Fraction Division

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Answer Key & Explanations

Fraction Division · Grade 5 · Worksheet 1

1. Matiu has 3 cups of flour. A recipe for one batch of cookies uses 3 cup of flour. How many batches of cookies can Matiu make? Answer: 1 Solution: We need to find how many 3-cup portions fit into 3 cups. This is division: 3 ÷ 3 = 3 ÷ 3. 3 ÷ 3 = 1.
   Full step-by-step solution

   Step 1: We need to find how many 3-cup portions fit into 3 cups. Step 2: This is division: 3 ÷ 3 = 3 ÷ 3. Step 3: 3 ÷ 3 = 1. The answer is 1 batches.

2. 2/3 ÷ 1/5 = ? Answer: 10/3 Solution: Write the division problem: 2/3 ÷ 1/5 Change division to multiplication by the reciprocal of the second fraction. The reciprocal of 1/5 is 5/1.
   Full step-by-step solution

   Step 1: Write the division problem: 2/3 ÷ 1/5 Step 2: Change division to multiplication by the reciprocal of the second fraction. The reciprocal of 1/5 is 5/1. Step 3: Rewrite the problem as multiplication: 2/3 × 5/1 Step 4: Multiply the numerators: 2 × 5 = 10 Step 5: Multiply the denominators: 3 × 1 = 3 Step 6: Write the resulting fraction: 10/3 The answer is 10/3.

3. 5/6 ÷ 2/3 = ? Answer: 5/4 Solution: Write the division problem: 5/6 ÷ 2/3 Change division to multiplication by the reciprocal of the second fraction: 5/6 × 3/2 Multiply the numerators: 5 × 3 = 15 Multiply the denominators: 6 × 2 = 12 Write the resulting fraction: 15/12 Simplify the fraction by dividing numerator and denominator by…
   Full step-by-step solution

   Step 1: Write the division problem: 5/6 ÷ 2/3 Step 2: Change division to multiplication by the reciprocal of the second fraction: 5/6 × 3/2 Step 3: Multiply the numerators: 5 × 3 = 15 Step 4: Multiply the denominators: 6 × 2 = 12 Step 5: Write the resulting fraction: 15/12 Step 6: Simplify the fraction by dividing numerator and denominator by 3: 15 ÷ 3 = 5, 12 ÷ 3 = 4 Step 7: The simplified fraction is 5/4 The answer is 5/4.

4. 8/9 ÷ 2/3 = ? Answer: 4/3 Solution: Write the division problem: 8/9 ÷ 2/3 Change division to multiplication by the reciprocal of the second fraction. The reciprocal of 2/3 is 3/2.
   Full step-by-step solution

   Step 1: Write the division problem: 8/9 ÷ 2/3 Step 2: Change division to multiplication by the reciprocal of the second fraction. The reciprocal of 2/3 is 3/2. Step 3: Rewrite the problem as multiplication: 8/9 × 3/2 Step 4: Multiply the numerators: 8 × 3 = 24 Step 5: Multiply the denominators: 9 × 2 = 18 Step 6: Simplify the fraction: 24/18 = 4/3 The answer is 4/3.

5. 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.

6. 5/7 ÷ 1/3 = ? Answer: 15/7 Solution: Write the division problem: 5/7 ÷ 1/3 Change division to multiplication by the reciprocal of the second fraction. The reciprocal of 1/3 is 3/1.
   Full step-by-step solution

   Step 1: Write the division problem: 5/7 ÷ 1/3 Step 2: Change division to multiplication by the reciprocal of the second fraction. The reciprocal of 1/3 is 3/1. Step 3: Rewrite the problem as multiplication: 5/7 × 3/1 Step 4: Multiply the numerators: 5 × 3 = 15 Step 5: Multiply the denominators: 7 × 1 = 7 Step 6: Write the result as a fraction: 15/7 The answer is 15/7.

7. 3/4 ÷ 1/5 = ? Answer: 15/4 Solution: Write the division problem: 3/4 ÷ 1/5 Change division to multiplication by the reciprocal of the second fraction. The reciprocal of 1/5 is 5/1.
   Full step-by-step solution

   Step 1: Write the division problem: 3/4 ÷ 1/5 Step 2: Change division to multiplication by the reciprocal of the second fraction. The reciprocal of 1/5 is 5/1. Step 3: Rewrite the problem as multiplication: 3/4 × 5/1 Step 4: Multiply the numerators: 3 × 5 = 15 Step 5: Multiply the denominators: 4 × 1 = 4 Step 6: Write the answer as a fraction: 15/4 The answer is 15/4.

8. 3/4 ÷ 2/3 = ? Answer: 9/8 Solution: To divide fractions, we use the rule: dividing by a fraction is the same as multiplying by its reciprocal. Write down the problem. 3/4 ÷ 2/3 Change the division to multiplication by the reciprocal of the second fraction.
   Full step-by-step solution

   To divide fractions, we use the rule: dividing by a fraction is the same as multiplying by its reciprocal. Step 1: Write down the problem. 3/4 ÷ 2/3 Step 2: Change the division to multiplication by the reciprocal of the second fraction. The reciprocal of a fraction is created by swapping its numerator and denominator. The reciprocal of 2/3 is 3/2. So the problem becomes: 3/4 × 3/2 Step 3: Multiply the fractions. To multiply fractions, multiply the numerators together and multiply the denominators together. Numerator: 3 × 3 = 9 Denominator: 4 × 2 = 8 This gives us the new fraction: 9/8 Step 4: Check if the fraction can be simplified. 9/8 is already in its simplest form because 9 and 8 have no common factors other than 1. Therefore, the final answer is 9/8.

9. Mason is making a model sailboat. He has a rectangular piece of fabric that is 7/12 of a square yard. He wants to cut the fabric into equal square pieces, each with an area of 1/12 of a square yard, to use as sails. How many square pieces of fabric can Mason cut? Imagine the fabric as a rectangle divided into 12 equal smaller squares. Only 7 of those squares are shaded to show the fabric he has. Answer: 7 Solution: Mason has 7/12 of a square yard of fabric and wants to cut it into pieces that are each 1/12 of a square yard. This is 7/12 divided by 1/12. Write the division problem: 7/12 divided by 1/12.
   Full step-by-step solution

   Step 1: Understand the problem. Mason has 7/12 of a square yard of fabric and wants to cut it into pieces that are each 1/12 of a square yard. This is 7/12 divided by 1/12. Step 2: Write the division problem: 7/12 divided by 1/12. Step 3: To divide fractions, multiply by the reciprocal of the second fraction. The reciprocal of 1/12 is 12/1. So, 7/12 divided by 1/12 = 7/12 times 12/1. Step 4: Multiply the numerators: 7 times 12 = 84. Step 5: Multiply the denominators: 12 times 1 = 12. Step 6: Simplify the fraction: 84/12 = 7. Step 7: Mason can cut 7 square pieces of fabric.