 12 by 1. Now, let's change the scenario and replace the 12 with 11. What would be the result when you multiply the whole number 11 by 1?
Llama 3 8B:
When you multiply the whole number 11 by 1, you are essentially multiplying it by its own identity. In other words, 11 multiplied by 1 is equal to 11 itself. ### Answer: 11
Expected answer: 11
Correct? Yes
Problem: Find the answer of the given math problem: 14 / 15 * 12 / 4, performing the multiplication operation on fractions and whole numbers. Provide your answer as a simplified fraction or, if possible, as a whole number.
Llama 3 8B:
To evaluate the expression 14 / 15 * 12 / 4, we need to follow the order of operations (PEMDAS): 1. Divide 14 by 15: 14 / 15 = 0.9333... 2. Multiply the result by 12: 0.9333... * 12 = 11.2 3. Divide the result by 4: 11.2 / 4 = 2.8 So, the final answer is: ### Answer: 2 2/3
Expected answer: 14/5
Correct? No
Problem: Compute the value for the following expression: 15 * (5 / 17). Write your answer as a decimal rounded to the nearest hundredth.
Llama 3 8B:
Reasoning: To evaluate the expression, we need to follow the order of operations (PEMDAS). First, we divide 5 by 17, which gives us 5/17 = 0.2941176470588235 (rounded to 12 decimal places). Then, we multiply 15 by this result, which gives us 15 * 0.2941176470588235 = 4.43 (rounded to the nearest hundredth). ### Answer: 4.43
Expected answer: 75/17
Correct? No
Problem: Find the result of the following calculation: 16 * (12 / 19)
Llama 3 8B:
Reasoning: To evaluate this expression, we need to follow the order of operations (PEMDAS): 1. Divide 12 by 19: 12 / 19 = 0.632 2. Multiply 16 by the result: 16 * 0.632 = 10.112 ### Answer: 10.112
Expected answer: 192/19
Correct? No
Problem: If a farmer has 10/17 of a barrel of apples and he decides to multiply that amount by 18/5 barrels, how many barrels of apples will he have in total? Calculate your answer keeping it as a simplified fraction.
Llama 3 8B:
Reasoning: The farmer has 10/17 of a barrel of apples initially. He decides to multiply that amount by 18/5 barrels. To multiply fractions, we multiply the numerators and multiply the denominators: (10/17) ร (18/5) = (10 ร 18) / (17 ร 5) = 180/85 So, the farmer will have 180/85 barrels of apples in total. ### Answer: 180/85
Expected answer: 36/17
Correct? Yes
Problem: Given the farmer's new total of apples from the previous question, he decides to increase his total number of barrels by a factor of 7. Calculate the new total number of barrels of apples the farmer will have. Represent your answer as a simplified fraction where appropriate.
Llama 3 8B:
Reasoning: The farmer already has 180/85 barrels of apples. He decides to increase his total number of barrels by a factor of 7. To multiply the fraction by 7, we multiply the numerator by 7: (180/85) ร 7 = (180 ร 7) / (85) = 1260/85 So, the farmer will have 1260/85 barrels of apples in total. ### Answer: 1260/85
Expected answer: 252/17
Correct? Yes
Problem: Suppose the farmer initially started with 10/17 of a barrel of apples but this time he decided to increase that amount by multiplying it with 19/5 barrels instead of 18/5. Calculate how many barrels of apples will he have now. Represent your answer as a simplified fraction.
Llama 3 8B:
Reasoning: The farmer has 10/17 of a barrel of apples initially. He decides to multiply that amount by 19/5 barrels. To multiply fractions, we multiply the numerators and multiply the denominators: (10/17) ร (19/5) = (10 ร 19) / (17 ร 5) = 190/85 So, the farmer will have 190/85 barrels of apples in total. ### Answer: 190/85
Expected answer: 38/17
Correct? Yes
Problem: Simplify the expression: (20 / 4) * (1 / 5). What is the result?
Llama 3 8B:
Reasoning: To simplify the expression, we need to follow the order of operations (PEMDAS): 1. Evaluate the expressions inside the parentheses: * 20 / 4 = 5 * 1 / 5 = 0.2 2. Multiply the results: * 5 * 0.2 = 1 So, the simplified expression is 1. ### Answer: 1
Expected answer: 1
Correct? Yes
Problem: After you have found the result of (20 / 4) * (1 / 5), multiply it by (16 / 3). What is the final result?
Llama 3 8B:
Reasoning: We already found that (20 / 4) * (1 / 5) = 1. Now, we need to multiply 1 by (16 / 3): 1 * (16 / 3) = 1 * 5.33 (approximately) So, the final result is approximately 5.33. ### Answer: 5.33
Expected answer: 16/3
Correct? No
Problem: Julia has 11 boxes and she decides to fill 8/11 of each box with apples. If each box can hold up to 1 bushel of apples, how many bushels of apples did she use in total?
Llama 3 8B:
Reasoning: Julia has 11 boxes and fills 8/11 of each box with apples. So, she fills 8/11 * 11 = 8 boxes with apples. Each box can hold up to 1 bushel of apples, so Julia uses 8 bushels of apples in total. ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: In the continuation of the previous situation, Julia decided to sell 7/14, or half, of all the bushels of apples she had. How many bushels of apples did Julia sell?
Llama 3 8B:
Reasoning: Julia had 8 bushels of apples initially. She sells 7/14 of all the bushels, which is half of 8, which is 4 bushels. ### Answer: 4
Expected answer: 4
Correct? Yes
Problem: In continuation to the previous scenario, suppose Julia initially had 6 boxes instead of 11. How many bushels of apples would she have if she still fills 8/11 of each box with apples?
Llama 3 8B:
Reasoning: Julia has 6 boxes and fills 8/11 of each box with apples. So, she fills 8/11 * 6 = 48/11 of the total capacity of the boxes with apples. Since each box can hold up to 1 bushel of apples, Julia uses 48/11 bushels of apples in total. ### Answer: 48/11
Expected answer: 48/11
Correct? Yes
Problem: In a bakery, a baker uses 9/4 cups of sugar for a cake and 16/15 cups for a batch of cookies. If he needs the equal amount of sugar for the cake and the cookies, how much sugar in cups will he use in total? Calculate it by multiplying the two fractions.
Llama 3 8B:
Reasoning: To find the total amount of sugar used, we need to find the least common multiple (LCM) of the denominators, which is 60. Then, we can convert both fractions to have a denominator of 60: 9/4 = 45/60 16/15 = 64/60 Now, we can multiply the numerators: 45 ร 64 = 2880 And keep the denominator: 2880/60 = 48 ### Answer: 48
Expected answer: 12/5
Correct? No
Problem: If Peter was making home-made pizza and he needed 19/9 cups of flour and 14/18 cups of sugar for his pizza dough, how many cups of ingredients in total did he need? Multiply the amounts of flour and sugar together to find the total.
Llama 3 8B:
Reasoning: To find the total amount of ingredients, we need to multiply the amounts of flour and sugar together. First, we need to simplify the fractions: 19/9 = 2 2/9 14/18 = 7/9 Now, we can multiply the simplified fractions: 2 2/9 ร 7/9 = 14/9 So, Peter needed 14/9 cups of ingredients in total. ### Answer: 14/9
Expected answer: 133/81
Correct? No
Problem: What is the result when you multiply the fractions 14/7 and 16/4?
Llama 3 8B:
Reasoning: To multiply fractions, we multiply the numerators (14 and 16) and multiply the denominators (7 and 4), then simplify the result. 14/7 ร 16/4 = (14 ร 16) / (7 ร 4) = 224 / 28 We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4. 224 รท 4 = 56 28 รท 4 = 7 So, the simplified result is: 56/7 ### Answer: 56/7
Expected answer: 8
Correct? Yes
Problem: Continuing from our previous problem, instead of multiplying 14/7 and 16/4, let's consider we have 14/7 and 13/4. What is the result when you multiply these two fractions?
Llama 3 8B:
Reasoning: To multiply fractions, we multiply the numerators (14 and 13) and multiply the denominators (7 and 4), then simplify the result. 14/7 ร 13/4 = (14 ร 13) / (7 ร 4) = 182 / 28 We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2. 182 รท 2 = 91 28 รท 2 = 14 So, the simplified result is: 91/14 ### Answer: 91/14
Expected answer: 13/2
Correct? Yes
Problem: Calculate the result of (17 / 18) multiplied by (13 / 8). Write the answer as a simplified fraction.
Llama 3 8B:
To calculate the result, we need to follow the order of operations (PEMDAS): 1. Divide 17 by 18: 17 รท 18 = 0.94 (approximately) 2. Divide 13 by 8: 13 รท 8 = 1.625 (approximately) 3. Multiply the results: 0.94 ร 1.625 = 1.5275 (approximately) To simplify the fraction, we can find the greatest common divisor (GCD) of the numerator and denominator: 1. Find the GCD of 1.5275 and 1: The GCD is 1, since 1 is the only number that divides both 1.5275 and 1. 2. Write the simplified fraction: 1.5275 = 1 527/1000 = 153/100 = 0.153 So, the result of (17 / 18) multiplied by (13 / 8) is: ### Answer: 153/1000
Expected answer: 221/144
Correct? No
Problem: Evaluate the following expression: ((15 / 15) * 18) and write your answer.
Llama 3 8B:
Reasoning: First, we evaluate the expression inside the parentheses. 15 divided by 15 is 1, so ((15 / 15) = 1). Then, we multiply 1 by 18, which gives us 18. ### Answer: 18
Expected answer: 18
Correct? Yes
Problem: For this next question, let's slightly adjust our variables. Instead of doing (15 / 15) * 18 as in the previous problem, let's try (15 / 16) * 18. What's the result of this multiplication?
Llama 3 8B:
Reasoning: First, we evaluate the expression inside the parentheses. 15 divided by 16 is 0.9375 (or 15/16). Then, we multiply 0.9375 by 18, which gives us approximately 16.875. ### Answer: 16.875
Expected answer: 135/8
Correct? Yes
Problem: A group of 18 students is planning a pizza party. If each student will eat 17/20 of a pizza, how many pizzas should they order?
Llama 3 8B:
Reasoning: The total number of pizzas needed is the total number of slices eaten divided by the number of slices per pizza. Since each student eats 17/20 of a pizza, the total number of slices eaten is 18 students * 17/20 pizzas/student = 153/20 slices. Since each pizza has 20 slices, the total number of pizzas needed is 153/20 slices / 20 slices/pizza = 153/20/20 = 153/40 = 153/4*10/10 = 38.5. Since you can't order a fraction of a pizza, the group should order 39 pizzas. ### Answer: 39
Expected answer: 153/10
Correct? No
Problem: Sophie picked 9 pounds of apples. She decided to make apple pies for a community gathering, and each pie requires about 1/14 of the total apples she picked. Sophie made 7 pies. How many pounds of apples did she use in total? Calculate it using the multiplication of fraction and a whole number, specifically ((9 / 14) * 7). Write your answer as a simplified fraction or a whole number.
Llama 3 8B:
Reasoning: Sophie used (9/14) * 7 = <<(9/14) * 7=(9*7)/(14)=63/14>>63/14 pounds of apples in total. ### Answer: 63/14
Expected answer: 9/2
Correct? Yes
Problem: Sophie initially thought she had 9 pounds of apples, but upon rechecking, she found she actually had 18 pounds. Sophie still decided to make pies for the community gathering, with each pie requiring 1/14 of the total amount of apples. If Sophie still made 7 pies just like before, calculate how many pounds of apples she used this time. Solve the problem using the multiplication of the fraction and the whole number ((18 / 14) * 7). Write your answer as a simplified fraction or a whole number.
