Gemma 2B on 5.NF.B.4
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.
Gemma 2B:
Reasoning: 8/9 x 19/3 = (8 x 19) / (9 x 3) = 152/27 = 4.44... The product of 8/9 and 19/3 is 4.44...
Expected answer: 152/27
Correct? No
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.
Gemma 2B:
Reasoning: The usable part of each section of rope is 13/2 x 5/7 = <<13/2 x 5/7= 5>>5 feet. ### Answer: 5
Expected answer: 65/14
Correct? No
Problem: What is the result when you multiply the whole number 12 by 1?
Gemma 2B:
Reasoning: 12 x 1 = <<12 x 1=12>>12. ### 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.
Gemma 2B:
### Answer: 0.75
Expected answer: 21/4
Correct? No
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?
Gemma 2B:
### 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.
Gemma 2B:
Reasoning: 14/15 * 12/4 = (14 * 12) / (15 * 4) = 168/60 = 4/5. The final answer is 4/5.
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.
Gemma 2B:
Reasoning: 15 * (5/17) = 75/17. The final answer is 4.37.
Expected answer: 75/17
Correct? No
Problem: Find the result of the following calculation: 16 * (12 / 19)
Gemma 2B:
Reasoning: 16 * (12/19) = 16 * 4/19 = 64/19 = 3.42. ### Answer: 3.42
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.
Gemma 2B:
Reasoning: 10/17 * 18/5 = <<(10/17) * (18/5) = 36/85>>36/85. The farmer will have 36/85 barrels of apples in total.
Expected answer: 36/17
Correct? No
Problem: Simplify the expression: (20 / 4) * (1 / 5). What is the result?
Gemma 2B:
Reasoning: First, we calculate 20/4 = 5. Then, we calculate 1/5. The result is 5/5 = 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?
Gemma 2B:
### Answer: 64
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?
Gemma 2B:
Reasoning: Julia filled 8/11 of 11 boxes with apples, which is equal to 8 boxes. Therefore, Julia used 8 boxes worth of apples in total.
Expected answer: 8
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.
Gemma 2B:
Reasoning: 9/4 = 16/15. 9/4 * 15/16 = 120/64 = 1.5. The baker will use 1.5 cups of sugar in total. ### Answer: 1.5
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.
Gemma 2B:
Reasoning: 19/9 * 14/18 = <<(19/9)*(14/18)=19/9>>19/9 cups of ingredients in total.
Expected answer: 133/81
Correct? No
Problem: What is the result when you multiply the fractions 14/7 and 16/4?
Gemma 2B:
Answer: 14/7 * 16/4 = 224/28 = 8
Expected answer: 8
Correct? Yes
Problem: Calculate the result of (17 / 18) multiplied by (13 / 8). Write the answer as a simplified fraction.
Gemma 2B:
Reasoning: (17/18) * (13/8) = (17 * 13) / (18 * 8) = 231/144. ### Answer: 1.68
Expected answer: 221/144
Correct? No
Problem: Evaluate the following expression: ((15 / 15) * 18) and write your answer.
Gemma 2B:
Reasoning: 15/15 = 1, so the expression is equal to 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?
Gemma 2B:
### Answer: 135/16
Expected answer: 135/8
Correct? No
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?
Gemma 2B:
Reasoning: Each student will eat 17/20 of a pizza, which is equivalent to 0.85 pizzas. Therefore, 18 students will need 18 x 0.85 = <<18 x 0.85=15.6>>15.6 pizzas to order. ### Answer: 15.6
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.
Gemma 2B:
### Answer: 35
Expected answer: 9/2
Correct? No
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?
Gemma 2B:
Reasoning: John bought 2 * 6/8 = <<2 * 6/8=1>>1 dozen cookies in total. ### Answer: 1
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?
Gemma 2B:
Reasoning: 6 gallons is 100% of 16/17 of 6. Therefore, Tom can store 100% of 16/17 of 6 = 16 gallons of paint in the box. ### Answer: 16
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?
Gemma 2B:
Reasoning: After giving away 4/10 of 14 marbles, Mary has 14 - (14 x 4/10) = 14 - 7 = <<14-7=7>>7 marbles left. ### Answer: 7
Expected answer: 28/5
Correct? No
Problem: Calculate the product of 19/6 and 4/4. Write the resulting answer as a simplified fraction.
