Fraction ÷ Whole

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Answer Key & Explanations

Fraction ÷ Whole · Grade 5 · Worksheet 1

1. 4/7 ÷ 6 = ? Answer: 4/42 Solution: Write the division problem: 4/7 ÷ 6 Rewrite the whole number as a fraction: 4/7 ÷ 6/1 Change division to multiplication by the reciprocal: 4/7 × 1/6 Multiply the numerators: 4 × 1 = 4 Multiply the denominators: 7 × 6 = 42 Write the result: 4/42 The answer is 4/42.
   Full step-by-step solution

   Step 1: Write the division problem: 4/7 ÷ 6 Step 2: Rewrite the whole number as a fraction: 4/7 ÷ 6/1 Step 3: Change division to multiplication by the reciprocal: 4/7 × 1/6 Step 4: Multiply the numerators: 4 × 1 = 4 Step 5: Multiply the denominators: 7 × 6 = 42 Step 6: Write the result: 4/42 The answer is 4/42.

2. Liam is baking cookies for a school bake sale. He has 3/4 of a cup of chocolate chips to divide equally among 6 batches of cookies. What fraction of a cup of chocolate chips should he use for each batch? Answer: 1/8 Solution: Liam has 3/4 of a cup of chocolate chips total. He needs to divide this equally among 6 batches. Write the problem as a division.
   Full step-by-step solution

   Liam has 3/4 of a cup of chocolate chips total. He needs to divide this equally among 6 batches. Step 1: Write the problem as a division. We need to divide 3/4 by 6. That is: (3/4) ÷ 6 Step 2: Dividing by a whole number is the same as multiplying by its reciprocal. The reciprocal of 6 is 1/6. So, (3/4) ÷ 6 = (3/4) × (1/6) Step 3: Multiply the numerators and the 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 simplifies to 1/8. Conclusion: Liam should use 1/8 of a cup of chocolate chips for each batch.

3. 3/5 ÷ 7 = ? Answer: 3/35 Solution: Write the division problem: 3/5 ÷ 7 Rewrite the whole number as a fraction: 3/5 ÷ 7/1 Change division to multiplication by the reciprocal: 3/5 × 1/7 Multiply the numerators: 3 × 1 = 3 Multiply the denominators: 5 × 7 = 35 Write the result: 3/35 The answer is 3/35.
   Full step-by-step solution

   Step 1: Write the division problem: 3/5 ÷ 7 Step 2: Rewrite the whole number as a fraction: 3/5 ÷ 7/1 Step 3: Change division to multiplication by the reciprocal: 3/5 × 1/7 Step 4: Multiply the numerators: 3 × 1 = 3 Step 5: Multiply the denominators: 5 × 7 = 35 Step 6: Write the result: 3/35 The answer is 3/35.

4. 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 snack bags. What fraction of a pound of almonds should go into each bag? Answer: 1/12 Solution: Start with the fraction of almonds: 2/3 pound Divide this amount equally among 8 bags: (2/3) ÷ 8 Dividing by 8 is the same as multiplying by 1/8: (2/3) × (1/8) Multiply the numerators: 2 × 1 = 2 Multiply the denominators: 3 × 8 = 24 The fraction is 2/24 Simplify by dividing numerator and…
   Full step-by-step solution

   Step 1: Start with the fraction of almonds: 2/3 pound Step 2: Divide this amount equally among 8 bags: (2/3) ÷ 8 Step 3: Dividing by 8 is the same as multiplying by 1/8: (2/3) × (1/8) Step 4: Multiply the numerators: 2 × 1 = 2 Step 5: Multiply the denominators: 3 × 8 = 24 Step 6: The fraction is 2/24 Step 7: Simplify by dividing numerator and denominator by 2: 2÷2/24÷2 = 1/12 Each bag gets 1/12 pound of almonds.