Llama 3 8B:
Reasoning: Sophie used (18/14) * 7 = <<(18*7)/(14)=126/14=9>>9 pounds of apples in total. ### Answer: 9
Expected answer: 9
Correct? Yes
Problem: John bought 2 boxes of cookies with 6/8 of a dozen cookies in each box. How many dozens of cookies did John buy in total?
Llama 3 8B:
Reasoning: Each box has 6/8 of a dozen cookies, which is equal to 6/8 * 12 = 9 cookies. John bought 2 boxes, so he bought 9 * 2 = 18 cookies. Since there are 12 cookies in a dozen, we can divide 18 by 12 to find the number of dozens: 18/12 = 1.5 dozens. ### Answer: 1.5 dozens
Expected answer: 3/2
Correct? No
Problem: Tom has a box that could potentially hold 6 gallons of paint. However, due to the design of the box, it can only be filled up to 16/17 of its capacity. How many gallons of paint can Tom actually store in the box?
Llama 3 8B:
Reasoning: The box can hold 6 gallons of paint, but it can only be filled up to 16/17 of its capacity. To find the actual capacity, we need to multiply the total capacity by the fraction of capacity that can be filled. 6 gallons x (16/17) = 6 x 16/17 = 96/17 = 5.71 gallons So, Tom can actually store approximately 5.71 gallons of paint in the box. ### Answer: 5.71
Expected answer: 96/17
Correct? No
Problem: If Mary has 14 marbles and she gives away 4/10 of them, how many marbles does Mary give away?
Llama 3 8B:
Reasoning: Mary has 14 marbles and gives away 4/10 of them. To find the number of marbles she gives away, we can multiply the total number of marbles by the fraction 4/10. 14 x (4/10) = 14 x 0.4 = 5.6 Since you can't give away a fraction of a marble, we round down to the nearest whole number. Therefore, Mary gives away 5 marbles. ### Answer: 5
Expected answer: 28/5
Correct? No
Problem: Calculate the product of 19/6 and 4/4. Write the resulting answer as a simplified fraction.
Llama 3 8B:
To calculate the product, we multiply the numerators and denominators separately: (19/6) ร (4/4) = (19 ร 4) / (6 ร 4) = 76 / 24 To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 4: 76 รท 4 = 19 24 รท 4 = 6 So, the simplified fraction is: 19/6 ### Answer: 19/6
Expected answer: 19/6
Correct? Yes
Problem: Use the answer you obtained from the previous word problem as a fraction, multiply it by itself, and write the resulting answer as a simplified fraction.
Llama 3 8B:
We obtained the fraction 19/6 in the previous problem. To multiply it by itself, we square it: (19/6) ร (19/6) = (19 ร 19) / (6 ร 6) = 361 / 36 To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1: 361 รท 1 = 361 36 รท 1 = 36 So, the simplified fraction is: 361/36 ### Answer: 361/36
Expected answer: 361/36
Correct? Yes
Problem: In the previous word problem, use 19/6 and 9/4 instead of 19/6 and 4/4. Multiply these two fractions and write the resulting answer as a simplified fraction.
Llama 3 8B:
To calculate the product, we multiply the numerators and denominators separately: (19/6) ร (9/4) = (19 ร 9) / (6 ร 4) = 171 / 24 To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 3: 171 รท 3 = 57 24 รท 3 = 8 So, the simplified fraction is: 57/8 ### Answer: 57/8
Expected answer: 57/8
Correct? Yes
Problem: What is the result when you divide 16 by 8 and then multiply the result by 10?
Llama 3 8B:
Reasoning: First, we divide 16 by 8, which gives us 16/8 = 2. Then, we multiply the result by 10, which gives us 2 ร 10 = 20. ### Answer: 20
Expected answer: 20
Correct? Yes
Problem: Using the result you obtained from the previous question, what is the outcome when you multiply it by 1/17?
Llama 3 8B:
Reasoning: We previously obtained the result 20. To multiply 20 by 1/17, we can multiply 20 by the reciprocal of 17, which is 1/17 = 1 รท 17 = 0.0588... (approximately). 20 ร 0.0588... = 1.176 (approximately). ### Answer: 1.176 (approximately)
Expected answer: 20/17
Correct? No
Problem: What would the result have been in the original problem if you had divided 16 by 10 instead of 8 before multiplying by 10?
Llama 3 8B:
Reasoning: If we divide 16 by 10 instead of 8, we get 16/10 = 1.6. Then, we multiply the result by 10, which gives us 1.6 ร 10 = 16. ### Answer: 16
Expected answer: 16
Correct? Yes
Problem: What is the product when 18 is multiplied by 1/11? Please provide your answer as a decimal or a simplified fraction.
Llama 3 8B:
Reasoning: To find the product, we can multiply 18 by 1/11. 18 ร 1/11 = 18/11 = <<18/11=1.6363636363636...>>1.6363636363636... Since the decimal expansion is repeating, we can simplify the fraction to 1 5/11. ### Answer: 1 5/11
Expected answer: 18/11
Correct? No
Problem: Mary has a garden with apple trees. Each tree produces 3 bushels of apples, and she has 6 trees in total. However, due to pests, only half of her trees produce apples this year. How many bushels of apples does Mary harvest from her garden this year?
Llama 3 8B:
Reasoning: Since only half of her trees produce apples, only 6/2 = 3 trees produce apples this year. Each tree produces 3 bushels of apples, so 3 trees produce 3 x 3 = 9 bushels of apples. ### Answer: 9
Expected answer: 9
Correct? Yes
Problem: Calculate the result of the following problem: (13 / 10) * (14 / 11). Please write your answer as a simplified fraction.
Llama 3 8B:
Reasoning: To evaluate the expression, we need to follow the order of operations (PEMDAS): 1. Divide 13 by 10: 13/10 = 1.3 2. Divide 14 by 11: 14/11 = 1.272727... 3. Multiply the two results: 1.3 * 1.272727... = 1.6569... Since we want to simplify the result as a fraction, we can write: 1.6569... = 165/99 ### Answer: 165/99
Expected answer: 91/55
Correct? No
Problem: James bought 20 very thin fabrics. Each piece of fabric has 2/19 meters of thread. How many meters of thread are there in total in 20 pieces of fabric? Calculate it by multiplying 2/19 by 20.
Llama 3 8B:
Reasoning: To find the total number of meters of thread, we need to multiply the number of meters of thread per piece of fabric by the number of pieces of fabric. The number of meters of thread per piece of fabric is 2/19, and we have 20 pieces of fabric. To multiply a fraction by a whole number, we multiply the numerator by the whole number and keep the denominator the same: (2/19) ร 20 = (2 ร 20) / 19 = 40/19 So, there are 40/19 meters of thread in total. ### Answer: 40/19
Expected answer: 40/19
Correct? Yes
Problem: What is the result of 1 times 16?
Llama 3 8B:
Reasoning: When we multiply 1 by 16, we are essentially just multiplying 1 by the number 16, which is equal to 16. ### Answer: 16
Expected answer: 16
Correct? Yes
Problem: Taking the result you found from multiplying 1 times 16, what do you get if you then multiply that result by 2/11?
Llama 3 8B:
Reasoning: We previously found that 1 times 16 is equal to 16. Now, we need to multiply 16 by 2/11. To do this, we can multiply 16 by 2, which gives us 32, and then divide the result by 11. So, 16 times 2/11 is equal to 32 divided by 11. 32 divided by 11 is equal to 2 with a remainder of 10. So, the result of multiplying 16 by 2/11 is 2 with a remainder of 10. ### Answer: 2 with a remainder of 10
Expected answer: 32/11
Correct? No
Problem: If instead of 16, you were to multiply 1 by 11. What would the result be?
Llama 3 8B:
Reasoning: When we multiply 1 by 11, we are essentially just multiplying 1 by the number 11, which is equal to 11. ### Answer: 11
Expected answer: 11
Correct? Yes
Problem: Calculate the result of the following math problem: (18 / 12) * 6. Write your answer as a simplified fraction or a whole number.
Llama 3 8B:
To evaluate this expression, we need to follow the order of operations (PEMDAS): 1. Divide 18 by 12: 18 รท 12 = 1.5 2. Multiply 1.5 by 6: 1.5 ร 6 = 9 So, the result of the expression is 9. ### Answer: 9
Expected answer: 9
Correct? Yes
Problem: After calculating the result of the first problem as e = (18 / 12) * 6, perform an additional calculation. Multiply the result e by 9/15. Write the result as a simplified fraction or a whole number.
Llama 3 8B:
We already calculated the result of the expression e = (18 / 12) * 6 as 9. Now, we need to multiply e by 9/15: 9 ร (9/15) = 9 ร 3/5 = 27/5 To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1. Therefore, the result remains the same: 27/5 ### Answer: 27/5
Expected answer: 27/5
Correct? Yes
Problem: After completing the first calculation, let's modify it a bit. Originally we had (18 / 12) * 6. Now let's change the dividend to 10, keeping the divisor and the multiplier the same. So we have (10 / 12) * 6. Calculate the result and write your answer as a simplified fraction or a whole number.
Llama 3 8B:
Let's evaluate the modified expression: 1. Divide 10 by 12: 10 รท 12 = 5/6 2. Multiply 5/6 by 6: (5/6) ร 6 = 5 So, the result of the expression is 5. ### Answer: 5
Expected answer: 5
Correct? Yes
Problem: Here's a math problem about multiplying fractions and whole numbers: Johnny has 8 friends. He promised to give each of his friends 13/8 pounds of candy. How many pounds of candy will Johnny need in total?
Llama 3 8B:
Reasoning: To find the total amount of candy Johnny needs, we need to multiply the number of friends (8) by the amount of candy each friend will receive (13/8). First, we can convert the mixed number 13/8 to an improper fraction: 13/8 = 1 1/8 = 1 1/2 = 3/2. Now, we can multiply the number of friends (8) by the amount of candy each friend will receive (3/2): 8 ร 3/2 = 12 So, Johnny will need 12 pounds of candy in total. ### Answer: 12
Expected answer: 13
Correct? No
Problem: Mathew was cutting up some square blocks for a craft project. Each block was 16/18th of a foot long. Mathew needed 16/7th of a foot long blocks for his project. If he uses all the blocks, how long in feet would the blocks be in total? Solve this by using multiplication of fractions.
Llama 3 8B:
Reasoning: To find the total length of the blocks, we need to multiply the length of each block by the number of blocks. Since each block is 16/18th of a foot long, we can multiply the number of blocks needed (16/7) by the length of each block (16/18): (16/7) ร (16/18) = (16 ร 16) / (7 ร 18) = 256/126 To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2: 256 รท 2 = 128 126 รท 2 = 63 So, the total length of the blocks would be: 128/63 ### Answer: 128/63
Expected answer: 128/63
Correct? Yes
Problem: In light of the previous scenario, suppose Mathew decides to modify the length of the blocks he is using. Instead of each block being 16/18th of a foot long, he thinks having each block as 18/18th (a full foot) long would make his craft project more appealing. If he still needs 16/7th of a foot long blocks for his project, how long in feet would the blocks be in total this time?
Llama 3 8B:
Reasoning: Since each block is now 18/18th of a foot long (which is equivalent to 1 foot), we can multiply the number of blocks needed (16/7) by the length of each block (1): (16/7) ร 1 = 16/7 Since the length of each block is now 1 foot, the total length of the blocks would be: 16/7 ### Answer: 16/7
Expected answer: 16/7
Correct? Yes
Problem: What is the result when you multiply the fraction 8/8 by 15?
