Comprehensive worksheet designed to help students practice reducing fractions to their simplest form.

Let's solve each of these fraction reduction problems step by step. The goal is to reduce each fraction to its simplest form by dividing both the numerator and denominator by their greatest common divisor (GCD).

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🔢 Step-by-step solutions:

#### 1) $\frac{10}{20}$
- GCD of 10 and 20 is 10
- $\frac{10 \div 10}{20 \div 10} = \frac{1}{2}$

#### 2) $\frac{20}{70}$
- GCD of 20 and 70 is 10
- $\frac{20 \div 10}{70 \div 10} = \frac{2}{7}$

#### 3) $\frac{3}{12}$
- GCD of 3 and 12 is 3
- $\frac{3 \div 3}{12 \div 3} = \frac{1}{4}$

#### 4) $\frac{4}{18}$
- GCD of 4 and 18 is 2
- $\frac{4 \div 2}{18 \div 2} = \frac{2}{9}$

#### 5) $\frac{16}{80}$
- GCD of 16 and 80 is 16
- $\frac{16 \div 16}{80 \div 16} = \frac{1}{5}$

#### 6) $\frac{40}{48}$
- GCD of 40 and 48 is 8
- $\frac{40 \div 8}{48 \div 8} = \frac{5}{6}$

#### 7) $\frac{48}{54}$
- GCD of 48 and 54 is 6
- $\frac{48 \div 6}{54 \div 6} = \frac{8}{9}$

#### 8) $\frac{6}{9}$
- GCD of 6 and 9 is 3
- $\frac{6 \div 3}{9 \div 3} = \frac{2}{3}$

#### 9) $\frac{4}{20}$
- GCD of 4 and 20 is 4
- $\frac{4 \div 4}{20 \div 4} = \frac{1}{5}$

#### 10) $\frac{9}{15}$
- GCD of 9 and 15 is 3
- $\frac{9 \div 3}{15 \div 3} = \frac{3}{5}$

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#### 11) $\frac{50}{100}$
- GCD of 50 and 100 is 50
- $\frac{50 \div 50}{100 \div 50} = \frac{1}{2}$

#### 12) $\frac{30}{40}$
- GCD of 30 and 40 is 10
- $\frac{30 \div 10}{40 \div 10} = \frac{3}{4}$

#### 13) $\frac{18}{24}$
- GCD of 18 and 24 is 6
- $\frac{18 \div 6}{24 \div 6} = \frac{3}{4}$

#### 14) $\frac{2}{12}$
- GCD of 2 and 12 is 2
- $\frac{2 \div 2}{12 \div 2} = \frac{1}{6}$

#### 15) $\frac{5}{35}$
- GCD of 5 and 35 is 5
- $\frac{5 \div 5}{35 \div 5} = \frac{1}{7}$

#### 16) $\frac{21}{35}$
- GCD of 21 and 35 is 7
- $\frac{21 \div 7}{35 \div 7} = \frac{3}{5}$

#### 17) $\frac{12}{18}$
- GCD of 12 and 18 is 6
- $\frac{12 \div 6}{18 \div 6} = \frac{2}{3}$

#### 18) $\frac{7}{14}$
- GCD of 7 and 14 is 7
- $\frac{7 \div 7}{14 \div 7} = \frac{1}{2}$

#### 19) $\frac{35}{40}$
- GCD of 35 and 40 is 5
- $\frac{35 \div 5}{40 \div 5} = \frac{7}{8}$

#### 20) $\frac{21}{30}$
- GCD of 21 and 30 is 3
- $\frac{21 \div 3}{30 \div 3} = \frac{7}{10}$

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#### 21) $\frac{10}{40}$
- GCD of 10 and 40 is 10
- $\frac{10 \div 10}{40 \div 10} = \frac{1}{4}$

#### 22) $\frac{3}{6}$
- GCD of 3 and 6 is 3
- $\frac{3 \div 3}{6 \div 3} = \frac{1}{2}$

#### 23) $\frac{10}{20}$
- Same as #1 → $\frac{1}{2}$

#### 24) $\frac{14}{49}$
- GCD of 14 and 49 is 7
- $\frac{14 \div 7}{49 \div 7} = \frac{2}{7}$

#### 25) $\frac{21}{27}$
- GCD of 21 and 27 is 3
- $\frac{21 \div 3}{27 \div 3} = \frac{7}{9}$

#### 26) $\frac{9}{15}$
- Same as #10 → $\frac{3}{5}$

#### 27) $\frac{10}{40}$
- Same as #21 → $\frac{1}{4}$

#### 28) $\frac{20}{30}$
- GCD of 20 and 30 is 10
- $\frac{20 \div 10}{30 \div 10} = \frac{2}{3}$

#### 29) $\frac{5}{10}$
- GCD of 5 and 10 is 5
- $\frac{5 \div 5}{10 \div 5} = \frac{1}{2}$

#### 30) $\frac{25}{35}$
- GCD of 25 and 35 is 5
- $\frac{25 \div 5}{35 \div 5} = \frac{5}{7}$

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✔ Final Answers:

| Problem | Reduced Fraction |
|--------|------------------|
| 1) | $\frac{1}{2}$ |
| 2) | $\frac{2}{7}$ |
| 3) | $\frac{1}{4}$ |
| 4) | $\frac{2}{9}$ |
| 5) | $\frac{1}{5}$ |
| 6) | $\frac{5}{6}$ |
| 7) | $\frac{8}{9}$ |
| 8) | $\frac{2}{3}$ |
| 9) | $\frac{1}{5}$ |
| 10) | $\frac{3}{5}$ |
| 11) | $\frac{1}{2}$ |
| 12) | $\frac{3}{4}$ |
| 13) | $\frac{3}{4}$ |
| 14) | $\frac{1}{6}$ |
| 15) | $\frac{1}{7}$ |
| 16) | $\frac{3}{5}$ |
| 17) | $\frac{2}{3}$ |
| 18) | $\frac{1}{2}$ |
| 19) | $\frac{7}{8}$ |
| 20) | $\frac{7}{10}$ |
| 21) | $\frac{1}{4}$ |
| 22) | $\frac{1}{2}$ |
| 23) | $\frac{1}{2}$ |
| 24) | $\frac{2}{7}$ |
| 25) | $\frac{7}{9}$ |
| 26) | $\frac{3}{5}$ |
| 27) | $\frac{1}{4}$ |
| 28) | $\frac{2}{3}$ |
| 29) | $\frac{1}{2}$ |
| 30) | $\frac{5}{7}$ |

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📝 Summary:

All fractions have been reduced by finding the greatest common divisor (GCD) of the numerator and denominator, then dividing both by that number. This ensures the fraction is in its simplest form.

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