5. Liam is making a large batch of lemonade for a school event. He has 3/4 of a gallon of lemonade concentrate and needs to divide it equally among 6 pitchers. What fraction of a gallon of concentrate should go into each pitcher? Answer: 1/8 Solution: We start with 3/4 of a gallon of lemonade concentrate. Liam needs to divide it equally among 6 pitchers. Write the division problem.
   Full step-by-step solution

   We start with 3/4 of a gallon of lemonade concentrate. Liam needs to divide it equally among 6 pitchers. Step 1: Write the division problem. Dividing 3/4 gallon among 6 pitchers means: (3/4) ÷ 6 Step 2: Understand that dividing by 6 is the same as multiplying by 1/6. So: (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. 3/24 can be simplified because both numerator and denominator are divisible by 3. 3 ÷ 3 = 1 24 ÷ 3 = 8 So 3/24 = 1/8 Step 5: Conclusion. Each pitcher gets 1/8 of a gallon of concentrate. Final answer: 1/8

6. 7/10 ÷ 8 = ? Answer: 7/80 Solution: Write the division problem: 7/10 ÷ 8 Rewrite the whole number as a fraction: 7/10 ÷ 8/1 Change division to multiplication by the reciprocal: 7/10 × 1/8 Multiply the numerators: 7 × 1 = 7 Multiply the denominators: 10 × 8 = 80 Write the result: 7/80 The answer is 7/80.
   Full step-by-step solution

   Step 1: Write the division problem: 7/10 ÷ 8 Step 2: Rewrite the whole number as a fraction: 7/10 ÷ 8/1 Step 3: Change division to multiplication by the reciprocal: 7/10 × 1/8 Step 4: Multiply the numerators: 7 × 1 = 7 Step 5: Multiply the denominators: 10 × 8 = 80 Step 6: Write the result: 7/80 The answer is 7/80.

7. A rectangular chocolate bar is divided into 15 equal square pieces arranged in 3 rows and 5 columns. If 2/3 of the chocolate bar is shared equally among 4 friends, what fraction of the whole chocolate bar does each friend get? Answer: 1/6 Solution: The chocolate bar has 15 equal pieces total. 2/3 of the chocolate bar is being shared. Calculate this: 2/3 × 15 = 30/3 = 10 pieces.
   Full step-by-step solution

   Step 1: The chocolate bar has 15 equal pieces total. Step 2: 2/3 of the chocolate bar is being shared. Calculate this: 2/3 × 15 = 30/3 = 10 pieces. Step 3: These 10 pieces are shared equally among 4 friends. Calculate each friend's share: 10 ÷ 4 = 10/4 = 5/2 pieces. Step 4: To find what fraction of the whole chocolate bar this represents: (5/2) ÷ 15 = 5/2 × 1/15 = 5/30 = 1/6. Each friend gets 1/6 of the whole chocolate bar.

8. 5/6 ÷ 4 = ? Answer: 5/24 Solution: Write the division as a fraction: 5/6 ÷ 4 = (5/6) ÷ (4/1) Change division to multiplication by the reciprocal: (5/6) × (1/4) Multiply the numerators: 5 × 1 = 5 Multiply the denominators: 6 × 4 = 24 Write the result: 5/24 The answer is 5/24.
   Full step-by-step solution

   Step 1: Write the division as a fraction: 5/6 ÷ 4 = (5/6) ÷ (4/1) Step 2: Change division to multiplication by the reciprocal: (5/6) × (1/4) Step 3: Multiply the numerators: 5 × 1 = 5 Step 4: Multiply the denominators: 6 × 4 = 24 Step 5: Write the result: 5/24 The answer is 5/24.

9. 7/9 ÷ 5 = ? Answer: 7/45 Solution: Write the division problem: 7/9 ÷ 5 Rewrite the whole number as a fraction: 7/9 ÷ 5/1 Change division to multiplication by the reciprocal: 7/9 × 1/5 Multiply the numerators: 7 × 1 = 7 Multiply the denominators: 9 × 5 = 45 Write the result: 7/45 The answer is 7/45.
   Full step-by-step solution

   Step 1: Write the division problem: 7/9 ÷ 5 Step 2: Rewrite the whole number as a fraction: 7/9 ÷ 5/1 Step 3: Change division to multiplication by the reciprocal: 7/9 × 1/5 Step 4: Multiply the numerators: 7 × 1 = 7 Step 5: Multiply the denominators: 9 × 5 = 45 Step 6: Write the result: 7/45 The answer is 7/45.