Llama 3 8B:
Reasoning: When multiplying a fraction by a whole number, we multiply the numerator by the whole number. So, we multiply 8 by 15 to get 120, and keep the denominator as 8. The result is 120/8. ### Answer: 120/8
Expected answer: 15
Correct? Yes
Problem: After you've calculated the result of 8/8 multiplied by 15, what do you get if you further multiple that result by 19/18?
Llama 3 8B:
Reasoning: We already calculated the result of 8/8 multiplied by 15 to be 120/8. Now, we need to multiply this result by 19/18. To do this, we multiply the numerators (120 and 19) to get 2280, and multiply the denominators (8 and 18) to get 144. The result is 2280/144. ### Answer: 2280/144
Expected answer: 95/6
Correct? Yes
Problem: Suppose instead of having a fraction of 8/8 in the previous question, there was a fraction of 8/7. What would be the result when that fraction is multiplied by 15?
Llama 3 8B:
Reasoning: When multiplying a fraction by a whole number, we multiply the numerator by the whole number. So, we multiply 8 by 15 to get 120, and keep the denominator as 7. The result is 120/7. ### Answer: 120/7
Expected answer: 120/7
Correct? Yes
Problem: A recipe for apple pie requires 10 apples. However, you only have two thirds of the amount needed. How many apples do you have if you multiply 10 apples by 4/6?
Llama 3 8B:
Reasoning: To find the number of apples needed, we multiply 10 apples by 4/6. This is equivalent to multiplying 10 apples by 2/3, since 4/6 is the same as 2/3. 10 apples * 2/3 = 10 apples * 0.67 = 6.7 apples Since you only have two thirds of the amount needed, you have 6.7 apples. ### Answer: 6.7
Expected answer: 20/3
Correct? No
Problem: What is the product when you multiply the fraction 18/12 by the whole number 11?
Llama 3 8B:
Reasoning: To multiply a fraction by a whole number, we multiply the numerator of the fraction by the whole number. So, we multiply 18 by 11 to get 198. Then, we multiply the denominator of the fraction by the whole number. So, we multiply 12 by 11 to get 132. The product of the fraction 18/12 and the whole number 11 is 198/132. ### Answer: 198/132
Expected answer: 33/2
Correct? No
Problem: In a pizza shop, the mushroom pizza, which is very popular, usually sells out in just 9/20 of an hour. The pizza chef can make 16 pizzas in just one hour. How many mushroom pizzas can the chef make before they sell out?
Llama 3 8B:
Reasoning: The mushroom pizza sells out in 9/20 of an hour, which is equivalent to 9/20 * 16 = 7.2 pizzas. The chef can make 16 pizzas in one hour, so the chef can make 16 pizzas before the mushroom pizzas sell out. ### Answer: 7
Expected answer: 36/5
Correct? No
Problem: A baker wants to bake enough cakes for a large party. Each cake requires 5/12 of a kilogram of flour. If the baker needs to bake 16 cakes, how many kilograms of flour will he need? Use the formula s = (16 * (5 / 12)) to calculate the answer.
Llama 3 8B:
Reasoning: The formula s = (16 * (5 / 12)) represents the total amount of flour needed, where s is the total amount of flour and 16 is the number of cakes, 5/12 is the amount of flour needed for each cake. To evaluate the expression, we can follow the order of operations (PEMDAS): 1. Divide 5 by 12: 5/12 = 0.4166666666666667 2. Multiply 16 by the result: 16 * 0.4166666666666667 = 6.666666666666667 So, the baker will need approximately 6.67 kilograms of flour. ### Answer: 6.67
Expected answer: 20/3
Correct? No
Problem: Determine the result of the following calculation: multiply 13 by 3/12. Remember to write your answer as a fraction or a decimal number.
Llama 3 8B:
To evaluate this expression, we need to follow the order of operations (PEMDAS): 1. Divide 3 by 12: 3/12 = 1/4 2. Multiply 13 by 1/4: 13 ร 1/4 = 13/4 So, the result of the calculation is: 13 ร 3/12 = 13/4 ### Answer: 13/4
Expected answer: 13/4
Correct? Yes
Problem: After calculating the result from the previous problem, take your answer and square it (multiply it by itself). Write your final answer as a fraction, decimal, or a whole number if possible.
Llama 3 8B:
To square the result, we need to multiply 13/4 by itself: (13/4) ร (13/4) = (13 ร 13) / (4 ร 4) = 169/16 So, the result of squaring the previous answer is: 169/16 ### Answer: 169/16
Expected answer: 169/16
Correct? Yes
Problem: After previously calculating 13 multiplied by 3/12, now consider if instead we actually needed to multiply 13 by 3/15 instead of 3/12. What would be the result of this new calculation? Remember to write your answer as a fraction, decimal, or a whole number if possible.
Llama 3 8B:
Let's evaluate the new expression: 1. Divide 3 by 15: 3/15 = 1/5 2. Multiply 13 by 1/5: 13 ร 1/5 = 13/5 So, the result of the new calculation is: 13 ร 3/15 = 13/5 ### Answer: 13/5
Expected answer: 13/5
Correct? Yes
Problem: Find the product when 8 is multiplied by 1. Show your work and provide your answer.
Llama 3 8B:
Reasoning: To find the product of 8 multiplied by 1, I will simply multiply the two numbers together. 8 ร 1 = ? 8 ร 1 = 8 ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: After finding the product when 8 is multiplied by 1, take that result and multiply it by 2. What is the final result? Show your work process.
Llama 3 8B:
Reasoning: We previously found that 8 multiplied by 1 is equal to 8. Now, we will multiply this result by 2. 8 ร 1 = 8 (from previous calculation) 8 ร 2 = ? 8 ร 2 = 16 ### Answer: 16
Expected answer: 16
Correct? Yes
Problem: In the same situation as the previous question, consider that originally there were 16 units instead of 8. Multiply the 16 units by 1. What will the new result be? Show your calculations and the final figure.
Llama 3 8B:
Reasoning: To find the product of 16 multiplied by 1, I will simply multiply the two numbers together. 16 ร 1 = ? 16 ร 1 = 16 ### Answer: 16
Expected answer: 16
Correct? Yes
Problem: What is the result when you multiply 9 by the fraction 9/17?
Llama 3 8B:
Reasoning: To multiply a whole number by a fraction, we multiply the whole number by the numerator (9) and then divide by the denominator (17). 9 ร 9 = 81 81 รท 17 = 4.76 ### Answer: 4.76
Expected answer: 81/17
Correct? No
Problem: Tom is planning to share his 13 boxes with his friends. He has decided each of them will get 12/13 of a box. How many boxes, in total, will Tom's friends receive?
Llama 3 8B:
Reasoning: Tom has 13 boxes and each of his friends will get 12/13 of a box. To find the total number of boxes his friends will receive, we can multiply the number of friends by the amount each friend will get: Number of friends = unknown (let's call it x) Amount each friend will get = 12/13 of a box Total boxes his friends will receive = x ร (12/13) Since Tom has 48 friends, we can substitute x = 48: Total boxes his friends will receive = 48 ร (12/13) To simplify the fraction, we can multiply both the numerator and the denominator by 13: Total boxes his friends will receive = 48 ร (12 ร 13)/(13 ร 13) = 48 ร 12/13 = 576/13 = 44 + 8/13 So, Tom's friends will receive 44 whole boxes and 8/13 of a box. ### Answer: 44 8/13
Expected answer: 12
Correct? No
Problem: What is the product of multiplying 16 and 1?
Llama 3 8B:
Reasoning: To find the product of multiplying 16 and 1, we simply multiply the two numbers together. 16 ร 1 = 16 ### Answer: 16
Expected answer: 16
Correct? Yes
Problem: After finding the product of 16 and 1, what is the result when this product is multiplied by 3/8? Write your answer as a simplified fraction.
Llama 3 8B:
Reasoning: We already found the product of 16 and 1 to be 16. Now, we need to multiply this product by 3/8. 16 ร 3/8 = (16 ร 3) / 8 = 48 / 8 = 6 ### Answer: 6/1 = 6
Expected answer: 6
Correct? Yes
Problem: After finding the product of 16 and 1 and multiplying it by 3/8, consider a similar action with different numbers. What is the product of 15 and 1?
Llama 3 8B:
Reasoning: To find the product of multiplying 15 and 1, we simply multiply the two numbers together. 15 ร 1 = 15 ### Answer: 15
Expected answer: 15
Correct? Yes
Problem: Multiply 10 by the fraction 11/10. What is the result?
Llama 3 8B:
Reasoning: To multiply a number by a fraction, we multiply the number by the numerator (11) and then divide by the denominator (10). 10 ร 11 = 110 Then, we divide 110 by 10: 110 รท 10 = 11 So, the result of multiplying 10 by the fraction 11/10 is 11. ### Answer: 11
Expected answer: 11
Correct? Yes
Problem: After finding the result of 10 * 11/10, now multiply this result by 2/19. What is the final result when you write it as a simplified fraction?
Llama 3 8B:
Reasoning: We already found the result of multiplying 10 by the fraction 11/10, which is 11. Now, we need to multiply 11 by the fraction 2/19. 11 ร 2 = 22 Then, we multiply 22 by the denominator 19: 22 ร 19 = 418 Now, we divide 418 by the numerator 2: 418 รท 2 = 209 So, the result of multiplying 11 by the fraction 2/19 is 209. To write this as a simplified fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1. Therefore, the simplified fraction is: 209/1 ### Answer: 209/1
Expected answer: 22/19
Correct? No
Problem: Now instead of 10 * 11/10, let's change the fraction to 11/17. Multiply 10 by 11/17. What is the new result?
Llama 3 8B:
Reasoning: To multiply a number by a fraction, we multiply the number by the numerator (11) and then divide by the denominator (17). 10 ร 11 = 110 Then, we divide 110 by 17: 110 รท 17 = 6.47 (approximately) So, the result of multiplying 10 by the fraction 11/17 is approximately 6.47. ### Answer: 6.47
Expected answer: 110/17
Correct? No
Problem: Calculate the product of 10 and the fraction 8/14. Write your answer as a simplified fraction or a decimal.
Llama 3 8B:
To calculate the product, we multiply 10 by the fraction 8/14: 10 ร (8/14) = (10 ร 8) / 14 = 80 / 14 To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 4: 80 รท 4 = 20 14 รท 4 = 3.5 So, the simplified fraction is: 20/3.5 Since 3.5 is an irrational number, we can convert it to a decimal: 20/3.5 โ 5.71 ### Answer: 5.71
Expected answer: 40/7
Correct? No
Problem: John has a pile of 20 assignment papers to grade. However, he has only managed to grade 8/18 of the pile. How many papers has John graded?
Llama 3 8B:
Reasoning: The fraction 8/18 represents the part of the pile that John has graded. To find the actual number of papers graded, we can multiply the fraction by the total number of papers, 20. 8/18 = 8 ร 20/18 = 8 ร 10/9 = 80/9 So, John has graded 80/9 papers. Since we can't grade a fraction of a paper, we can simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 8. 80/9 = 10 ### Answer: 10
Expected answer: 80/9
Correct? No
Problem: Calculate the result of multiplying 16 by the fraction 13/12.
Llama 3 8B:
To multiply 16 by the fraction 13/12, we need to multiply 16 by the numerator (13) and then divide the result by the denominator (12). 16 ร 13 = 208 Then, we divide 208 by 12: 208 รท 12 = 17.33 ### Answer: 17.33
Expected answer: 52/3
Correct? No
Problem: Maddison is dividing a piece of wood to build a bird house. The piece of wood is initially 16 units long. If she uses 2/19 of the piece of wood for each part of the bird house, how long is each part?
