Convert between Improper Fractions and Mixed Numbers Worksheets - Free Printable

Sure! Let’s solve each part of the worksheet step by step, with clear explanations.

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## Part A: Convert each improper fraction to a mixed number

An improper fraction has a numerator ≥ denominator. To convert it to a mixed number, divide the numerator by the denominator:

- The quotient becomes the whole number.
- The remainder becomes the new numerator.
- The denominator stays the same.

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1) \(\frac{9}{5}\)

Divide 9 ÷ 5 = 1 remainder 4

→ Mixed number: \(1 \frac{4}{5}\)

✔ Answer: \(1 \frac{4}{5}\)

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2) \(\frac{53}{12}\)

53 ÷ 12 = 4 remainder 5 (since 12 × 4 = 48; 53 - 48 = 5)

→ Mixed number: \(4 \frac{5}{12}\)

✔ Answer: \(4 \frac{5}{12}\)

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3) \(\frac{10}{3}\)

10 ÷ 3 = 3 remainder 1

→ Mixed number: \(3 \frac{1}{3}\)

✔ Answer: \(3 \frac{1}{3}\)

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4) \(\frac{8}{7}\)

8 ÷ 7 = 1 remainder 1

→ Mixed number: \(1 \frac{1}{7}\)

✔ Answer: \(1 \frac{1}{7}\)

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5) \(\frac{65}{11}\)

65 ÷ 11 = 5 remainder 10 (11 × 5 = 55; 65 - 55 = 10)

→ Mixed number: \(5 \frac{10}{11}\)

✔ Answer: \(5 \frac{10}{11}\)

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6) \(\frac{31}{4}\)

31 ÷ 4 = 7 remainder 3

→ Mixed number: \(7 \frac{3}{4}\)

✔ Answer: \(7 \frac{3}{4}\)

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7) \(\frac{29}{6}\)

29 ÷ 6 = 4 remainder 5

→ Mixed number: \(4 \frac{5}{6}\)

✔ Answer: \(4 \frac{5}{6}\)

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8) \(\frac{74}{9}\)

74 ÷ 9 = 8 remainder 2 (9 × 8 = 72; 74 - 72 = 2)

→ Mixed number: \(8 \frac{2}{9}\)

✔ Answer: \(8 \frac{2}{9}\)

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## Part B: Rewrite each mixed number as an improper fraction

To convert a mixed number to an improper fraction:

- Multiply the whole number by the denominator.
- Add the numerator.
- Keep the same denominator.

Formula:
\[
\text{Improper Fraction} = \frac{(\text{Whole Number} \times \text{Denominator}) + \text{Numerator}}{\text{Denominator}}
\]

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1) \(9 \frac{3}{10}\)

= \(\frac{(9 × 10) + 3}{10} = \frac{90 + 3}{10} = \frac{93}{10}\)

✔ Answer: \(\frac{93}{10}\)

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2) \(7 \frac{1}{2}\)

= \(\frac{(7 × 2) + 1}{2} = \frac{14 + 1}{2} = \frac{15}{2}\)

✔ Answer: \(\frac{15}{2}\)

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3) \(1 \frac{1}{6}\)

= \(\frac{(1 × 6) + 1}{6} = \frac{6 + 1}{6} = \frac{7}{6}\)

✔ Answer: \(\frac{7}{6}\)

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4) \(2 \frac{6}{11}\)

= \(\frac{(2 × 11) + 6}{11} = \frac{22 + 6}{11} = \frac{28}{11}\)

✔ Answer: \(\frac{28}{11}\)

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5) \(4 \frac{5}{8}\)

= \(\frac{(4 × 8) + 5}{8} = \frac{32 + 5}{8} = \frac{37}{8}\)

✔ Answer: \(\frac{37}{8}\)

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6) \(1 \frac{3}{5}\)

= \(\frac{(1 × 5) + 3}{5} = \frac{5 + 3}{5} = \frac{8}{5}\)

✔ Answer: \(\frac{8}{5}\)

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7) \(6 \frac{2}{7}\)

= \(\frac{(6 × 7) + 2}{7} = \frac{42 + 2}{7} = \frac{44}{7}\)

✔ Answer: \(\frac{44}{7}\)

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8) \(5 \frac{8}{9}\)

= \(\frac{(5 × 9) + 8}{9} = \frac{45 + 8}{9} = \frac{53}{9}\)

✔ Answer: \(\frac{53}{9}\)

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## ✔ Final Answers:

A) Improper → Mixed

1) \(1 \frac{4}{5}\)
2) \(4 \frac{5}{12}\)
3) \(3 \frac{1}{3}\)
4) \(1 \frac{1}{7}\)
5) \(5 \frac{10}{11}\)
6) \(7 \frac{3}{4}\)
7) \(4 \frac{5}{6}\)
8) \(8 \frac{2}{9}\)

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B) Mixed → Improper

1) \(\frac{93}{10}\)
2) \(\frac{15}{2}\)
3) \(\frac{7}{6}\)
4) \(\frac{28}{11}\)
5) \(\frac{37}{8}\)
6) \(\frac{8}{5}\)
7) \(\frac{44}{7}\)
8) \(\frac{53}{9}\)

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