Fraction Division

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Answer Key & Explanations

Fraction Division · Grade 5 · Worksheet 2

1. Emma is making a large batch of cookies for a bake sale. The recipe requires 3/4 cup of chocolate chips for each batch. If she has a total of 4 1/2 cups of chocolate chips, how many full batches of cookies can Emma make? Answer: 6 Solution: Convert the mixed number to an improper fraction. Emma has 4 1/2 cups of chocolate chips. 4 1/2 = (4 * 2 + 1)/2 = 9/2 cups.
   Full step-by-step solution

   Step 1: Convert the mixed number to an improper fraction. Emma has 4 1/2 cups of chocolate chips. 4 1/2 = (4 * 2 + 1)/2 = 9/2 cups. Step 2: Each batch requires 3/4 cup of chocolate chips. To find how many batches she can make, divide the total amount by the amount per batch: (9/2) ÷ (3/4). Step 3: Dividing by a fraction is the same as multiplying by its reciprocal. So, (9/2) * (4/3). Step 4: Multiply the numerators: 9 * 4 = 36. Step 5: Multiply the denominators: 2 * 3 = 6. Step 6: This gives the fraction 36/6. Step 7: Simplify 36/6 = 6. Step 8: The problem asks for full batches, and 6 is a whole number, so Emma can make 6 full batches. The answer is 6.

2. Liam is making a recipe that requires 3/4 cup of flour for each batch. He has 4 1/2 cups of flour total. How many complete batches of the recipe can Liam make? Answer: 6 Solution: Each batch needs 3/4 cup of flour. Liam has 4 1/2 cups of flour total. Write the total flour as an improper fraction.
   Full step-by-step solution

   Let's work through the problem step by step. Step 1: Understand the problem. Each batch needs 3/4 cup of flour. Liam has 4 1/2 cups of flour total. Step 2: Write the total flour as an improper fraction. 4 1/2 = 4 + 1/2 = 8/2 + 1/2 = 9/2 cups. Step 3: We want the number of batches. Number of batches = (total flour) ÷ (flour per batch) = (9/2) ÷ (3/4) Step 4: Dividing by a fraction is the same as multiplying by its reciprocal. (9/2) ÷ (3/4) = (9/2) × (4/3) Step 5: Multiply the fractions. Multiply numerators: 9 × 4 = 36 Multiply denominators: 2 × 3 = 6 So we have 36/6. Step 6: Simplify 36/6. 36 ÷ 6 = 6. Step 7: Interpret the result. The calculation gives exactly 6, meaning Liam can make 6 complete batches with no leftover flour. Final answer: 6

3. Emma is making a large batch of cookies for a bake sale. The recipe requires 3/4 cup of chocolate chips for each batch. If she has a 5-pound bag of chocolate chips that contains 12 cups total, how many full batches of cookies can Emma make? Answer: 16 Solution: Identify what we know - Emma has 12 total cups of chocolate chips, and each batch requires 3/4 cup.
   Full step-by-step solution

   Step 1: Identify what we know - Emma has 12 total cups of chocolate chips, and each batch requires 3/4 cup. Step 2: To find how many batches she can make, divide the total amount by the amount per batch: 12 ÷ 3/4 Step 3: Dividing by a fraction is the same as multiplying by its reciprocal: 12 × 4/3 Step 4: Multiply 12 by 4: 12 × 4 = 48 Step 5: Divide 48 by 3: 48 ÷ 3 = 16 Step 6: Since the question asks for full batches, and 16 is a whole number, Emma can make 16 full batches. The answer is 16.

4. Emma is planting a garden. They have a ribbon that is 1 yard long. They need to cut the ribbon into pieces that are each 4 yard long for marking rows. How many pieces of ribbon can Emma cut? Answer: 0 Solution: The ribbon is 1 yard long. Each piece is 4 yard long. We are asking: How many 4-yard pieces fit into 1 yards?
   Full step-by-step solution

   Step 1: The ribbon is 1 yard long. Step 2: Each piece is 4 yard long. Step 3: We are asking: How many 4-yard pieces fit into 1 yards? This means 1 ÷ 4. Step 4: 1 ÷ 4 = 1/4. Since 1 < 4, this fraction is less than 1. Step 5: That means Emma can only cut 0 piece, because 1 yard is smaller than 4 yard. The answer is 0.