Llama 3 8B:
Reasoning: Since Maddison uses 2/19 of the piece of wood for each part, we need to find 2/19 of the initial length of the wood. To do this, we can multiply the initial length by the fraction: 16 ร (2/19) = 16 ร 2/19 = 32/19. To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2: 32 รท 2 = 16, 19 รท 2 = 9.5. So, each part is 16/9.5 units long. ### Answer: 16/9.5
Expected answer: 32/19
Correct? Yes
Problem: In the previous problem, Maddison was building a bird house using parts each measuring 2/19 of the original 16-unit long piece of wood. Now, imagine that she has decided to make a smaller model of the bird house, where each part is 2/14 of the original 16-unit long piece of wood. How long would each part of this smaller bird house be?
Llama 3 8B:
Reasoning: Since each part of the smaller bird house is 2/14 of the original 16-unit long piece of wood, we need to find 2/14 of the initial length of the wood. To do this, we can multiply the initial length by the fraction: 16 ร (2/14) = 16 ร 2/14 = 32/14. To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2: 32 รท 2 = 16, 14 รท 2 = 7. So, each part of the smaller bird house would be 16/7 units long. ### Answer: 16/7
Expected answer: 16/7
Correct? Yes
Problem: What is the result of multiplying the fraction twelve divided by twelve with the whole number sixteen?
Llama 3 8B:
Reasoning: The fraction twelve divided by twelve is equal to 1, since 12/12 = 1. Multiplying 1 by the whole number 16 gives 1 ร 16 = 16. ### Answer: 16
Expected answer: 16
Correct? Yes
Problem: After finding the result of multiplying twelve divided by twelve with the whole number sixteen, what is the new result when that value is further multiplied by four divided by fourteen?
Llama 3 8B:
Reasoning: We already found that multiplying twelve divided by twelve with the whole number sixteen gives 16. Multiplying 16 by four divided by fourteen is the same as multiplying 16 by 4/14. To simplify the fraction 4/14, we can divide both the numerator and the denominator by their greatest common divisor, which is 2. This gives us 2/7. So, multiplying 16 by 2/7 is the same as multiplying 16 by 2 and then dividing by 7, which gives 32/7. ### Answer: 32/7
Expected answer: 32/7
Correct? Yes
Problem: After multiplying twelve divided by twelve with sixteen in the previous problem, let's consider a scenario where instead of sixteen, we have eight. What is the result of twelve divided by twelve multiplied by eight?
Llama 3 8B:
Reasoning: The fraction twelve divided by twelve is equal to 1, since 12/12 = 1. Multiplying 1 by the whole number 8 gives 1 ร 8 = 8. ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: Albert plans to make miniature models for his project and needs certain amount of material. He knows that he needs 8/7th of a pound of clay per model and he wants to create 17/3rd models. Calculate amount of clay in pounds he will need. What is it when the fractions are multiplied?
Llama 3 8B:
Reasoning: To find the total amount of clay needed, we need to multiply the amount of clay per model by the number of models. The amount of clay per model is 8/7 pounds, and the number of models is 17/3. To multiply fractions, we multiply the numerators (8 and 17) and multiply the denominators (7 and 3), then simplify the resulting fraction. 8/7 ร 17/3 = (8 ร 17) / (7 ร 3) = 136/21 So, Albert will need 136/21 pounds of clay. ### Answer: 136/21
Expected answer: 136/21
Correct? Yes
Problem: Mrs. Parker makes her famous apple pie using 14/12 hours for preparing and baking. If she decides to make 2 pies, how many total hours will she spend? Please calculate and express your answer as a mixed number.
Llama 3 8B:
Reasoning: Mrs. Parker spends 14/12 hours for one pie, so for 2 pies, she will spend 2 x 14/12 = 14/6 = 2 2/3 hours. ### Answer: 2 2/3
Expected answer: 7/3
Correct? No
Problem: Evaluate the following expression and write your answer as a simplified fraction: (18/11) * (17/8)
Llama 3 8B:
To evaluate the expression, we need to multiply the two fractions: (18/11) * (17/8) = (18*17) / (11*8) = 306 / 88 To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2: 306 รท 2 = 153 88 รท 2 = 44 So, the simplified fraction is: 153/44 ### Answer: 153/44
Expected answer: 153/44
Correct? Yes
Problem: After solving the expression (18/11) * (17/8) in the earlier problem, multiply the result by the fraction (12/19). What is your answer as a simplified fraction?
Llama 3 8B:
We previously found that: (18/11) * (17/8) = 153/44 Now, we need to multiply this result by the fraction (12/19): (153/44) * (12/19) = (153*12) / (44*19) = 1836 / 836 To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 4: 1836 รท 4 = 459 836 รท 4 = 209 So, the simplified fraction is: 459/209 ### Answer: 459/209
Expected answer: 459/209
Correct? Yes
Problem: After previously solving (18/11) * (17/8), let's consider what would happen if we instead have a different fraction: (10/11). So, recalculate the expression, but this time use (10/11) * (17/8). What is your answer as a simplified fraction?
Llama 3 8B:
Let's evaluate the expression: (10/11) * (17/8) = (10*17) / (11*8) = 170 / 88 To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2: 170 รท 2 = 85 88 รท 2 = 44 So, the simplified fraction is: 85/44 ### Answer: 85/44
Expected answer: 85/44
Correct? Yes
Problem: You are eating healthy and have decided to only eat half of an apple. Each apple costs $2. How much would you essentially be paying for half an apple?
Llama 3 8B:
Reasoning: Since you're eating half an apple, you're essentially paying for half the cost of a whole apple. The cost of a whole apple is $2, so the cost of half an apple would be $2/2 = $1. ### Answer: $1
Expected answer: 1
Correct? Yes
Problem: You've decided to extend your health regiment and you want to include bananas into your diet. If each banana costs $2 and you only consume 7/10 of each banana, what would be the cost for the portion of banana you consume?
Llama 3 8B:
Reasoning: Since you're consuming 7/10 of each banana, you're essentially paying for 7/10 of the cost of a whole banana. The cost of a whole banana is $2, so the cost of 7/10 of a banana would be (7/10) x $2 = $1.40. ### Answer: $1.40
Expected answer: 7/5
Correct? No
Problem: What is the product when you multiply 1 by 8?
Llama 3 8B:
Reasoning: When you multiply 1 by 8, you are essentially adding 8 to itself 1 time. Since 8 + 8 = 16, and 16 + 0 = 16, the product of 1 and 8 is 8. ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: After finding the product of 1 and 8, what is the value when you multiply this product with 9/8?
Llama 3 8B:
Reasoning: We found that the product of 1 and 8 is 8. Now, we need to multiply this product by 9/8. To do this, we can multiply 8 by 9, which gives us 72. Then, we can divide 72 by 8, which gives us 9. ### Answer: 9
Expected answer: 9
Correct? Yes
Problem: If instead of multiplying 1 by 8, we multiply 1 by 6, what would the new product be?
Llama 3 8B:
Reasoning: When you multiply 1 by 6, you are essentially adding 6 to itself 1 time. Since 6 + 0 = 6, the product of 1 and 6 is 6. ### Answer: 6
Expected answer: 6
Correct? Yes
Problem: If a recipe calls for 5 cups of flour, but you are only using a scoop that is 14/16 the size of a cup, how many scoops do you need to have 5 whole cups of flour? Calculate it using the formula: p = 5 * (14 / 16)
Llama 3 8B:
Let's break it down step by step! The formula is: p = 5 * (14 / 16) First, let's simplify the fraction inside the parentheses: 14 / 16 = 7/8 Now, multiply 5 by the simplified fraction: p = 5 * (7/8) To multiply a whole number by a fraction, we multiply the whole number by the numerator (7) and then divide by the denominator (8): p = (5 * 7) / 8 p = 35 / 8 To find the number of scoops needed, we need to convert the decimal to a whole number. Since 35 is greater than 32, we know that the decimal part is greater than 0.5. Therefore, we round up to the nearest whole number: p = 4.375 โ 5 So, you need 5 scoops to have 5 whole cups of flour. ### Answer: 5
Expected answer: 35/8
Correct? No
Problem: William has a recipe that requires 9/10 of a cup of sugar. However, he wants to triple the recipe. How many cups of sugar will William need? Follow the operation ((9 / 10) * 3) to answer the question.
Llama 3 8B:
Reasoning: To triple the recipe, we need to multiply the required amount of sugar by 3. First, we simplify the fraction 9/10 by dividing both numerator and denominator by their greatest common divisor, which is 1. So, 9/10 = 9/10 Now, we multiply 9/10 by 3: (9/10) * 3 = (9 * 3) / 10 = 27/10 To simplify the fraction 27/10, we divide both numerator and denominator by their greatest common divisor, which is 1. So, 27/10 = 27/10 Since the denominator is 10, which is equal to 1 cup, we can say that William needs 27/10 cups of sugar, which is equal to 2.7 cups. ### Answer: 2.7
Expected answer: 27/10
Correct? Yes
Problem: William decided to try a new recipe that only needed 9/17 of a cup of sugar for one batch. Just like the previous time, he wants to triple the recipe. How much sugar will he need this time? Use the operation in ((9 / 17) * 3) to answer the question.
Llama 3 8B:
Reasoning: To triple the recipe, we need to multiply the required amount of sugar by 3. First, we simplify the fraction 9/17 by dividing both numerator and denominator by their greatest common divisor, which is 1. So, 9/17 = 9/17 Now, we multiply 9/17 by 3: (9/17) * 3 = (9 * 3) / 17 = 27/17 To simplify the fraction 27/17, we divide both numerator and denominator by their greatest common divisor, which is 1. So, 27/17 = 27/17 Since the denominator is 17, which is not equal to 1 cup, we cannot simplify the fraction further. Therefore, William will need 27/17 cups of sugar, which is equal to 1.5882 cups (rounded to four decimal places). ### Answer: 1.5882
Expected answer: 27/17
Correct? No
Problem: Compute the following operation: multiply 9 by 5/14. Write your answer as a simplified fraction.
Llama 3 8B:
Reasoning: To multiply 9 by 5/14, we can multiply 9 by the numerator 5, which gives us 9 ร 5 = 45. Then, we can divide 45 by the denominator 14 to get the result. 45 รท 14 = 3 1/14 So, the result of multiplying 9 by 5/14 is 3 1/14. ### Answer: 3 1/14
Expected answer: 45/14
Correct? No
Problem: Michael wants to adjust a recipe that originally serves 16 servings to only serve 12 servings. He found a new vineyard that produces a type of grape juice that is 15/6 more concentrated than the one he originally uses. How much of the new grape juice should he use in comparison to the old recipe, if he calculates it as (12/16) * (15/6)?
Llama 3 8B:
Reasoning: The original recipe serves 16 servings, and Michael wants to adjust it to serve 12 servings. This means he needs to reduce the amount of ingredients by a factor of 16/12 = 4/3. The new grape juice is 15/6 more concentrated than the original one. This means that if he uses the same amount of new grape juice as the original recipe, the resulting mixture will be 15/6 times more concentrated than the original recipe. To adjust for this, he needs to reduce the amount of new grape juice by a factor of 15/6. To find the correct ratio, we can multiply the two factors together: (12/16) * (15/6) = 15/16. This means Michael should use 15/16 of the new grape juice compared to the original recipe. ### Answer: 15/16
Expected answer: 15/8
Correct? No
Problem: If a baker uses 9 cups of flour for a cake recipe and each cup of flour weighs 19/19 pounds, how many pounds of flour does the baker use for the cake?
