Fraction Division

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Answer Key & Explanations

Fraction Division · Grade 5 · Worksheet 2

1. Hana has a large rectangular garden that covers 6/8 of her backyard. She wants to divide this garden into smaller rectangular plots, each covering 2/8 of the backyard. How many plots can she make? Draw a picture in your mind: imagine a rectangle split into 8 equal parts, with 6 of them shaded to show the garden. How many groups of 2 shaded parts can you find? Answer: 3 Solution: We are dividing 6/8 of the backyard into plots that are each 2/8 of the backyard. This is 6/8 divided by 2/8. Rewrite the division as multiplication by the reciprocal: 6/8 divided by 2/8 equals 6/8 times 8/2.
   Full step-by-step solution

   Step 1: Understand the problem. We are dividing 6/8 of the backyard into plots that are each 2/8 of the backyard. This is 6/8 divided by 2/8. Step 2: Rewrite the division as multiplication by the reciprocal: 6/8 divided by 2/8 equals 6/8 times 8/2. Step 3: Multiply the numerators: 6 times 8 = 48. Step 4: Multiply the denominators: 8 times 2 = 16. Step 5: Simplify the fraction: 48/16 = 3. Step 6: The answer is 3 plots.

2. 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

3. 3/4 ÷ 1/6 = ? Answer: 9/2 Solution: Write the division problem: 3/4 ÷ 1/6 Change division to multiplication by the reciprocal of the second fraction. The reciprocal of 1/6 is 6/1.
   Full step-by-step solution

   Step 1: Write the division problem: 3/4 ÷ 1/6 Step 2: Change division to multiplication by the reciprocal of the second fraction. The reciprocal of 1/6 is 6/1. Step 3: Rewrite the problem as multiplication: 3/4 × 6/1 Step 4: Multiply the numerators: 3 × 6 = 18 Step 5: Multiply the denominators: 4 × 1 = 4 Step 6: Write the result as a fraction: 18/4 Step 7: Simplify the fraction by dividing numerator and denominator by 2: 18 ÷ 2 = 9, 4 ÷ 2 = 2 Step 8: The simplified answer is 9/2.

4. Liam is making a large batch of lemonade for a school event. He has 3/4 of a cup of lemon juice concentrate and needs to divide it equally among 6 pitchers. What fraction of a cup of lemon juice concentrate should he put in each pitcher? Answer: 1/8 Solution: Liam has 3/4 of a cup of lemon juice concentrate. He needs to divide it equally among 6 pitchers.
   Full step-by-step solution

   Liam has 3/4 of a cup of lemon juice concentrate. He needs to divide it equally among 6 pitchers. Step 1: Understand the operation. Dividing 3/4 cup among 6 pitchers means we need to calculate: (3/4) ÷ 6 Step 2: Dividing by a whole number is the same as multiplying by its reciprocal. So, (3/4) ÷ 6 = (3/4) × (1/6) Step 3: Multiply the numerators and denominators. Numerator: 3 × 1 = 3 Denominator: 4 × 6 = 24 So we get 3/24 Step 4: Simplify the fraction. Both 3 and 24 can be divided by 3: 3 ÷ 3 = 1 24 ÷ 3 = 8 So, 3/24 = 1/8 Therefore, Liam should put 1/8 of a cup of lemon juice concentrate in each pitcher.

5. A construction crew needs to build a fence that is 750 meters long. They have completed 2/5 of the fence. How many meters of fencing have they installed so far? Answer: 300 Solution: The total length of the fence is 750 meters. The crew has completed 2/5 of the total fence. We need to find out how many meters that 2/5 represents.
   Full step-by-step solution

   Step 1: Understand the problem. The total length of the fence is 750 meters. The crew has completed 2/5 of the total fence. We need to find out how many meters that 2/5 represents. Step 2: Write the relationship. The installed length is 2/5 of 750 meters. "Of" in math often means multiplication. So, installed length = (2/5) × 750. Step 3: Perform the multiplication. We can multiply 2/5 by 750 in two steps. First, multiply 2 × 750 = 1500. Then divide by 5: 1500 ÷ 5 = 300. Step 4: Interpret the result. The installed length is 300 meters. Step 5: Check the answer. If 300 meters is 2/5 of the total, then total should be 300 ÷ (2/5) = 300 × (5/2) = 1500/2 = 750 meters, which matches the problem. Final Answer: 300 meters of fencing have been installed.