5. 3/5 ÷ 1/4 = ? Answer: 12/5 Solution: Write the division problem: 3/5 ÷ 1/4 Change division to multiplication by the reciprocal of the second fraction. The reciprocal of 1/4 is 4/1.
   Full step-by-step solution

   Step 1: Write the division problem: 3/5 ÷ 1/4 Step 2: Change division to multiplication by the reciprocal of the second fraction. The reciprocal of 1/4 is 4/1. Step 3: Rewrite the problem as multiplication: 3/5 × 4/1 Step 4: Multiply the numerators: 3 × 4 = 12 Step 5: Multiply the denominators: 5 × 1 = 5 Step 6: Write the answer as a fraction: 12/5 The answer is 12/5.

6. A construction crew needs to build a fence that is 750 meters long. They have completed 1/3 of the fence. How many meters of fencing have they installed so far? Answer: 250 Solution: The total length of the fence is 750 meters. The crew has completed 1/3 of the total fence. We need to find out how many meters that 1/3 represents.
   Full step-by-step solution

   Step 1: Understand the problem. The total length of the fence is 750 meters. The crew has completed 1/3 of the total fence. We need to find out how many meters that 1/3 represents. Step 2: Write the relationship. The installed length is equal to 1/3 of the total length. So, installed length = (1/3) × total length. Step 3: Substitute the total length. Total length = 750 meters. So, installed length = (1/3) × 750. Step 4: Perform the multiplication. (1/3) × 750 = 750 / 3. Step 5: Divide 750 by 3. 750 ÷ 3 = 250. Step 6: State the final answer. The crew has installed 250 meters of fencing so far.

7. Emma is making a large batch of her famous chocolate chip cookies for a school bake sale. The recipe requires 3/4 cup of brown sugar for each batch. She has a large bag containing 5 1/4 cups of brown sugar. How many complete batches of cookies can Emma make with the brown sugar she has? Answer: 7 Solution: Convert the mixed number to an improper fraction. Emma has 5 1/4 cups of brown sugar. 5 1/4 = (5 × 4 + 1)/4 = 21/4 cups.
   Full step-by-step solution

   Step 1: Convert the mixed number to an improper fraction. Emma has 5 1/4 cups of brown sugar. 5 1/4 = (5 × 4 + 1)/4 = 21/4 cups. Step 2: Each batch requires 3/4 cup of brown sugar. To find how many batches she can make, divide the total brown sugar by the brown sugar per batch: (21/4) ÷ (3/4). Step 3: Dividing by a fraction is the same as multiplying by its reciprocal. So, (21/4) ÷ (3/4) = (21/4) × (4/3). Step 4: Multiply the fractions: (21 × 4) / (4 × 3) = 84 / 12. Step 5: Simplify the fraction: 84 ÷ 12 = 7. Step 6: The problem asks for complete batches, and the result is a whole number, so Emma can make 7 complete batches. The answer is 7.

8. Liam is making a recipe that requires 3/4 cup of flour for one batch. He only has 2 1/4 cups of flour left. How many full batches of the recipe can Liam make with the flour he has? Answer: 3 Solution: Liam has 2 1/4 cups of flour. Each batch requires 3/4 cup of flour. To find how many full batches he can make, we divide the total flour by the flour per batch.
   Full step-by-step solution

   Liam has 2 1/4 cups of flour. Each batch requires 3/4 cup of flour. To find how many full batches he can make, we divide the total flour by the flour per batch. Step 1: Convert 2 1/4 to an improper fraction. 2 1/4 = 2 + 1/4 = 8/4 + 1/4 = 9/4. Step 2: Divide total flour by flour per batch: (9/4) ÷ (3/4) = 9/4 × 4/3. Step 3: Multiply the fractions: (9 × 4) / (4 × 3) = 36 / 12. Step 4: Simplify 36/12 = 3. Step 5: Since the result is exactly 3, Liam can make 3 full batches. Answer: 3

9. Liam is making a special fruit punch for a party. The recipe calls for 3/4 cup of orange juice per serving. If Liam has 6 cups of orange juice, how many full servings of fruit punch can he make? Answer: 8 Solution: We are told that each serving requires 3/4 cup of orange juice, and Liam has 6 cups of orange juice total. We need to find how many full servings can be made.
   Full step-by-step solution

   We are told that each serving requires 3/4 cup of orange juice, and Liam has 6 cups of orange juice total. Step 1: Understand the problem We need to find how many full servings can be made. This means we divide the total orange juice by the orange juice per serving. Step 2: Write the division Total cups ÷ cups per serving = number of servings 6 ÷ (3/4) = ? Step 3: Recall dividing by a fraction Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 3/4 is 4/3. So: 6 ÷ (3/4) = 6 × (4/3) Step 4: Multiply 6 × (4/3) = (6 × 4) / 3 = 24 / 3 = 8 Step 5: Interpret the result We get exactly 8, which is a whole number. This means Liam can make 8 full servings with no leftover orange juice. Step 6: Final answer Liam can make 8 full servings.