Mixed Numbers and Improper Fractions (B) Worksheet | Cazoom Maths ... - Free Printable

Let's solve this step by step, explaining each part clearly.

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Section A: Change the mixed numbers to improper fractions, and improper fractions to mixed numbers.

#### Rules:
- To convert improper fraction → mixed number:
- Divide numerator by denominator.
- Quotient = whole number.
- Remainder becomes new numerator.
- Denominator stays same.

- To convert mixed number → improper fraction:
- Multiply whole number × denominator.
- Add numerator.
- Result is new numerator; denominator stays same.

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#### Section A Solutions:

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

- $ 9 ÷ 5 = 1 $ remainder $ 4 $
- So, $ \frac{9}{5} = 1\frac{4}{5} $

✔ Answer: $ 1\frac{4}{5} $

2) $ \frac{14}{3} $

- $ 14 ÷ 3 = 4 $ remainder $ 2 $
- So, $ \frac{14}{3} = 4\frac{2}{3} $

✔ Answer: $ 4\frac{2}{3} $

3) $ \frac{16}{5} $

- $ 16 ÷ 5 = 3 $ remainder $ 1 $
- So, $ \frac{16}{5} = 3\frac{1}{5} $

✔ Answer: $ 3\frac{1}{5} $

4) $ \frac{27}{7} $

- $ 27 ÷ 7 = 3 $ remainder $ 6 $
- So, $ \frac{27}{7} = 3\frac{6}{7} $

✔ Answer: $ 3\frac{6}{7} $

5) $ 4\frac{2}{9} $

- $ 4 × 9 = 36 $, then $ 36 + 2 = 38 $
- So, $ 4\frac{2}{9} = \frac{38}{9} $

✔ Answer: $ \frac{38}{9} $

6) $ 7\frac{1}{8} $

- $ 7 × 8 = 56 $, $ 56 + 1 = 57 $
- So, $ 7\frac{1}{8} = \frac{57}{8} $

✔ Answer: $ \frac{57}{8} $

7) $ 3\frac{2}{11} $

- $ 3 × 11 = 33 $, $ 33 + 2 = 35 $
- So, $ 3\frac{2}{11} = \frac{35}{11} $

✔ Answer: $ \frac{35}{11} $

8) $ 2\frac{3}{20} $

- $ 2 × 20 = 40 $, $ 40 + 3 = 43 $
- So, $ 2\frac{3}{20} = \frac{43}{20} $

✔ Answer: $ \frac{43}{20} $

9) $ 8\frac{7}{12} $

- $ 8 × 12 = 96 $, $ 96 + 7 = 103 $
- So, $ 8\frac{7}{12} = \frac{103}{12} $

✔ Answer: $ \frac{103}{12} $

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Section B: Simplify your answers where possible.

We now simplify both mixed numbers and improper fractions.

#### 1) $ 1\frac{3}{9} $

- First, simplify $ \frac{3}{9} = \frac{1}{3} $
- So, $ 1\frac{3}{9} = 1\frac{1}{3} $

✔ Answer: $ 1\frac{1}{3} $

#### 2) $ 6\frac{2}{12} $

- Simplify $ \frac{2}{12} = \frac{1}{6} $
- So, $ 6\frac{2}{12} = 6\frac{1}{6} $

✔ Answer: $ 6\frac{1}{6} $

#### 3) $ 8\frac{3}{15} $

- Simplify $ \frac{3}{15} = \frac{1}{5} $
- So, $ 8\frac{3}{15} = 8\frac{1}{5} $

✔ Answer: $ 8\frac{1}{5} $

#### 4) $ 10\frac{12}{26} $

- Simplify $ \frac{12}{26} = \frac{6}{13} $
- So, $ 10\frac{12}{26} = 10\frac{6}{13} $

✔ Answer: $ 10\frac{6}{13} $

#### 5) $ \frac{14}{4} $

- $ 14 ÷ 4 = 3 $ remainder $ 2 $ → $ 3\frac{2}{4} $
- But $ \frac{2}{4} = \frac{1}{2} $
- So, $ \frac{14}{4} = 3\frac{1}{2} $

✔ Answer: $ 3\frac{1}{2} $

#### 6) $ \frac{24}{15} $

- $ 24 ÷ 15 = 1 $ remainder $ 9 $ → $ 1\frac{9}{15} $
- Simplify $ \frac{9}{15} = \frac{3}{5} $
- So, $ \frac{24}{15} = 1\frac{3}{5} $