Gemma 2B:
Reasoning: 19/6 = <<19/6=3.25>>3.25 and 4/4 = 1. The product of 19/6 and 4/4 is 3.25 * 1 = 3.25. ### Answer: 3.25
Expected answer: 19/6
Correct? No
Problem: What is the result when you divide 16 by 8 and then multiply the result by 10?
Gemma 2B:
Reasoning: 16 ÷ 8 = <<16 ÷ 8=2>>2. Multiplying 2 by 10 = <<2 x 10=20>>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?
Gemma 2B:
Reasoning: 20 x 1/17 = <<20 x 1/17=1.15>>1.15. ### Answer: 1.15
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?
Gemma 2B:
### 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.
Gemma 2B:
Reasoning: 18 x 1/11 = 1.73. The final answer is 1.73.
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?
Gemma 2B:
Reasoning: Since each tree produces 3 apples, and only half of the trees produce apples, Mary will harvest 3/2 * 6 = <<3/2 * 6=9>>9 apples from her garden this year. ### 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.
Gemma 2B:
Reasoning: (13/10) * (14/11) = (13 * 14) / (10 * 11) = 182/110. ### Answer: 1.73
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.
Gemma 2B:
Reasoning: 20 x 2/19 = <<20x2/19=4>>4 meters of thread in total. ### Answer: 4
Expected answer: 40/19
Correct? No
Problem: What is the result of 1 times 16?
Gemma 2B:
Reasoning: 1 x 16 = <<1x16=16>>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?
Gemma 2B:
### Answer: 16/11
Expected answer: 32/11
Correct? No
Problem: If instead of 16, you were to multiply 1 by 11. What would the result be?
Gemma 2B:
### 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.
Gemma 2B:
Reasoning: 18/12 = <<18/12=0.15>>0.15, which is equivalent to 3/6. Therefore, (18/12) * 6 = 3.
Expected answer: 9
Correct? No
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?
Gemma 2B:
### Answer: 13
Expected answer: 13
Correct? Yes
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.
Gemma 2B:
Reasoning: If each block was 16/18th of a foot long, then 16/7th of a foot long blocks would be 16/7 * 1/2 = 8/7 of a foot long. Therefore, Mathew would use 8/7 of a foot long blocks for his craft project. ### Answer: 8/7
Expected answer: 128/63
Correct? No
Problem: What is the result when you multiply the fraction 8/8 by 15?
Gemma 2B:
Answer: 120 Reasoning: 8/8 = 1, so 8/8 x 15 = 15.
Expected answer: 15
Correct? No
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?
Gemma 2B:
Reasoning: 10 x 4/6 = <<10 x 4/6=4>>4 apples. Therefore, you have 4 apples if you multiply 10 apples by 4/6.
Expected answer: 20/3
Correct? No
Problem: What is the product when you multiply the fraction 18/12 by the whole number 11?
Gemma 2B:
Reasoning: 18/12 = <<18/12=3/2>>3/2. The product is 3/2 * 11 = <<3/2 * 11=11/2>>11/2. ### Answer: 11/2
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?
Gemma 2B:
Reasoning: The chef can make 16/9/20 = <<16/9/20=0.8>>0.8 mushroom pizzas before they sell out. ### Answer: 0.8
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.
Gemma 2B:
Reasoning: s = (16 * (5 / 12)) = 16 * 5/12 = 5 kg. ### Answer: 5
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.
Gemma 2B:
Reasoning: 13 x 3/12 = <<13 x 3/12 =0.4166...>>0.4166... The result of the calculation is 0.4166...
Expected answer: 13/4
Correct? No
Problem: Find the product when 8 is multiplied by 1. Show your work and provide your answer.
Gemma 2B:
Reasoning: 8 x 1 = <<8 x 1=8>>8. The product of 8 and 1 is 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.
Gemma 2B:
Reasoning: 8 x 1 = <<8 x 1=8>>8. 8 x 2 = <<8 x 2=16>>16. The final result of 8 multiplied by 1 and multiplied by 2 is 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.
Gemma 2B:
Reasoning: 16 x 1 = <<16 x 1=16>>16. The final result is 16.
