Fraction ÷ Whole

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Answer Key & Explanations

Fraction ÷ Whole · Grade 5 · Worksheet 3

1. 3/4 ÷ 6 = ? Answer: 1/8 Solution: Write the problem: 3/4 ÷ 6 Dividing by 6 is the same as multiplying by 1/6, so rewrite as: 3/4 × 1/6 Multiply the numerators: 3 × 1 = 3 Multiply the denominators: 4 × 6 = 24 The result is 3/24 Simplify the fraction by dividing numerator and denominator by 3: 3 ÷ 3 = 1, 24 ÷ 3 = 8 The simplified…
   Full step-by-step solution

   Step 1: Write the problem: 3/4 ÷ 6 Step 2: Dividing by 6 is the same as multiplying by 1/6, so rewrite as: 3/4 × 1/6 Step 3: Multiply the numerators: 3 × 1 = 3 Step 4: Multiply the denominators: 4 × 6 = 24 Step 5: The result is 3/24 Step 6: Simplify the fraction by dividing numerator and denominator by 3: 3 ÷ 3 = 1, 24 ÷ 3 = 8 Step 7: The simplified fraction is 1/8 The answer is 1/8.

2. Liam is making fruit punch for a party and needs to divide 3/4 of a gallon of orange juice equally among 6 pitchers. What fraction of a gallon of orange juice should go into each pitcher? Answer: 1/8 Solution: We start with the problem: Liam has 3/4 of a gallon of orange juice and wants to divide it equally among 6 pitchers. Dividing 3/4 gallon among 6 pitchers means we need to perform: 3/4 ÷ 6. Write 6 as a fraction.
   Full step-by-step solution

   We start with the problem: Liam has 3/4 of a gallon of orange juice and wants to divide it equally among 6 pitchers. Step 1: Understand the operation. Dividing 3/4 gallon among 6 pitchers means we need to perform: 3/4 ÷ 6. Step 2: Write 6 as a fraction. 6 is the same as 6/1, so: 3/4 ÷ 6/1. Step 3: Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 6/1 is 1/6. So: 3/4 × 1/6. Step 4: Multiply the fractions. Multiply the numerators: 3 × 1 = 3. Multiply the denominators: 4 × 6 = 24. So we get 3/24. Step 5: Simplify the fraction. 3 and 24 have a common factor of 3. Divide numerator and denominator by 3: 3 ÷ 3 = 1, 24 ÷ 3 = 8. So 3/24 simplifies to 1/8. Step 6: Conclusion. Each pitcher gets 1/8 of a gallon of orange juice. Final answer: 1/8

3. 7/8 ÷ 5 = ? Answer: 7/40 Solution: Write the problem: 7/8 ÷ 5 Write the whole number as a fraction: 7/8 ÷ 5/1 Change division to multiplication by the reciprocal: 7/8 × 1/5 Multiply the numerators: 7 × 1 = 7 Multiply the denominators: 8 × 5 = 40 Write the result: 7/40 The answer is 7/40.
   Full step-by-step solution

   Step 1: Write the problem: 7/8 ÷ 5 Step 2: Write the whole number as a fraction: 7/8 ÷ 5/1 Step 3: Change division to multiplication by the reciprocal: 7/8 × 1/5 Step 4: Multiply the numerators: 7 × 1 = 7 Step 5: Multiply the denominators: 8 × 5 = 40 Step 6: Write the result: 7/40 The answer is 7/40.

4. 7/9 ÷ 8 = ? Answer: 7/72 Solution: Write the division problem: 7/9 ÷ 8 Rewrite the whole number as a fraction: 7/9 ÷ 8/1 Change division to multiplication by the reciprocal: 7/9 × 1/8 Multiply the numerators: 7 × 1 = 7 Multiply the denominators: 9 × 8 = 72 Write the result: 7/72 The answer is 7/72.
   Full step-by-step solution

   Step 1: Write the division problem: 7/9 ÷ 8 Step 2: Rewrite the whole number as a fraction: 7/9 ÷ 8/1 Step 3: Change division to multiplication by the reciprocal: 7/9 × 1/8 Step 4: Multiply the numerators: 7 × 1 = 7 Step 5: Multiply the denominators: 9 × 8 = 72 Step 6: Write the result: 7/72 The answer is 7/72.

