Dividing whole number by fractions worksheets - Math Worksheets ... - Free Printable

Let's solve each of these fraction division problems step by step and verify the given answers. The general rule for dividing fractions is:

> To divide by a fraction, multiply by its reciprocal.

Also, if you have a mixed number, convert it to an improper fraction first.

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1. $ 5\frac{3}{5} \div \frac{1}{5} $

Step 1: Convert $ 5\frac{3}{5} $ to improper fraction:
$ 5\frac{3}{5} = \frac{5 \times 5 + 3}{5} = \frac{25 + 3}{5} = \frac{28}{5} $

Step 2: Divide by $ \frac{1}{5} $:
$ \frac{28}{5} \div \frac{1}{5} = \frac{28}{5} \times \frac{5}{1} = 28 $

✔ Answer: 28 → Correct

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2. $ 11\frac{1}{2} \div \frac{1}{2} $

Step 1: Convert $ 11\frac{1}{2} = \frac{23}{2} $

Step 2: $ \frac{23}{2} \div \frac{1}{2} = \frac{23}{2} \times \frac{2}{1} = 23 $

✔ Answer: 23 → Correct

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3. $ 15\frac{2}{3} \div \frac{1}{3} $

Step 1: $ 15\frac{2}{3} = \frac{47}{3} $

Step 2: $ \frac{47}{3} \div \frac{1}{3} = \frac{47}{3} \times \frac{3}{1} = 47 $

✔ Answer: 47 → Correct

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4. $ 11\frac{3}{4} \div \frac{1}{4} $

Step 1: $ 11\frac{3}{4} = \frac{47}{4} $

Step 2: $ \frac{47}{4} \div \frac{1}{4} = \frac{47}{4} \times \frac{4}{1} = 47 $

✔ Answer: 47 → Correct

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5. $ 15\frac{4}{6} \div \frac{3}{6} $

Note: Simplify $ \frac{4}{6} = \frac{2}{3} $, so $ 15\frac{4}{6} = 15\frac{2}{3} $

But let’s work with original:

Step 1: $ 15\frac{4}{6} = \frac{15 \times 6 + 4}{6} = \frac{90 + 4}{6} = \frac{94}{6} $

Simplify: $ \frac{94}{6} = \frac{47}{3} $

Step 2: $ \frac{47}{3} \div \frac{3}{6} = \frac{47}{3} \div \frac{1}{2} $ (since $ \frac{3}{6} = \frac{1}{2} $)

Now: $ \frac{47}{3} \times \frac{2}{1} = \frac{94}{3} = 31\frac{1}{3} $

✔ Answer: $ 31\frac{1}{3} $ → Correct

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6. $ 2\frac{5}{10} \div \frac{8}{10} $

Step 1: Simplify fractions:
$ 2\frac{5}{10} = 2\frac{1}{2} = \frac{5}{2} $
$ \frac{8}{10} = \frac{4}{5} $

Step 2: $ \frac{5}{2} \div \frac{4}{5} = \frac{5}{2} \times \frac{5}{4} = \frac{25}{8} = 3\frac{1}{8} $

✔ Answer: $ 3\frac{1}{8} $ → Correct

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7. $ 9\frac{11}{12} \div \frac{3}{12} $

Step 1: $ 9\frac{11}{12} = \frac{9 \times 12 + 11}{12} = \frac{108 + 11}{12} = \frac{119}{12} $

$ \frac{3}{12} = \frac{1}{4} $

Step 2: $ \frac{119}{12} \div \frac{1}{4} = \frac{119}{12} \times \frac{4}{1} = \frac{476}{12} $

Simplify: $ \frac{476 \div 4}{12 \div 4} = \frac{119}{3} = 39\frac{2}{3} $

✔ Answer: $ 39\frac{2}{3} $ → Correct

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8. $ 6\frac{1}{9} \div \frac{7}{9} $

Step 1: $ 6\frac{1}{9} = \frac{55}{9} $

Step 2: $ \frac{55}{9} \div \frac{7}{9} = \frac{55}{9} \times \frac{9}{7} = \frac{55}{7} = 7\frac{6}{7} $

✔ Answer: $ 7\frac{6}{7} $ → Correct

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9. $ 1\frac{1}{2} \div \frac{1}{2} $

Step 1: $ 1\frac{1}{2} = \frac{3}{2} $

Step 2: $ \frac{3}{2} \div \frac{1}{2} = \frac{3}{2} \times \frac{2}{1} = 3 $

✔ Answer: 3 → Correct

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10. $ 10\frac{1}{3} \div \frac{1}{3} $

Step 1: $ 10\frac{1}{3} = \frac{31}{3} $

Step 2: $ \frac{31}{3} \div \frac{1}{3} = \frac{31}{3} \times \frac{3}{1} = 31 $

✔ Answer: 31 → Correct

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✔ Final Answer:

All the answers provided in the worksheet are correct.

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🔍 Summary of Key Concepts:

- Convert mixed numbers to improper fractions.
- Dividing by a fraction = multiplying by its reciprocal.
- Simplify before or after multiplication.
- Always simplify final answers.

Let me know if you'd like a printable version or explanation for any specific problem!