✔ Answer: $ 1\frac{3}{5} $

#### 7) $ \frac{32}{12} $

- $ 32 ÷ 12 = 2 $ remainder $ 8 $ → $ 2\frac{8}{12} $
- Simplify $ \frac{8}{12} = \frac{2}{3} $
- So, $ \frac{32}{12} = 2\frac{2}{3} $

✔ Answer: $ 2\frac{2}{3} $

#### 8) $ \frac{81}{18} $

- $ 81 ÷ 18 = 4 $ remainder $ 9 $ → $ 4\frac{9}{18} $
- $ \frac{9}{18} = \frac{1}{2} $
- So, $ \frac{81}{18} = 4\frac{1}{2} $

✔ Answer: $ 4\frac{1}{2} $

#### 9) $ \frac{112}{35} $

- $ 112 ÷ 35 = 3 $ remainder $ 7 $ → $ 3\frac{7}{35} $
- $ \frac{7}{35} = \frac{1}{5} $
- So, $ \frac{112}{35} = 3\frac{1}{5} $

✔ Answer: $ 3\frac{1}{5} $

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Extension: Convert decimals and percentages to mixed numbers and improper fractions.

We need to write:

1. 2.08
2. 160%
3. 112.5%

as mixed numbers and improper fractions, simplified.

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#### 1) 2.08

- Write as a fraction: $ 2.08 = \frac{208}{100} $
- Simplify $ \frac{208}{100} $: divide numerator and denominator by 4 → $ \frac{52}{25} $
- Now, $ \frac{52}{25} = 2\frac{2}{25} $ (since $ 25×2=50 $, remainder 2)

✔ Mixed Number: $ 2\frac{2}{25} $
✔ Improper Fraction: $ \frac{52}{25} $

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#### 2) 160%

- $ 160\% = \frac{160}{100} = \frac{16}{10} = \frac{8}{5} $
- $ \frac{8}{5} = 1\frac{3}{5} $

✔ Mixed Number: $ 1\frac{3}{5} $
✔ Improper Fraction: $ \frac{8}{5} $

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#### 3) 112.5%

- $ 112.5\% = \frac{112.5}{100} $
- Multiply numerator and denominator by 2 to eliminate decimal: $ \frac{225}{200} $
- Simplify $ \frac{225}{200} $: divide by 25 → $ \frac{9}{8} $
- $ \frac{9}{8} = 1\frac{1}{8} $

✔ Mixed Number: $ 1\frac{1}{8} $
✔ Improper Fraction: $ \frac{9}{8} $

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✔ Final Answers:

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Section A:

1) $ \frac{9}{5} = \boxed{1\frac{4}{5}} $
2) $ \frac{14}{3} = \boxed{4\frac{2}{3}} $
3) $ \frac{16}{5} = \boxed{3\frac{1}{5}} $
4) $ \frac{27}{7} = \boxed{3\frac{6}{7}} $
5) $ 4\frac{2}{9} = \boxed{\frac{38}{9}} $
6) $ 7\frac{1}{8} = \boxed{\frac{57}{8}} $
7) $ 3\frac{2}{11} = \boxed{\frac{35}{11}} $
8) $ 2\frac{3}{20} = \boxed{\frac{43}{20}} $
9) $ 8\frac{7}{12} = \boxed{\frac{103}{12}} $

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Section B:

1) $ 1\frac{3}{9} = \boxed{1\frac{1}{3}} $
2) $ 6\frac{2}{12} = \boxed{6\frac{1}{6}} $
3) $ 8\frac{3}{15} = \boxed{8\frac{1}{5}} $
4) $ 10\frac{12}{26} = \boxed{10\frac{6}{13}} $
5) $ \frac{14}{4} = \boxed{3\frac{1}{2}} $
6) $ \frac{24}{15} = \boxed{1\frac{3}{5}} $
7) $ \frac{32}{12} = \boxed{2\frac{2}{3}} $
8) $ \frac{81}{18} = \boxed{4\frac{1}{2}} $
9) $ \frac{112}{35} = \boxed{3\frac{1}{5}} $

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Extension:

| Value | Mixed Number | Improper Fraction |
|-----------|-------------------|-------------------|
| 2.08 | $ 2\frac{2}{25} $ | $ \frac{52}{25} $ |
| 160% | $ 1\frac{3}{5} $ | $ \frac{8}{5} $ |
| 112.5% | $ 1\frac{1}{8} $ | $ \frac{9}{8} $ |

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✔ All answers are simplified and correct! Let me know if you'd like a printable version or explanations in another format.