Expected answer: 16
Correct? Yes
Problem: What is the result when you multiply 9 by the fraction 9/17?
Gemma 2B:
Reasoning: 9/17 is the same as 0.555... when expressed as a decimal. Therefore, 9 * 0.555... = 4.99... ### Answer: 4.99...
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?
Gemma 2B:
Reasoning: Each friend will get 12/13 of 13 = 12 boxes. Tom's friends will receive 13 * 12 = <<13 * 12 = 168>>168 boxes in total. ### Answer: 168
Expected answer: 12
Correct? No
Problem: What is the product of multiplying 16 and 1?
Gemma 2B:
Answer: 16 x 1 = 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.
Gemma 2B:
Answer: 16 x (1/3/8) = 16 x 8/3 = 64/3 = 21.33
Expected answer: 6
Correct? No
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?
Gemma 2B:
Answer: 15 x 1 = 15
Expected answer: 15
Correct? Yes
Problem: Multiply 10 by the fraction 11/10. What is the result?
Gemma 2B:
Reasoning: 10 x 11/10 = 11. Therefore, 11/10 = 11.
Expected answer: 11
Correct? Yes
Problem: Calculate the product of 10 and the fraction 8/14. Write your answer as a simplified fraction or a decimal.
Gemma 2B:
Reasoning: 10 x 8/14 = 80/14 = 5. The final answer is 5.
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?
Gemma 2B:
Reasoning: John has graded 20 x 8/18 = <<20 x 8/18=8>>8 papers. ### Answer: 8
Expected answer: 80/9
Correct? No
Problem: Calculate the result of multiplying 16 by the fraction 13/12.
Gemma 2B:
Reasoning: 16 x 13/12 = <<16 x 13/12 = 160/120>>160/120. Therefore, 16 x 13/12 = 160/120.
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?
Gemma 2B:
Reasoning: If 16 is divided by 2/19, we get that each part is 8 units long. ### Answer: 8
Expected answer: 32/19
Correct? No
Problem: What is the result of multiplying the fraction twelve divided by twelve with the whole number sixteen?
Gemma 2B:
Reasoning: 12/12 x 16 = 1. Therefore, 12/12 x 16 = 1. ### Answer: 1
Expected answer: 16
Correct? No
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?
Gemma 2B:
Reasoning: 8/7th of a pound of clay per model = 8/7 * 1 = 8/7 pounds of clay per model. 17/3rd models = 17/3 * 1 = 51/3 pounds of clay. Amount of clay in pounds = 8/7 + 51/3 = (56+49)/21 = 105/21 = 5.19. ### Answer: 5.19
Expected answer: 136/21
Correct? No
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.
Gemma 2B:
Reasoning: If she makes 2 pies, she will spend 2 * 14/12 = <<2*14/12=7>>7 hours preparing and baking each pie. Therefore, Mrs. Parker will spend 7 hours making 2 pies.
Expected answer: 7/3
Correct? No
Problem: Evaluate the following expression and write your answer as a simplified fraction: (18/11) * (17/8)
Gemma 2B:
Reasoning: (18/11) * (17/8) = (18 * 17) / (11 * 8) = 34/88 = 7/22.
Expected answer: 153/44
Correct? No
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?
Gemma 2B:
Reasoning: Each apple costs $2, and half an apple costs half of $2, which is $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?
Gemma 2B:
Reasoning: Each banana costs $2, and 7/10 of a banana is 7/10 * 2 = <<7/10 * 2 = 7/5>>7/5 bananas. Therefore, the cost of the portion of banana you consume is 7/5 * $2 = <<7/5 * $2 = $14/5>>$14/5. ### Answer: $14/5
Expected answer: 7/5
Correct? No
Problem: What is the product when you multiply 1 by 8?
Gemma 2B:
Answer: 8 Reasoning: 1 x 8 = <<1x8=8>> which is the product when you multiply 1 by 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?
Gemma 2B:
Answer: 0.125 Reasoning: 1 x 8/9 = <<1x8/9=0.88>>0.88 which is the product when you multiply 1 by 8/9.
Expected answer: 9
Correct? No
Problem: If instead of multiplying 1 by 8, we multiply 1 by 6, what would the new product be?