6. Emma is making a quilt and has a piece of fabric that is 5/6 yard long. She needs to cut it into strips that are each 1/12 yard long for the border. How many strips can Emma cut from her fabric? Answer: 10 Solution: We need to find how many 1/12 yard strips fit into 5/6 yard of fabric. This is a division problem: 5/6 ÷ 1/12 To divide fractions, we multiply by the reciprocal. The reciprocal of 1/12 is 12/1.
   Full step-by-step solution

   Step 1: We need to find how many 1/12 yard strips fit into 5/6 yard of fabric. This is a division problem: 5/6 ÷ 1/12 Step 2: To divide fractions, we multiply by the reciprocal. The reciprocal of 1/12 is 12/1. Step 3: Multiply the fractions: 5/6 × 12/1 = (5 × 12)/(6 × 1) = 60/6 Step 4: Simplify the fraction: 60 ÷ 6 = 10 Step 5: Emma can cut 10 strips from her fabric. The answer is 10.

7. Emma has a ribbon that is 3/4 of a metre long. She wants to cut it into equal pieces, each 1/8 of a metre long. How many pieces can she cut? Answer: 6 Solution: Write the division problem: 3/4 divided by 1/8. To divide fractions, multiply by the reciprocal: 3/4 x 8/1. Multiply the numerators: 3 x 8 = 24.
   Full step-by-step solution

   Step 1: Write the division problem: 3/4 divided by 1/8. Step 2: To divide fractions, multiply by the reciprocal: 3/4 x 8/1. Step 3: Multiply the numerators: 3 x 8 = 24. Step 4: Multiply the denominators: 4 x 1 = 4. Step 5: Simplify: 24/4 = 6. Emma can cut 6 pieces of ribbon.

8. Emma is making a quilt for her grandmother. She has a piece of fabric that is 5/6 yard long and needs to cut it into strips that are each 1/12 yard long for the border. How many strips can Emma cut from the fabric? Answer: 10 Solution: To find how many strips Emma can cut, divide the total fabric length by the length of each strip: 5/6 ÷ 1/12 When dividing fractions, multiply by the reciprocal of the second fraction: 5/6 × 12/1 Multiply the numerators: 5 × 12 = 60 Multiply the denominators: 6 × 1 = 6 Simplify the fraction:…
   Full step-by-step solution

   Step 1: To find how many strips Emma can cut, divide the total fabric length by the length of each strip: 5/6 ÷ 1/12 Step 2: When dividing fractions, multiply by the reciprocal of the second fraction: 5/6 × 12/1 Step 3: Multiply the numerators: 5 × 12 = 60 Step 4: Multiply the denominators: 6 × 1 = 6 Step 5: Simplify the fraction: 60/6 = 10 Emma can cut 10 strips from the fabric.

9. Matiu has a piece of rope that is 4/5 of a metre long. He needs to cut it into equal pieces, each 1/10 of a metre long, to use for a craft project. How many pieces of rope will Matiu have? Answer: 8 Solution: We are sharing 4/5 of a metre into pieces that are each 1/10 of a metre. This is 4/5 divided by 1/10. Rewrite the division as multiplication by the reciprocal.
   Full step-by-step solution

   Step 1: Understand the problem. We are sharing 4/5 of a metre into pieces that are each 1/10 of a metre. This is 4/5 divided by 1/10. Step 2: Rewrite the division as multiplication by the reciprocal. 4/5 divided by 1/10 equals 4/5 times 10/1. Step 3: Multiply the numerators: 4 times 10 = 40. Step 4: Multiply the denominators: 5 times 1 = 5. Step 5: Simplify the fraction: 40/5 = 8. Step 6: The answer is 8 pieces of rope.