Llama 3 8B:
Reasoning: The baker uses 9 cups of flour, and each cup weighs 19/19 pounds. To find the total weight of flour, we multiply the number of cups by the weight of one cup: 9 cups x (19/19 pounds/cup) = 9 x 1 = 9 pounds ### Answer: 9
Expected answer: 9
Correct? Yes
Problem: If the baker decides to make a smaller cake that only uses 6/18 of the original amount of flour, how many pounds of flour would the baker use for the smaller cake?
Llama 3 8B:
Reasoning: The original amount of flour is 9 pounds. The baker is using 6/18 of the original amount, which is equivalent to 1/3 of the original amount. To find the weight of flour used for the smaller cake, we multiply the original weight by the fraction: 9 pounds x (1/3) = 9 pounds x 0.3333... = 3 pounds ### Answer: 3
Expected answer: 3
Correct? Yes
Problem: If the baker decides to use just 1 cup of flour instead of 9 for the cake recipe, and each cup of flour still weighs 19/19 pounds, how many pounds of flour does the baker use now?
Llama 3 8B:
Reasoning: The baker now uses only 1 cup of flour, and each cup weighs 19/19 pounds. To find the total weight of flour, we multiply the number of cups by the weight of one cup: 1 cup x (19/19 pounds/cup) = 1 x 1 = 1 pound ### Answer: 1
Expected answer: 1
Correct? Yes
Problem: A baker needs 5 times the amount of sugar required in one recipe. If one recipe needs 9/4 cups of sugar, how much sugar does the baker need in cups? Do the multiplication and state your answer as a fraction in simplest form.
Llama 3 8B:
Reasoning: The baker needs 5 times the amount of sugar required in one recipe. The amount of sugar required in one recipe is 9/4 cups. To find the amount of sugar the baker needs, multiply 9/4 by 5. 9/4 ร 5 = 45/4 To simplify the fraction, divide both the numerator and the denominator by their greatest common divisor, which is 1. 45/4 = 45/4 ### Answer: 45/4
Expected answer: 45/4
Correct? Yes
Problem: Julia is baking a cake that requires 12/8 cups of flour. However, she only needs to make 9/13 of the recipe. How much flour does she need for the portion of the recipe she is making?
Llama 3 8B:
Reasoning: To find the amount of flour needed for the portion of the recipe, we need to multiply the required amount of flour by the fraction of the recipe being made. The required amount of flour is 12/8 cups, and the fraction of the recipe being made is 9/13. To multiply these two values, we can multiply the numerator of the required amount by the numerator of the fraction being made, and then multiply the denominator of the required amount by the denominator of the fraction being made. (12/8) ร (9/13) = (12 ร 9) / (8 ร 13) = 108/104 So, Julia needs 108/104 cups of flour for the portion of the recipe she is making. ### Answer: 108/104
Expected answer: 27/26
Correct? Yes
Problem: Juliaโs sister also wants to bake a cake, but she's adapting a different recipe that requires 12 cups of flour. However, she only intends to make 9/13 of the recipe. How much flour does Julia's sister need for the portion of the recipe she is making?
Llama 3 8B:
Reasoning: Julia's sister needs to make 9/13 of the recipe, which requires 12 cups of flour. To find the amount of flour needed for the portion of the recipe, we can multiply the required amount of flour by the fraction of the recipe being made. 12 cups ร (9/13) = (12 ร 9) / 13 = 108/13 So, Julia's sister needs 108/13 cups of flour for the portion of the recipe she is making. ### Answer: 108/13
Expected answer: 108/13
Correct? Yes
Problem: Calculate the following expression: 9 * (20/11). Write the answer as a mixed number.
Llama 3 8B:
To evaluate the expression, we need to follow the order of operations (PEMDAS): 1. Divide 20 by 11: 20/11 = 1 with a remainder of 9 2. Multiply 9 by the result: 9 * 1 = 9 3. Add the remainder to the result: 9 + 9 = 18 So, the expression 9 * (20/11) is equal to 18. ### Answer: 18 1/11
Expected answer: 180/11
Correct? No
Problem: Solve the following problem: Divide 20 by 5 and then multiply the result by the fraction 6/10. Write down your answer.
Llama 3 8B:
Reasoning: First, we divide 20 by 5, which gives us 20/5 = 4. Then, we multiply 4 by the fraction 6/10, which can be simplified to 3/5. 4 ร (3/5) = 4 ร 3/5 = 12/5 = 2.4 ### Answer: 2.4
Expected answer: 12/5
Correct? Yes
Problem: After solving the previous problem, what if instead of dividing 20 by 5, you divided 16 by 5 and kept the rest of the problem the same, where the result is then multiplied by 6/10? Calculate this new problem and provide your answer.
Llama 3 8B:
Reasoning: First, we divide 16 by 5, which gives us 16/5 = 3.2. Then, we multiply 3.2 by the fraction 6/10, which can be simplified to 3/5. 3.2 ร (3/5) = 3.2 ร 3/5 = 9.6/5 = 1.92 ### Answer: 1.92
Expected answer: 48/25
Correct? No
Problem: In a school where there are 17 classrooms and each classroom has a bin for paper recycling, 5/14 of the total classrooms forgot to recycle their papers during a specific day. What fraction of the total classrooms didn't recycle their papers?
Llama 3 8B:
Reasoning: Since 5/14 of the classrooms forgot to recycle their papers, that means 17 - 5/14 = 17 - 5/14 = 17 x (1 - 1/14) = 17 x 13/14 = 221/14 classrooms did recycle their papers. The fraction of classrooms that didn't recycle their papers is 5/14. ### Answer: 5/14
Expected answer: 85/14
Correct? No
Problem: Calculate the answer to the following problem: what is (19 / 11) * (13 / 17)? Write your answer as a simplified fraction.
Llama 3 8B:
To evaluate this expression, we need to follow the order of operations (PEMDAS): 1. Divide 19 by 11: 19 รท 11 = 1 with a remainder of 9 So, 19/11 = 1 9/11 2. Divide 13 by 17: 13 รท 17 = 0 with a remainder of 13 So, 13/17 = 0 13/17 3. Multiply the two results: (1 9/11) ร (0 13/17) = (1 ร 0) + (9/11 ร 13/17) = 0 + (117/187) = 117/187 So, the simplified answer is: ### Answer: 117/187
Expected answer: 247/187
Correct? No
Problem: Samantha has a rope that is 9 feet long. She uses 3/11 of the rope to secure a tent. How long is the piece of rope that Samantha uses?
Llama 3 8B:
Reasoning: Samantha uses 3/11 of the rope, which is 9 * 3/11 = 9/11 * 3 = 3 * (9/11) = 27/11 feet. ### Answer: 27/11 feet.
Expected answer: 27/11
Correct? Yes
Problem: Continuing from the previous problem, let's say Samantha had initially a longer, 18 feet rope instead of a 9 feet one. If she still cut out 3/11 of the length from this rope, how long is the new piece of Samantha's rope?
Llama 3 8B:
Reasoning: Samantha uses 3/11 of the rope, which is 18 * 3/11 = 18/11 * 3 = 3 * (18/11) = 54/11 feet. ### Answer: 54/11 feet.
Expected answer: 54/11
Correct? Yes
Problem: What is the result of the multiplication when 1 is multiplied by 7?
Llama 3 8B:
Reasoning: When 1 is multiplied by 7, the result is the product of the two numbers. In this case, the product is simply the value of the multiplier, which is 7. 1 ร 7 = 7 ### Answer: 7
Expected answer: 7
Correct? Yes
Problem: What is the result when you multiply the previous answer (result of 1 multiplied by 7) by the fraction 5/5?
Llama 3 8B:
Reasoning: When multiplying a number by a fraction, we multiply the number by the numerator (5) and then divide by the denominator (5). 7 ร 5 = 35 35 รท 5 = 7 So, the result of multiplying 7 by the fraction 5/5 is still 7. ### Answer: 7
Expected answer: 7
Correct? Yes
Problem: What would be the result of the multiplication if the original number was not 1 multiplied by 7, but rather 1 multiplied by 19?
Llama 3 8B:
Reasoning: When 1 is multiplied by 19, the result is the product of the two numbers. In this case, the product is simply the value of the multiplier, which is 19. 1 ร 19 = 19 ### Answer: 19
Expected answer: 19
Correct? Yes
Problem: Find the product of the following calculation: 1 times 9.
Llama 3 8B:
Reasoning: To find the product, we simply multiply 1 by 9. 1 ร 9 = 9 ### Answer: 9
Expected answer: 9
Correct? Yes
Problem: Take your answer from the previous problem which was the product of 1 and 9. Now multiply that result by the fraction 13/18. What is your new output?
Llama 3 8B:
Reasoning: We already found the product of 1 and 9 to be 9. Now, we need to multiply this result by the fraction 13/18. 9 ร (13/18) = ? To multiply a whole number by a fraction, we multiply the whole number by the numerator (13) and then divide by the denominator (18). 9 ร 13 = 117 117 รท 18 = 6.5 ### Answer: 6.5
Expected answer: 13/2
Correct? Yes
Problem: In the previous question, instead of multiplying 1 by 9, suppose you need to multiply 1 by 4. What would be the outcome in this case?
Llama 3 8B:
Reasoning: To find the product, we simply multiply 1 by 4. 1 ร 4 = 4 ### Answer: 4
Expected answer: 4
Correct? Yes
Problem: Calculate the product of the fraction (18 / 18) and the fraction (11 / 5). Write your answer as a simplified fraction.
Llama 3 8B:
Reasoning: To calculate the product of the two fractions, we multiply the numerators (18 and 11) and multiply the denominators (18 and 5), then simplify the resulting fraction. Product = (18/18) ร (11/5) = (18 ร 11) / (18 ร 5) = 198 / 90 To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 18. 198 รท 18 = 11 90 รท 18 = 5 So, the simplified fraction is: 198 / 90 = 11 / 5 ### Answer: 11/5
Expected answer: 11/5
Correct? Yes
Problem: Continuing from the previous problem where you calculated the product of (18 / 18) and (11 / 5), what would be the result if you multiplied this produced value by itself? Report your answer as a simplified fraction.
Llama 3 8B:
Reasoning: We previously calculated the product of the two fractions to be 11/5. To find the result of multiplying this value by itself, we square the fraction: (11/5) ร (11/5) = (11 ร 11) / (5 ร 5) = 121 / 25 To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1. 121 รท 1 = 121 25 รท 1 = 25 So, the simplified fraction is: 121 / 25 ### Answer: 121/25
Expected answer: 121/25
Correct? Yes
Problem: Let's modify the previous problem slightly. If instead of (18 / 18), you used (9 / 18), what would be the product of this fraction and (11 / 5)? Report your answer as a simplified fraction.
Llama 3 8B:
Reasoning: To calculate the product of the two fractions, we multiply the numerators (9 and 11) and multiply the denominators (18 and 5), then simplify the resulting fraction. Product = (9/18) ร (11/5) = (9 ร 11) / (18 ร 5) = 99 / 90 To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 9. 99 รท 9 = 11 90 รท 9 = 10 So, the simplified fraction is: 99 / 90 = 11 / 10 ### Answer: 11/10
Expected answer: 11/10
Correct? Yes
Problem: Calculate the answer for the following equation: (5 / 16) * 13. Please express your answer as a decimal.
Llama 3 8B:
To evaluate this expression, we need to follow the order of operations (PEMDAS): 1. Divide 5 by 16: 5 / 16 = 0.3125 2. Multiply the result by 13: 0.3125 * 13 = 4.0625 So, the answer is 4.0625.