Gemma 2B:
Answer: 6 Reasoning: 1 x 6 = <<1x6=6>> which is the product when you multiply 1 by 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)
Gemma 2B:
### Answer: 7
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.
Gemma 2B:
Reasoning: (9 / 10) * 3 = <<(9 / 10) * 3 = 0.9 * 3 = 2.7>>2.7 cups of sugar will William need. ### Answer: 2.7
Expected answer: 27/10
Correct? Yes
Problem: Compute the following operation: multiply 9 by 5/14. Write your answer as a simplified fraction.
Gemma 2B:
Reasoning: 9 * 5/14 = (9 * 5) / (14) = 45/14. ### Answer: 3.125
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)?
Gemma 2B:
Reasoning: He should use 12/16 * 15/6 = <<(12/16) * (15/6)=3/2>>3/2 of the old recipe. ### Answer: 3/2
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?
Gemma 2B:
Reasoning: The baker uses 9 x 19/19 = <<9x19/19=18>>18 pounds of flour for the cake. ### Answer: 18
Expected answer: 9
Correct? No
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.
Gemma 2B:
Reasoning: If one recipe needs 9/4 cups of sugar, then 5 times that amount would be 5 * 9/4 = <<5 * 9/4=45/4>>45/4 cups of sugar. ### 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?
Gemma 2B:
Reasoning: Julia needs 12/8 = <<12/8=1.5>>1.5 cups of flour for the portion of the recipe she is making. ### Answer: 1.5
Expected answer: 27/26
Correct? No
Problem: Calculate the following expression: 9 * (20/11). Write the answer as a mixed number.
Gemma 2B:
Reasoning: 9 * (20/11) = 9 * 20/11 = 180/11. ### Answer: 18.09
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.
Gemma 2B:
Reasoning: 20 ÷ 5 = <<20 ÷ 5=4>>4. Multiplying 4 by 6/10 = <<4 × 6/10=0.6>>0.6. Therefore, the answer is 0.6.
Expected answer: 12/5
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?
Gemma 2B:
Reasoning: 5/14 of 17 = <<5/14 * 17 = 5>>5 classrooms forgot to recycle their papers. ### Answer: 5
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.
Gemma 2B:
Reasoning: (19 / 11) * (13 / 17) = (19 * 13) / (11 * 17) = 243 / 196. ### Answer: 1.25
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?
Gemma 2B:
Reasoning: 9 * 3/11 = <<9*3/11=3>>3 feet of rope is used to secure the tent. ### Answer: 3
Expected answer: 27/11
Correct? No
Problem: What is the result of the multiplication when 1 is multiplied by 7?
Gemma 2B:
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?
Gemma 2B:
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?
Gemma 2B:
Answer: 19
Expected answer: 19
Correct? Yes
Problem: Find the product of the following calculation: 1 times 9.
Gemma 2B:
Reasoning: 1 x 9 = <<1x9=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?
Gemma 2B:
### Answer: 0.55
Expected answer: 13/2
Correct? No
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?
Gemma 2B:
### 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.
Gemma 2B:
Reasoning: The product of the fractions is (18/18) * (11/5) = 1.88. The final answer is 1.88.
Expected answer: 11/5
Correct? No
Problem: Calculate the answer for the following equation: (5 / 16) * 13. Please express your answer as a decimal.
Gemma 2B:
Reasoning: (5/16) * 13 = 5/16 * 13 = 0.8125. ### Answer: 0.8125
Expected answer: 65/16
Correct? No
Problem: Find the result of the following calculation: Multiply the fraction 4/5 by the whole number 15. Write your answer in simplest form.
Gemma 2B:
Reasoning: 4/5 = 4/5. 4/5 x 15 = <<4/5 x 15=60>>60. ### Answer: 60
Expected answer: 12
Correct? No
Problem: What will be the result if you multiply the fraction 20/12 by the fraction 19/16?
Gemma 2B:
Reasoning: The fractions 20/12 and 19/16 are equivalent, meaning they have the same value. Therefore, 20/12 x 19/16 = <<20/12 x 19/16 =1>>1. ### Answer: 1
Expected answer: 95/48
Correct? No
Problem: Calculate the result of the following multiplication operation: 17/20 * 17/13. Write your answer as a simplified fraction.