5. A rectangular community garden is divided into 12 equal plots. The gardeners have planted vegetables in 3/4 of the entire garden. How many plots contain vegetables? Answer: 9 Solution: The garden has 12 equal plots total. The fraction of the garden planted with vegetables is 3/4.
   Full step-by-step solution

   Step 1: The garden has 12 equal plots total. Step 2: The fraction of the garden planted with vegetables is 3/4. Step 3: To find how many plots this represents, multiply the total plots by the fraction: 12 × 3/4 Step 4: Calculate 12 × 3 = 36 Step 5: Then divide by 4: 36 ÷ 4 = 9 Step 6: Therefore, 9 plots contain vegetables.

6. 3/4 ÷ 5 = ? Answer: 3/20 Solution: Write the division as a multiplication by the reciprocal: 3/4 ÷ 5 = 3/4 × 1/5 Multiply the numerators: 3 × 1 = 3 Multiply the denominators: 4 × 5 = 20 Combine the results: 3/20 The answer is 3/20.
   Full step-by-step solution

   Step 1: Write the division as a multiplication by the reciprocal: 3/4 ÷ 5 = 3/4 × 1/5 Step 2: Multiply the numerators: 3 × 1 = 3 Step 3: Multiply the denominators: 4 × 5 = 20 Step 4: Combine the results: 3/20 The answer is 3/20.

7. 7/9 ÷ 3 = ? Answer: 7/27 Solution: Write the problem: 7/9 ÷ 3 Write the whole number as a fraction: 7/9 ÷ 3/1 Change division to multiplication by the reciprocal: 7/9 × 1/3 Multiply the numerators: 7 × 1 = 7 Multiply the denominators: 9 × 3 = 27 Write the result: 7/27 The answer is 7/27.
   Full step-by-step solution

   Step 1: Write the problem: 7/9 ÷ 3 Step 2: Write the whole number as a fraction: 7/9 ÷ 3/1 Step 3: Change division to multiplication by the reciprocal: 7/9 × 1/3 Step 4: Multiply the numerators: 7 × 1 = 7 Step 5: Multiply the denominators: 9 × 3 = 27 Step 6: Write the result: 7/27 The answer is 7/27.

8. Emma is making trail mix for her hiking club. She has 2/3 of a pound of almonds and needs to divide them equally among 8 small bags. What fraction of a pound of almonds should she put in each bag? Answer: 1/12 Solution: Emma has 2/3 pound of almonds to divide among 8 bags.
   Full step-by-step solution

   Step 1: Emma has 2/3 pound of almonds to divide among 8 bags. Step 2: To divide a fraction by a whole number, we multiply the fraction by the reciprocal of the whole number: 2/3 ÷ 8 = 2/3 × 1/8 Step 3: Multiply the numerators: 2 × 1 = 2 Step 4: Multiply the denominators: 3 × 8 = 24 Step 5: The result is 2/24 Step 6: Simplify the fraction by dividing numerator and denominator by 2: 2÷2/24÷2 = 1/12 Step 7: Each bag gets 1/12 pound of almonds.

9. A rectangular prism-shaped fish tank has a length of 2 1/2 feet, a width of 1 1/4 feet, and a height of 1 1/2 feet. What is the volume of the fish tank in cubic feet? Answer: 4 11/16 Solution: Length: 2 1/2 = 5/2 Width: 1 1/4 = 5/4 Height: 1 1/2 = 3/2 Volume = (5/2) × (5/4) × (3/2) Multiply the numerators: 5 × 5 × 3 = 75 Multiply the denominators: 2 × 4 × 2 = 16 The volume is 75/16 cubic feet 75 ÷ 16 = 4 with remainder 11, so 75/16 = 4 11/16 The volume of the fish tank is 4 11/16…
   Full step-by-step solution

   Step 1: Convert all mixed numbers to improper fractions Length: 2 1/2 = 5/2 Width: 1 1/4 = 5/4 Height: 1 1/2 = 3/2 Step 2: Multiply the three dimensions to find the volume Volume = (5/2) × (5/4) × (3/2) Step 3: Multiply the numerators: 5 × 5 × 3 = 75 Step 4: Multiply the denominators: 2 × 4 × 2 = 16 Step 5: The volume is 75/16 cubic feet Step 6: Convert the improper fraction to a mixed number 75 ÷ 16 = 4 with remainder 11, so 75/16 = 4 11/16 The volume of the fish tank is 4 11/16 cubic feet.