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 the new numerator; denominator stays the same.
- To convert mixed number → improper fraction:
- Multiply the whole number by the denominator.
- Add the numerator.
- The result is the new numerator; denominator stays the same.

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#### 1) $ \frac{9}{5} $
- $ 9 \div 5 = 1 $ remainder $ 4 $
- So, $ \frac{9}{5} = 1\frac{4}{5} $

✔ Answer: $ 1\frac{4}{5} $

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#### 2) $ \frac{14}{3} $
- $ 14 \div 3 = 4 $ remainder $ 2 $
- So, $ \frac{14}{3} = 4\frac{2}{3} $

✔ Answer: $ 4\frac{2}{3} $

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#### 3) $ \frac{16}{5} $
- $ 16 \div 5 = 3 $ remainder $ 1 $
- So, $ \frac{16}{5} = 3\frac{1}{5} $

✔ Answer: $ 3\frac{1}{5} $

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#### 4) $ \frac{27}{7} $
- $ 27 \div 7 = 3 $ remainder $ 6 $
- So, $ \frac{27}{7} = 3\frac{6}{7} $

✔ Answer: $ 3\frac{6}{7} $

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#### 5) $ 4\frac{2}{9} $
- $ 4 \times 9 = 36 $, plus $ 2 = 38 $
- So, $ 4\frac{2}{9} = \frac{38}{9} $

✔ Answer: $ \frac{38}{9} $

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#### 6) $ 7\frac{1}{8} $
- $ 7 \times 8 = 56 $, plus $ 1 = 57 $
- So, $ 7\frac{1}{8} = \frac{57}{8} $

✔ Answer: $ \frac{57}{8} $

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#### 7) $ 3\frac{2}{11} $
- $ 3 \times 11 = 33 $, plus $ 2 = 35 $
- So, $ 3\frac{2}{11} = \frac{35}{11} $

✔ Answer: $ \frac{35}{11} $

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#### 8) $ 2\frac{3}{20} $
- $ 2 \times 20 = 40 $, plus $ 3 = 43 $
- So, $ 2\frac{3}{20} = \frac{43}{20} $

✔ Answer: $ \frac{43}{20} $

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#### 9) $ 8\frac{7}{12} $
- $ 8 \times 12 = 96 $, plus $ 7 = 103 $
- So, $ 8\frac{7}{12} = \frac{103}{12} $

✔ Answer: $ \frac{103}{12} $

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✔ Section A Answers:

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

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Section B: Simplify your answers where possible.

We now simplify both mixed numbers and improper fractions.

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#### 1) $ 1\frac{3}{9} $
- Simplify $ \frac{3}{9} = \frac{1}{3} $
- So, $ 1\frac{3}{9} = 1\frac{1}{3} $

✔ Answer: $ 1\frac{1}{3} $

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#### 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} $

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#### 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} $

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#### 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} $

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#### 5) $ \frac{14}{4} $
- Simplify $ \frac{14}{4} = \frac{7}{2} $
- Convert to mixed number: $ \frac{7}{2} = 3\frac{1}{2} $

✔ Answer: $ 3\frac{1}{2} $

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#### 6) $ \frac{24}{15} $
- Simplify $ \frac{24}{15} = \frac{8}{5} $
- Convert to mixed number: $ \frac{8}{5} = 1\frac{3}{5} $

✔ Answer: $ 1\frac{3}{5} $

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#### 7) $ \frac{32}{12} $
- Simplify $ \frac{32}{12} = \frac{8}{3} $
- Convert to mixed number: $ \frac{8}{3} = 2\frac{2}{3} $

✔ Answer: $ 2\frac{2}{3} $

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#### 8) $ \frac{81}{18} $
- Simplify $ \frac{81}{18} = \frac{9}{2} $
- Convert to mixed number: $ \frac{9}{2} = 4\frac{1}{2} $

✔ Answer: $ 4\frac{1}{2} $

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#### 9) $ \frac{112}{35} $
- Simplify $ \frac{112}{35} $: divide numerator and denominator by 7
- $ 112 \div 7 = 16 $, $ 35 \div 7 = 5 $
- So, $ \frac{112}{35} = \frac{16}{5} $
- Convert: $ \frac{16}{5} = 3\frac{1}{5} $

✔ Answer: $ 3\frac{1}{5} $

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✔ Section B Answers:

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

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Extension: Write percentages and decimals as mixed numbers and improper fractions.

We'll convert each value to a fraction, then simplify and write as mixed number and improper fraction.

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#### 1) 2.08

Convert decimal to fraction:
- $ 2.08 = 2 + 0.08 $
- $ 0.08 = \frac{8}{100} = \frac{2}{25} $
- So, $ 2.08 = 2\frac{2}{25} $

As improper fraction:
- $ 2 \times 25 = 50 $, plus $ 2 = 52 $
- So, $ \frac{52}{25} $

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

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#### 2) 160%

Convert percent to fraction:
- $ 160\% = \frac{160}{100} = \frac{16}{10} = \frac{8}{5} $
- As mixed number: $ \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%

Convert percent to fraction:
- $ 112.5\% = \frac{112.5}{100} $
- Multiply numerator and denominator by 2 to eliminate decimal:
- $ \frac{112.5 \times 2}{100 \times 2} = \frac{225}{200} $
- Simplify $ \frac{225}{200} $: divide numerator and denominator by 25
- $ 225 \div 25 = 9 $, $ 200 \div 25 = 8 $
- So, $ \frac{9}{8} $
- As mixed number: $ \frac{9}{8} = 1\frac{1}{8} $

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

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✔ Extension Table:

| 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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✔ Final Summary:

#### Section A:
1. $ 1\frac{4}{5} $
2. $ 4\frac{2}{3} $
3. $ 3\frac{1}{5} $
4. $ 3\frac{6}{7} $
5. $ \frac{38}{9} $
6. $ \frac{57}{8} $
7. $ \frac{35}{11} $
8. $ \frac{43}{20} $
9. $ \frac{103}{12} $

#### Section B:
1. $ 1\frac{1}{3} $
2. $ 6\frac{1}{6} $
3. $ 8\frac{1}{5} $
4. $ 10\frac{6}{13} $
5. $ 3\frac{1}{2} $
6. $ 1\frac{3}{5} $
7. $ 2\frac{2}{3} $
8. $ 4\frac{1}{2} $
9. $ 3\frac{1}{5} $

#### 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} $ |

All answers are simplified. Let me know if you'd like a printable version!