Gemma 2B:
Reasoning: 17/20 * 17/13 = <<17/20 * 17/13=1>>1. ### Answer: 1
Expected answer: 289/260
Correct? No
Problem: Solve the following problem: 5 * (13 / 12) and give your answer in the form of a mixed number or fraction where necessary.
Gemma 2B:
Reasoning: 5 * (13/12) = 5/12 * 13 = 65/12. Therefore, 5 * (13/12) = 65/12.
Expected answer: 65/12
Correct? Yes
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?
Gemma 2B:
Reasoning: Jack ate 3/4 of 1 bar = <<(3/4)*1=0.75>>0.75 pieces. ### Answer: 0.75
Expected answer: 3
Correct? No
Problem: Calculate the product of 17 and 9/18 without simplifying the fraction. What is the result?
Gemma 2B:
Reasoning: 17 x 9/18 = 153/18. The final answer is 153/18.
Expected answer: 17/2
Correct? Yes
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.
Gemma 2B:
Reasoning: 15/15 x 19 = 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.
Gemma 2B:
### Answer: 0.6
Expected answer: 57/5
Correct? No
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.
Gemma 2B:
### Answer: 15
Expected answer: 20
Correct? No
Problem: Mary has 16 apples. She shares 3/5 of them with her friends. How many apples does Mary share with her friends?
Gemma 2B:
Reasoning: 3/5 of 16 = <<3/5 * 16= 16 * 0.6>> 8 apples. Mary shares 8 apples with her friends.
Expected answer: 48/5
Correct? No
Problem: What is the product when you divide 12 by 3 and then multiply the result by 3?
Gemma 2B:
Reasoning: 12 ÷ 3 = <<12 ÷ 3=4>>4, and 4 × 3 = <<4 × 3=12>>12. Therefore, the product is 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?
Gemma 2B:
### Answer: 6
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.
Gemma 2B:
Reasoning: Each box contains 12/8 = 3 whole pieces of chocolate. There are 6 boxes, so there are 6 * 3 = <<6 * 3=18>>18 whole pieces of chocolate in total. ### Answer: 18
Expected answer: 9
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)
Gemma 2B:
Reasoning: She spent 10/19 * 14/7 = <<10/19 * 14/7=70/147>>70/147 of her weekly allowance on Tuesday. ### Answer: 70/147
Expected answer: 20/19
Correct? No
Problem: What is the product of 2 and 2?
Gemma 2B:
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?
Gemma 2B:
Answer: 5
Expected answer: 10
Correct? No
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?
Gemma 2B:
Reasoning: Each box has 8/5 = <<8/5=16/10>>16/10 dozen cookies. There are 48 boxes, so there are 48 * 16/10 = <<48*16/10=832>>832 dozens of cookies in total.
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.
Gemma 2B:
Reasoning: 6/18 = 1/3, so 1/3 * 3 = 1. Therefore, 6/18 * 3 = 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.
Gemma 2B:
### 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.
Gemma 2B:
### Answer: 17
Expected answer: 17/6
Correct? No
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.
Gemma 2B:
Reasoning: Lucy gave 5 bags to her friends, each bag containing 18 / 8 = <<18/8=2.25>>2.25 candies. Therefore, Lucy gave 5 * 2.25 = <<5 * 2.25=11.25>>11.25 candies away in total. ### Answer: 11.25
Expected answer: 45/4
Correct? Yes
Problem: Calculate the following multiplication of a whole number and a fraction. What is the result of 5 * (14 / 10)?
Gemma 2B:
Reasoning: 5 * (14 / 10) = 5 * 14/10 = 70/10 = 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?
Gemma 2B:
### Answer: 70/6 = 11.66...
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?
Gemma 2B:
### Answer: 7
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.
Gemma 2B:
Reasoning: 6 x (20/7) = (6 x 20) / (6 x 7) = 120/42 = 2 1/7. ### Answer: 2 1/7
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.
Gemma 2B:
Reasoning: 8/19 x 6 = (8 x 6) / (19 x 6) = 48/114. The product of 8/19 times 6 is 48/114.
Expected answer: 48/19
Correct? No
Problem: Calculate the answer to the following problem. What is the result of multiplying 8 by 1/1?