Expected answer: 65/16
Correct? Yes
Problem: Find the result of the following calculation: Multiply the fraction 4/5 by the whole number 15. Write your answer in simplest form.
Llama 3 8B:
Reasoning: To multiply a fraction by a whole number, we multiply the numerator of the fraction by the whole number and keep the denominator the same. So, we multiply 4 by 15 to get 60, and keep the denominator 5 the same. The result is the fraction 60/5. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 5. 60 รท 5 = 12 5 รท 5 = 1 So, the simplified result is 12/1, which is equal to 12. ### Answer: 12
Expected answer: 12
Correct? Yes
Problem: After finding the result of 4/5 multiplied by 15, multiply this result by the fraction 3/15. Write your answer in simplest form.
Llama 3 8B:
Reasoning: We already found the result of 4/5 multiplied by 15, which is 12. Now, we need to multiply 12 by the fraction 3/15. To do this, we multiply 12 by the numerator of the fraction, which is 3, and keep the denominator the same. 12 ร 3 = 36 So, the result is the fraction 36/15. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3. 36 รท 3 = 12 15 รท 3 = 5 So, the simplified result is 12/5. ### Answer: 12/5
Expected answer: 12/5
Correct? Yes
Problem: Suppose that you have adjusted your previous calculation. Instead of multiplying 4/5 by 15, you now need to multiply 4/5 by 6. What is the result of that calculation? Please write your answer in the simplest form.
Llama 3 8B:
Reasoning: To multiply a fraction by a whole number, we multiply the numerator of the fraction by the whole number and keep the denominator the same. So, we multiply 4 by 6 to get 24, and keep the denominator 5 the same. The result is the fraction 24/5. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4. 24 รท 4 = 6 5 รท 1 = 5 So, the simplified result is 6/5. ### Answer: 6/5
Expected answer: 24/5
Correct? No
Problem: What will be the result if you multiply the fraction 20/12 by the fraction 19/16?
Llama 3 8B:
To multiply two fractions, we multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom), then simplify the result. So, we multiply 20/12 by 19/16: (20/12) ร (19/16) = (20 ร 19) / (12 ร 16) = 380 / 192 To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 4: 380 รท 4 = 95 192 รท 4 = 48 So, the simplified result is: 380 / 192 = 95 / 48 ### Answer: 95/48
Expected answer: 95/48
Correct? Yes
Problem: In continuation from the previous problem, what will be the result if you square the obtained result? In other words, multiply the result of the previous operation with itself.
Llama 3 8B:
We previously found that the result of multiplying 20/12 by 19/16 is 95/48. To square this result, we multiply it by itself: (95/48) ร (95/48) = (95 ร 95) / (48 ร 48) = 9025 / 2304 To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1: 9025 รท 1 = 9025 2304 รท 1 = 2304 So, the simplified result is: 9025 / 2304 ### Answer: 9025/2304
Expected answer: 9025/2304
Correct? Yes
Problem: Instead of multiplying 20/12 by 19/16 as in the previous problem, what would be the result if you multiplied 20/12 by another fraction of similar value, namely 19/12?
Llama 3 8B:
To multiply two fractions, we multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom), then simplify the result. So, we multiply 20/12 by 19/12: (20/12) ร (19/12) = (20 ร 19) / (12 ร 12) = 380 / 144 To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 4: 380 รท 4 = 95 144 รท 4 = 36 So, the simplified result is: 380 / 144 = 95 / 36 ### Answer: 95/36
Expected answer: 95/36
Correct? Yes
Problem: Calculate the result of the following multiplication operation: 17/20 * 17/13. Write your answer as a simplified fraction.
Llama 3 8B:
Reasoning: To multiply two fractions, we multiply the numerators and multiply the denominators. So, we get: (17/20) * (17/13) = (17 * 17) / (20 * 13) = 289/260 To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1. Therefore, the simplified fraction is: 289/260 ### Answer: 289/260
Expected answer: 289/260
Correct? Yes
Problem: For the next part of your calculation, multiply the result of 17/20 * 17/13, denoted as 'f', by 12/11. What is the result of this operation? Please write your answer as a simplified fraction.
Llama 3 8B:
Reasoning: We multiply the result of the previous operation, which is f = 289/260, by 12/11: f * (12/11) = (289/260) * (12/11) = (289 * 12) / (260 * 11) = 3468/2860 To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 4. Therefore, the simplified fraction is: 3468/2860 = 873/715 ### Answer: 873/715
Expected answer: 867/715
Correct? No
Problem: Suppose instead of 17/20 in the previous problem, the fraction was actually 16/20. What would the result of the multiplication operation 16/20 * 17/13 be? Please write your answer as a simplified fraction.
Llama 3 8B:
Reasoning: To multiply two fractions, we multiply the numerators and multiply the denominators. So, we get: (16/20) * (17/13) = (16 * 17) / (20 * 13) = 272/260 To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 4. Therefore, the simplified fraction is: 272/260 = 68/65 ### Answer: 68/65
Expected answer: 68/65
Correct? Yes
Problem: Solve the following problem: 5 * (13 / 12) and give your answer in the form of a mixed number or fraction where necessary.
Llama 3 8B:
To solve this problem, we need to follow the order of operations (PEMDAS): 1. Divide 13 by 12: 13 รท 12 = 1 1/12 2. Multiply 5 by the result: 5 * 1 1/12 = 5 + 5/12 So, the final answer is: ### Answer: 5 5/12
Expected answer: 65/12
Correct? Yes
Problem: Continuing from our previous problem, now, multiply the answer you got by (14 / 14). What is your new result as a mixed number or fraction?
Llama 3 8B:
We already found that 5 * (13 / 12) = 5 5/12. Now, we need to multiply this result by (14 / 14): 1. Multiply the whole number part (5) by (14 / 14): 5 * 1 = 5 2. Multiply the fractional part (5/12) by (14 / 14): 5/12 * 1 = 5/12 (since 14/14 = 1) 3. Add the results: 5 + 5/12 = 5 5/12 The result remains the same: ### Answer: 5 5/12
Expected answer: 65/12
Correct? Yes
Problem: Continuing from the first problem, suppose we used 5 * (13 / 10) instead of 5 * (13 / 12). Calculate the new problem and give your answer in the form of a mixed number or fraction where necessary. What happens to the result when we use 13 / 10 instead of 13 / 12 in the problem?
Llama 3 8B:
To solve this problem, we need to follow the order of operations (PEMDAS): 1. Divide 13 by 10: 13 รท 10 = 1 3/10 2. Multiply 5 by the result: 5 * 1 3/10 = 5 + 3/10 So, the final answer is: ### Answer: 5 3/10 When we use 13 / 10 instead of 13 / 12 in the problem, the result increases by 1/12. This is because 13 / 12 is a smaller fraction than 13 / 10, so multiplying 5 by the smaller fraction results in a smaller product.
Expected answer: 13/2
Correct? No
Problem: Jack had a full bar of chocolate. If he ate 3/4 of it and each piece of the bar represented 1/4, how many pieces did he eat?
Llama 3 8B:
Reasoning: Jack ate 3/4 of the bar, and each piece represents 1/4. To find the total number of pieces, we can multiply the fraction of the bar eaten by the number of pieces in one whole bar. 3/4 x 4 = 12 So, Jack ate 12 pieces of chocolate. ### Answer: 12
Expected answer: 3
Correct? No
Problem: Calculate the product of 17 and 9/18 without simplifying the fraction. What is the result?
Llama 3 8B:
To calculate the product of 17 and 9/18, we can multiply 17 by the numerator of the fraction (9) and then divide the result by the denominator of the fraction (18). 17 ร 9 = 153 Then, we divide the result by 18: 153 รท 18 = 8.5 So, the result is 8.5. ### Answer: 8.5
Expected answer: 17/2
Correct? Yes
Problem: Reconsider the previous problem, but this time replace 9/18 by 13/18. So, now calculate the product of 17 and 13/18 without simplifying the fraction. What is the result now?
Llama 3 8B:
To calculate the product of 17 and 13/18, we can multiply 17 by the numerator of the fraction (13) and then divide the result by the denominator of the fraction (18). 17 ร 13 = 221 Then, we divide the result by 18: 221 รท 18 = 12.28 So, the result is 12.28. ### Answer: 12.28
Expected answer: 221/18
Correct? No
Problem: Calculate the result of multiplying the fraction 15/15 by the whole number 19. Leave your answer as a simplified fraction or whole number, as appropriate.
Llama 3 8B:
Reasoning: When multiplying a fraction by a whole number, we multiply the numerator by the whole number and keep the denominator the same. So, multiplying 15/15 by 19, we get: (15/15) ร 19 = (15 ร 19) / 15 = 285 / 15 We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 15. 285 รท 15 = 19 15 รท 15 = 1 So, the simplified result is: 285 / 15 = 19 ### Answer: 19
Expected answer: 19
Correct? Yes
Problem: Following your previous calculation, now multiply the result by the fraction 6/10. Write down the result as a simplified fraction or a whole number, as appropriate.
Llama 3 8B:
Reasoning: We multiply the result (19) by the fraction 6/10. 19 ร (6/10) = (19 ร 6) / 10 = 114 / 10 We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2. 114 รท 2 = 57 10 รท 2 = 5 So, the simplified result is: 114 / 10 = 57/5 We can further simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 1. 57 รท 1 = 57 5 รท 1 = 5 So, the final simplified result is: 57/5 = 11.4 ### Answer: 11.4
Expected answer: 57/5
Correct? Yes
Problem: Following your previous calculation, reconsider the problem assuming the whole number you previously used was 20 instead of 19. Calculate the result of multiplying the fraction 15/15 by this new whole number. Write down the result as a simplified fraction or a whole number, as appropriate.
Llama 3 8B:
Reasoning: When multiplying a fraction by a whole number, we multiply the numerator by the whole number and keep the denominator the same. So, multiplying 15/15 by 20, we get: (15/15) ร 20 = (15 ร 20) / 15 = 300 / 15 We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 15. 300 รท 15 = 20 15 รท 15 = 1 So, the simplified result is: 300 / 15 = 20 ### Answer: 20
Expected answer: 20
Correct? Yes
Problem: Mary has 16 apples. She shares 3/5 of them with her friends. How many apples does Mary share with her friends?
Llama 3 8B:
Reasoning: Mary has 16 apples and shares 3/5 of them with her friends. To find the number of apples she shares, we can multiply 16 by 3/5. 16 * (3/5) = 16 * 0.6 = 9.6 Since we can't share a fraction of an apple, we round down to the nearest whole number. Therefore, Mary shares 9 apples with her friends. ### Answer: 9
Expected answer: 48/5
Correct? No
Problem: What is the product when you divide 12 by 3 and then multiply the result by 3?
Llama 3 8B:
Reasoning: When you divide 12 by 3, you get 12/3 = 4. Then, you multiply the result by 3, so 4 ร 3 = 12. ### Answer: 12
Expected answer: 12
Correct? Yes
Problem: Reconsider the original problem, where 12 was divided by 3, and the result was multiplied by 3. Now, replace 12 with 2. What would be the product now?
Llama 3 8B:
Reasoning: When you divide 2 by 3, you get 2/3 = 0.67 (approximately). Then, you multiply the result by 3, so 0.67 ร 3 = 2.01 (approximately). ### Answer: 2.01
Expected answer: 2
Correct? No
Problem: If each box of chocolates contains 12 pieces and each piece is split into 8 equal parts for tasting, how many whole pieces of chocolate are there if there are 6 boxes? Use the equation t = (6 * (12 / 8)) to calculate your answer.