Gemma 2B:
Reasoning: 8 x 1/1 = 8. The result of multiplying 8 by 1/1 is 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?
Gemma 2B:
### Answer: 12 Reasoning: 8 x (1/1) x (3/2) = 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?
Gemma 2B:
### 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.
Gemma 2B:
Reasoning: Each piece is 5/15 = <<5/15>>0.1 meters long. The total length of all the 9 pieces is 9 * 0.1 = <<9 * 0.1=0.9>>0.9 meters. ### Answer: 0.9
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.
Gemma 2B:
### Answer: 13 feet
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.
Gemma 2B:
### Answer: 8 feet
Expected answer: 52/5
Correct? No
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.
Gemma 2B:
Reasoning: 6/5 = 6/5. Multiplying 6/5 by 1 results in 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.
Gemma 2B:
### Answer: 6
Expected answer: 36/25
Correct? No
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.
Gemma 2B:
Reasoning: 5/5 = 1, so 5/5 x 17/6 = 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.
Gemma 2B:
### Answer: 1
Expected answer: 1
Correct? Yes
Problem: What is the result of multiplying 8 by the result of 8 divided by 6?
Gemma 2B:
Reasoning: 8 * (8/6) = 8 * 1.67 = 13.36. ### Answer: 13.36
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?
Gemma 2B:
Reasoning: 9/16. Susan used 9/16 of the 9 apples to make the pie. ### Answer: 9/16
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).
Gemma 2B:
### Answer: 80
Expected answer: 40/7
Correct? No
Problem: What is the product of the fraction 3/3 and the mixed number 13/4? Write your answer as a simplified fraction.
Gemma 2B:
Reasoning: 3/3 = 1, and 13/4 is already a simplified fraction. The product of 1 and 13/4 is 13/4. ### Answer: 13/4
Expected answer: 13/4
Correct? Yes
Problem: Given the original question, but now let's consider a change in quantity. Instead of multiplying 13/4 with 3/3. Now assume you're multiplying 18/4 by 3/3. What would be the product of these numbers now? Write your answer as a simplified fraction.
Gemma 2B:
Reasoning: 18/4 divided by 3/3 is 6, which is also a simplified fraction. The product of 18/4 and 3/3 is 6. ### Answer: 6
Expected answer: 9/2
Correct? No
Problem: Calculate the result of multiplying thirteen by the ratio of two to two.
Gemma 2B:
Reasoning: The ratio of two to two is 2/2. 13 * (2/2) = 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?
Gemma 2B:
Reasoning: The fraction eight fourteenths is 8/14. 13 * (8/14) = 13 * 8/14 = 13. ### Answer: 13
Expected answer: 52/7
Correct? No
Problem: Calculate the value of the expression 17/6 * 6/4. Write your answer in the simplest form.
Gemma 2B:
Reasoning: 17/6 * 6/4 = 17/4 = 4.25. ### Answer: 4.25
Expected answer: 17/4
Correct? Yes
Problem: Find the product of 2 and 6.
Gemma 2B:
Reasoning: 2 x 6 = <<2x6=12>>12. The product of 2 and 6 is 12.
Expected answer: 12
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.
Gemma 2B:
Reasoning: 2/20 = 0.1, and 0.1 * 14 = <<0.1 * 14 = 1.4>>1.4. ### Answer: 1.4
Expected answer: 7/5
Correct? Yes
Problem: What is the result when 5/14 of a whole is multiplied by 18?
Gemma 2B:
Reasoning: 5/14 of a whole is equal to 5/14 of 14 = 1. 1 * 18 = 18. ### Answer: 18
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.
Gemma 2B:
Reasoning: 17/11 = 1.73, and 3 = 0.00. The product of 17/11 and 3 is 0.051.
Expected answer: 51/11
Correct? No
Problem: Calculate the following multiplication of fractions and integers: (11 / 8) * 5. What is the result?
Gemma 2B:
Reasoning: (11 / 8) * 5 = (11/8) * 5/1 = 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?
Gemma 2B:
### Answer: 11
Expected answer: 11/8
Correct? No
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?
Gemma 2B:
### Answer: 99/8
Expected answer: 99/8
Correct? Yes