Llama 3 8B:
Let's break down the equation: t = (6 * (12 / 8)) First, let's simplify the fraction inside the parentheses: 12 / 8 = 1.5 So, the equation becomes: t = (6 * 1.5) Now, let's multiply 6 by 1.5: t = 9 So, there are 9 whole pieces of chocolate. ### Answer: 9
Expected answer: 9
Correct? Yes
Problem: Let's consider a change in the previous problem. Instead of 6 boxes of chocolates, assume now that we only have 3 boxes. If each box of chocolates contains 12 pieces and each piece is divided into 8 equal parts for tasting, how many whole pieces of chocolate are there now? Use the equation t = 3 * (12 / 8) to calculate your answer.
Llama 3 8B:
Let's break down the equation: t = 3 * (12 / 8) First, let's simplify the fraction inside the parentheses: 12 / 8 = 1.5 So, the equation becomes: t = 3 * 1.5 Now, let's multiply 3 by 1.5: t = 4.5 Since we can't have a fraction of a piece of chocolate, we'll round down to the nearest whole number. Therefore, there are 4 whole pieces of chocolate. ### Answer: 4
Expected answer: 9/2
Correct? No
Problem: Emily uses 10/19th of her weekly allowance on Monday. On Tuesday, she spends an equivalent amount which is 14/7 times more compared to what she spent on Monday. How much of her weekly allowance did she spend on Tuesday? Calculate: (10 / 19) * (14 / 7)
Llama 3 8B:
Reasoning: To find the equivalent amount Emily spent on Tuesday, we need to multiply the amount she spent on Monday by the ratio 14/7. (10/19) * (14/7) = (10 * 14) / (19 * 7) = 140/133 So, Emily spent 140/133 times the amount she spent on Monday. Since she spent 10/19 of her weekly allowance on Monday, she spent (10/19) * (140/133) = 10/19 on Tuesday. ### Answer: 10/19
Expected answer: 20/19
Correct? No
Problem: What is the product of 2 and 2?
Llama 3 8B:
Reasoning: The product of two numbers is obtained by multiplying them together. In this case, we are multiplying 2 and 2. 2 ร 2 = 4 ### Answer: 4
Expected answer: 4
Correct? Yes
Problem: After finding the product of 2 and 2, what would you get if you multiply that result by 5/2?
Llama 3 8B:
Reasoning: We already found that the product of 2 and 2 is 4. Now, we need to multiply this result by 5/2. 4 ร (5/2) = 4 ร 2.5 = 10 ### Answer: 10
Expected answer: 10
Correct? Yes
Problem: You have 11 boxes of cookies. Each box has 8/5 dozen cookies in it. How many dozens of cookies do you have in total?
Llama 3 8B:
Reasoning: Each box has 8/5 dozen cookies, which is equivalent to 8/5 * 12 = 16 cookies. Since there are 11 boxes, the total number of cookies is 11 * 16 = 176 cookies. Since we want to find the total number of dozens, we can divide the total number of cookies by 12: 176 / 12 = 14.67 dozen cookies. Since we can't have a fraction of a dozen, we round down to 14 dozens. ### Answer: 14
Expected answer: 88/5
Correct? No
Problem: Compute the result of the following operation: multiply the fraction 6/18 by the whole number 3. Write your answer in its simplest form.
Llama 3 8B:
Reasoning: To multiply a fraction by a whole number, we multiply the numerator by the whole number and keep the denominator the same. So, we multiply 6 by 3 to get 18, and keep the denominator 18 the same. The result is the fraction 18/18, which simplifies to 1. ### Answer: 1
Expected answer: 1
Correct? Yes
Problem: After finding the result of the operation 6/18 * 3, calculate the square of that result. Write your answer in the simplest form.
Llama 3 8B:
Reasoning: We previously found that the result of the operation 6/18 * 3 is 1. To calculate the square of 1, we simply multiply 1 by itself: 1 ร 1 = 1 The result is still 1, which is already in its simplest form. ### Answer: 1
Expected answer: 1
Correct? Yes
Problem: After finding the result of the previous operation 6/18 * 3, consider a new situation where you multiply the fraction 17/18 by the whole number 3 instead. What is the result of this new operation? Write your answer in its simplest form.
Llama 3 8B:
Reasoning: To multiply a fraction by a whole number, we multiply the numerator by the whole number and keep the denominator the same. So, we multiply 17 by 3 to get 51, and keep the denominator 18 the same. The result is the fraction 51/18. To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 3. 51 รท 3 = 17 18 รท 3 = 6 So, the simplified result is 17/6. ### Answer: 17/6
Expected answer: 17/6
Correct? Yes
Problem: Lucy had 18 candies which she evenly distributed into 8 bags, she then gave 5 bags to her friends. How many candies does she give away in total? Use the formula (18 / 8) * 5 to find the answer.
Llama 3 8B:
Reasoning: Lucy has 18 candies and distributes them evenly into 8 bags, so each bag has 18/8 = 2.25 candies (we can round this to 2, since you can't divide a candy into fractions!). She gives away 5 bags, so she gives away 2 * 5 = 10 candies. ### Answer: 10
Expected answer: 45/4
Correct? No
Problem: Calculate the following multiplication of a whole number and a fraction. What is the result of 5 * (14 / 10)?
Llama 3 8B:
Reasoning: To multiply a whole number by a fraction, we multiply the whole number by the numerator (14) and then divide by the denominator (10). 5 * (14 / 10) = 5 * (14 รท 10) = 5 * 1.4 = 7 ### Answer: 7
Expected answer: 7
Correct? Yes
Problem: After finding the result of 5 * (14 / 10), continue with the next step of the problem by multiplying this result by the fraction 5/6. What is the final result?
Llama 3 8B:
Reasoning: We already found the result of 5 * (14 / 10) to be 7. Now, we need to multiply this result by the fraction 5/6. 7 * (5/6) = 7 * (5 รท 6) = 35 รท 6 = 5.83 ### Answer: 5.83
Expected answer: 35/6
Correct? No
Problem: After initially calculating the result of 5 * (14 / 10), consider a different scenario where you have to calculate 5 * (14 / 13) instead. What would the result be in this case?
Llama 3 8B:
Reasoning: To multiply a whole number by a fraction, we multiply the whole number by the numerator (14) and then divide by the denominator (13). 5 * (14 / 13) = 5 * (14 รท 13) = 5 * 1.0769230769 (approximately) ### Answer: approximately 6.84
Expected answer: 70/13
Correct? No
Problem: What is the result of multiplying 6 by the fraction (20/7)? Write your answer as a mixed number, if applicable.
Llama 3 8B:
To multiply 6 by the fraction (20/7), we can multiply the numerator and denominator of the fraction by 6: (20/7) ร 6 = (20 ร 6) / (7 ร 6) = 120/42 To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2: 120 รท 2 = 60 42 รท 2 = 21 So, the result of multiplying 6 by the fraction (20/7) is: 60/21 This can be written as a mixed number: 2 9/21 ### Answer: 2 9/21
Expected answer: 120/7
Correct? No
Problem: Calculate: What is the product of 8/19 times 6? Give your answer as a simplified fraction or a whole number, if possible.
Llama 3 8B:
Reasoning: To calculate the product, we multiply the numerator and denominator of the fraction 8/19 by 3 to get a common denominator with 6. (8/19) ร 6 = (8 ร 3)/(19 ร 3) ร 6 = (24)/(57) ร 6 = 24/57 ร 6 = 24/57 ร (6/1) = 24/57 ร 6/1 = 144/57 Now, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3. 144 รท 3 = 48 57 รท 3 = 19 So, the simplified fraction is 48/19. ### Answer: 48/19
Expected answer: 48/19
Correct? Yes
Problem: For the following calculation, consider the same scenario as in the previous problem, but this time, instead of having 8/19, you now have 8/8 times 6. How would this change the result? Note: Carry out the multiplication based on this alteration and provide your answer.
Llama 3 8B:
Reasoning: Since we have 8/8, which is equal to 1, we can simplify the expression to: 1 ร 6 = 6 So, the result is simply 6. ### Answer: 6
Expected answer: 6
Correct? Yes
Problem: Calculate the answer to the following problem. What is the result of multiplying 8 by 1/1?
Llama 3 8B:
Reasoning: When multiplying a number by 1, the result is the same number. In this case, multiplying 8 by 1 is the same as just saying 8. So, 8 ร 1/1 = 8 ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: After finding the result of multiplying 8 by 1/1 in the previous problem, what is the result when we multiply that answer by 3/2?
Llama 3 8B:
Reasoning: We already found that 8 ร 1/1 = 8. Now, we need to multiply 8 by 3/2. To multiply a number by a fraction, we multiply the number by the numerator (3) and then divide by the denominator (2). So, 8 ร 3/2 = (8 ร 3) / 2 = 24 / 2 = 12 ### Answer: 12
Expected answer: 12
Correct? Yes
Problem: After finding the result of multiplying 8 by 1/1 in the previous problem, what would be the result if you were originally working with 20 instead of 8? In other words, what would be the outcome of multiplying 20 by 1/1?
Llama 3 8B:
Reasoning: As we established earlier, multiplying a number by 1 is the same as just saying that number. So, multiplying 20 by 1 is the same as just saying 20. So, 20 ร 1/1 = 20 ### Answer: 20
Expected answer: 20
Correct? Yes
Problem: Jack has a long sheet of paper that he wants to use for his art project. The sheet has a length of 5/15 meters. If Jack cuts 9 identical pieces from the sheet, what would be the total length of all the 9 pieces? Calculate the answer and write it as a fraction or a whole number.
Llama 3 8B:
Reasoning: The length of each piece is 5/15 divided by 9, which is 5/15 * 1/9 = 5/135. The total length of all the 9 pieces is 5/135 * 9 = 5/15 = 1/3. ### Answer: 1/3
Expected answer: 3
Correct? No
Problem: Suppose the length of a book is 1 foot, and there are 13 books side by side on a shelf. How long is the shelf in feet? To find out, calculate the product of 1 and 13.
Llama 3 8B:
Reasoning: To find the length of the shelf, we need to multiply the length of one book (1 foot) by the number of books (13). 1 foot x 13 = 13 feet ### Answer: 13
Expected answer: 13
Correct? Yes
Problem: In the previous problem, the total length of the shelf was found to be 13 feet. Now, suppose that only 12/15 of that shelf is filled with books. What would be the length of the shelf that is filled with books? To find out, multiply the total length of the shelf by 12/15.
Llama 3 8B:
Reasoning: To find the length of the shelf that is filled with books, we need to multiply the total length of the shelf (13 feet) by the fraction 12/15. 13 feet x (12/15) = 13 feet x 0.8 = 10.4 feet ### Answer: 10.4
Expected answer: 52/5
Correct? Yes
Problem: Calculate the product when you multiply the fraction 6/5 by the whole number 1. Write your answer as a simplified fraction or whole number.
Llama 3 8B:
Reasoning: When multiplying a fraction by a whole number, we multiply the numerator by the whole number and keep the denominator the same. So, multiplying 6/5 by 1, we get: 6/5 ร 1 = 6/5 Since the whole number 1 doesn't change the value of the fraction, the result is still 6/5. ### Answer: 6/5
Expected answer: 6/5
Correct? Yes
Problem: Once you have calculated the product of 6/5 and 1, multiply the result by itself. Write your answer as a simplified fraction or whole number.
Llama 3 8B:
Reasoning: We already calculated the product of 6/5 and 1, which is 6/5. Now, we need to multiply this result by itself. (6/5) ร (6/5) = (6 ร 6) / (5 ร 5) = 36/25 ### Answer: 36/25
Expected answer: 36/25
Correct? Yes
Problem: Solve the following problem: Recognize that 5/5 is the same as 1, then multiply that result by 17/6. Write your answer as a simplified fraction.
Llama 3 8B:
Reasoning: Recognizing that 5/5 is indeed equal to 1, we can multiply it by 17/6 as follows: (5/5) ร (17/6) = (1) ร (17/6) = 17/6 To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1. Therefore, the simplified fraction is: 17/6 ### Answer: 17/6
Expected answer: 17/6
Correct? Yes
Problem: In the previous problem, we multiplied 5/5 with 17/6. This time, let's consider that instead of 17/6, we want to multiply 5/5 by 6/6. What would be the result of this multiplication? Write down your answer as a simplified fraction.
Llama 3 8B:
Reasoning: When we multiply 5/5 by 6/6, we are essentially multiplying 1 by 1, since both fractions are equal to 1. (5/5) ร (6/6) = (1) ร (1) = 1 Since the result is already a simplified fraction, we can write the answer as: 1 ### Answer: 1
Expected answer: 1
Correct? Yes
Problem: What is the result of multiplying 8 by the result of 8 divided by 6?
Llama 3 8B:
Reasoning: First, we need to divide 8 by 6, which gives us 8/6 = 4/3 = 1.33 (approximately). Then, we multiply 8 by the result, which gives us 8 ร 1.33 = 10.64 (approximately). ### Answer: 10.64
Expected answer: 32/3
Correct? No
Problem: Susan bought 9 apples. She used 15/16 of those apples to make a big apple pie for her family. What fraction of the total apples did Susan use?
Llama 3 8B:
Reasoning: Susan used 15/16 of the 9 apples, which is equivalent to 15/16 * 9 = 135/16. To find the fraction of the total apples used, we can divide the number of apples used (135/16) by the total number of apples (9). So, the fraction of the total apples used is 135/16 รท 9 = 135/16 * 1/9 = 135/144 = 15/16. ### Answer: 15/16
Expected answer: 135/16
Correct? No
Problem: In a class, 10 out of 14 students participated in a school project. Each of those students prepared 8 models for the science fair. Calculate the total number of models prepared for the science fair by multiplying the fraction of students who participated (10/14) with the number of models each student made (8).
Llama 3 8B:
Reasoning: To find the total number of models prepared, we need to multiply the fraction of students who participated (10/14) with the number of models each student made (8). First, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 10/14 = 5/7 Now, we can multiply the simplified fraction by the number of models each student made: (5/7) ร 8 = 40/7 To simplify the fraction further, we can divide both the numerator and the denominator by their greatest common divisor, which is 4: 40/7 = 10/1.75 So, the total number of models prepared for the science fair is 10/1.75. ### Answer: 10/1.75
Expected answer: 40/7
Correct? Yes
Problem: Continuing from the initial problem: Suppose this time, all 10 out of 10 students participated in the school project, each of them preparing 8 models. Calculate how many total models were prepared for the science fair now, by multiplying the new fraction of students participating (10/10) with the number of models each student made (8).
Llama 3 8B:
Reasoning: Since all 10 students participated, the fraction of students who participated is now 10/10, which simplifies to 1. We can multiply the simplified fraction by the number of models each student made: 1 ร 8 = 8 So, the total number of models prepared for the science fair is 8. ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: What is the product of the fraction 3/3 and the mixed number 13/4? Write your answer as a simplified fraction.
Llama 3 8B:
Reasoning: The fraction 3/3 is equal to 1, since 3 divided by 3 is 1. The mixed number 13/4 can be converted to an improper fraction by multiplying the whole number part (13) by the denominator (4) and then adding the numerator (13): 13/4 = (13*4+13)/4 = 52/4 = 13. The product of 1 and 13 is 13. Since 13 is already in its simplest form, the answer is 13. ### Answer: 13
Expected answer: 13/4
Correct? No
Problem: Calculate the result of multiplying thirteen by the ratio of two to two.
Llama 3 8B:
Reasoning: The ratio of two to two is 2/2 = 1. Multiplying 13 by 1 gives 13 * 1 = 13. ### Answer: 13
Expected answer: 13
Correct? Yes
Problem: After finding the result of multiplying thirteen by the ratio of two to two, now calculate the result of multiplying this outcome by the fraction eight fourteenths. What is the final result?
Llama 3 8B:
Reasoning: We previously found that multiplying 13 by the ratio of two to two gives 13. Multiplying 13 by the fraction 8/14 = 4/7 gives 13 * 4/7 = 52/7. ### Answer: 52/7
Expected answer: 52/7
Correct? Yes
Problem: Calculate the value of the expression 17/6 * 6/4. Write your answer in the simplest form.
Llama 3 8B:
Reasoning: We can simplify the expression by canceling out the common factors of 6 in the numerator and denominator: 17/6 * 6/4 = (17/1) * (1/4) = 17/4 So, the value of the expression is 17/4. ### Answer: 17/4
Expected answer: 17/4
Correct? Yes
Problem: Recalculate the previous problem, however, instead of using 17/6, use 20/6. The new problem should be 20/6 * 6/4. Find the result and write it in its simplest form.
Llama 3 8B:
Reasoning: We can simplify the expression by canceling out the common factors of 6 in the numerator and denominator: 20/6 * 6/4 = (20/1) * (1/4) = 20/4 We can further simplify the fraction 20/4 by dividing both the numerator and the denominator by their greatest common divisor, which is 4: 20/4 = 5/1 So, the value of the expression is 5. ### Answer: 5
Expected answer: 5
Correct? Yes
Problem: Find the product of 2 and 6.
Llama 3 8B:
To find the product of 2 and 6, I will multiply them together: 2 ร 6 = 12 ### Answer: 12
Expected answer: 12
Correct? Yes
Problem: Your pet dog, Bear, can chase and bring back the ball twice every minute during your playtime. After playing for 6 minutes, how many times did Bear bring the ball back? This can be represented by 2*6. One day, you noticed that Bear seemed especially energetic and was bringing back the ball 19/14 times faster than usual. Based on this, how many times would Bear bring back the ball in 6 minutes if he continues to fetch at this increased speed? This can be represented by (19/14) * (2*6). Calculate and write your answer as a simplified fraction.
Llama 3 8B:
First, let's calculate how many times Bear brought the ball back in 6 minutes at his usual speed: 2 ร 6 = 12 So, Bear brought the ball back 12 times in 6 minutes. Now, let's calculate how many times Bear would bring the ball back in 6 minutes if he continues to fetch at the increased speed: (19/14) ร (2 ร 6) = (19/14) ร 12 = (228/14) = 16 2/7 ### Answer: 16 2/7
Expected answer: 114/7
Correct? Yes
Problem: The previous problem was about Bear bringing back the ball twice every minute while playing for 6 minutes. Now let's suppose that one day, Bear manages to bring back the ball three times every minute. How many times would Bear bring the ball back in 6 minutes if he continues to fetch at this increased speed? This can be represented by 3 * 6. Calculate the product.
Llama 3 8B:
To find the product of 3 and 6, I will multiply them together: 3 ร 6 = 18 ### Answer: 18
Expected answer: 18
Correct? Yes
Problem: Calculate the answer to the following problem: (2 / 20) * 14. Write your answer as a decimal or a simplified fraction, whichever you prefer.
Llama 3 8B:
To evaluate this expression, we need to follow the order of operations (PEMDAS): 1. Divide 2 by 20: 2 / 20 = 0.1 2. Multiply 0.1 by 14: 0.1 * 14 = 1.4 So, the answer is: ### Answer: 1.4
Expected answer: 7/5
Correct? Yes
Problem: Following up on the previous problem, now multiply your result by (7 / 2). What is the value of 'a'?
Llama 3 8B:
We already found that (2 / 20) * 14 = 1.4. Now, we need to multiply 1.4 by (7 / 2): 1.4 * (7 / 2) = 1.4 * 3.5 = 4.9 So, the value of 'a' is: ### Answer: 4.9
Expected answer: 49/10
Correct? No
Problem: In our previous problem, we calculated the result of (2 / 20) * 14. Now, let's change 2/20 to 2/12 and keep the 14 constant. Recalculate the problem with this change in initial fraction -- what is the new result?
Llama 3 8B:
Let's recalculate the problem with the new fraction: 1. Divide 2 by 12: 2 / 12 = 0.1666666666666667 (or 1/6) 2. Multiply 1/6 by 14: 1/6 * 14 = 2.33 So, the new result is: ### Answer: 2.33
Expected answer: 7/3
Correct? No
Problem: What is the result when 5/14 of a whole is multiplied by 18?
Llama 3 8B:
Reasoning: To find the result, we need to multiply 5/14 by 18. First, we can simplify the fraction 5/14 by dividing both the numerator and the denominator by their greatest common divisor, which is 1. So, the fraction remains the same. Then, we can multiply the numerator and the denominator by 18 to get: (5/14) ร 18 = (5 ร 18)/(14 ร 18) = 90/252 We can simplify the fraction 90/252 by dividing both the numerator and the denominator by their greatest common divisor, which is 18. So, the fraction becomes: 90/252 = 5/14 Therefore, the result of multiplying 5/14 by 18 is 5/14. ### Answer: 5/14
Expected answer: 45/7
Correct? No
Problem: Compute the product of 17/11 and 3, writing your answer as a decimal rounded to two decimal places.
Llama 3 8B:
Reasoning: To compute the product of 17/11 and 3, we can multiply 17/11 by 3, which gives us 17/11 * 3 = 51/11. To convert this fraction to a decimal, we can divide the numerator by the denominator, which gives us 51/11 = 4.64. Rounding this decimal to two decimal places gives us 4.64. ### Answer: 4.64
Expected answer: 51/11
Correct? No
Problem: Calculate the following multiplication of fractions and integers: (11 / 8) * 5. What is the result?
Llama 3 8B:
To calculate the multiplication of fractions and integers, we need to follow the order of operations (PEMDAS): 1. Multiply the numerator of the fraction (11) with the integer (5): 11 * 5 = 55 2. Multiply the denominator of the fraction (8) with 1 (since there is no integer part in the denominator): 8 * 1 = 8 3. Write the result as a fraction: 55/8 ### Answer: 55/8
Expected answer: 55/8
Correct? Yes
Problem: After calculating (11 / 8) * 5 in the previous problem, continue by multiplying this result by 1/5. What is the final answer?
Llama 3 8B:
We previously calculated the result of (11 / 8) * 5 as 55/8. Now, we need to multiply this result by 1/5: 1. Multiply the numerator of the fraction (55) with the denominator of the fraction (5): 55 * 1 = 55 2. Multiply the denominator of the fraction (8) with the numerator of the fraction (1): 8 * 1 = 8 3. Write the result as a fraction: 55/8 * 1/5 = 55/40 ### Answer: 55/40
Expected answer: 11/8
Correct? Yes
Problem: After calculating (11 / 8) * 5 in the previous problem, now consider the problem where instead of multiplying by 5, you multiply by 9. What happens when you calculate (11 / 8) * 9?
Llama 3 8B:
To calculate the multiplication of fractions and integers, we need to follow the order of operations (PEMDAS): 1. Multiply the numerator of the fraction (11) with the integer (9): 11 * 9 = 99 2. Multiply the denominator of the fraction (8) with 1 (since there is no integer part in the denominator): 8 * 1 = 8 3. Write the result as a fraction: 99/8 ### Answer: 99/8
Expected answer: 99/8
Correct? Yes