Simplify fractions worksheet with ten problems for students to practice reducing fractions to their simplest form.

To simplify fractions, we need to find the greatest common divisor (GCD) of the numerator and the denominator and then divide both by this GCD. Let's solve each fraction step by step.

1. Simplify $\frac{4}{10}$

- Numerator: 4
- Denominator: 10
- GCD of 4 and 10: 2
- Divide both numerator and denominator by 2:
$$
\frac{4 \div 2}{10 \div 2} = \frac{2}{5}
$$
- Answer: $\frac{2}{5}$

2. Simplify $\frac{5}{15}$

- Numerator: 5
- Denominator: 15
- GCD of 5 and 15: 5
- Divide both numerator and denominator by 5:
$$
\frac{5 \div 5}{15 \div 5} = \frac{1}{3}
$$
- Answer: $\frac{1}{3}$

3. Simplify $\frac{9}{12}$

- Numerator: 9
- Denominator: 12
- GCD of 9 and 12: 3
- Divide both numerator and denominator by 3:
$$
\frac{9 \div 3}{12 \div 3} = \frac{3}{4}
$$
- Answer: $\frac{3}{4}$

4. Simplify $\frac{16}{24}$

- Numerator: 16
- Denominator: 24
- GCD of 16 and 24: 8
- Divide both numerator and denominator by 8:
$$
\frac{16 \div 8}{24 \div 8} = \frac{2}{3}
$$
- Answer: $\frac{2}{3}$

5. Simplify $\frac{7}{49}$

- Numerator: 7
- Denominator: 49
- GCD of 7 and 49: 7
- Divide both numerator and denominator by 7:
$$
\frac{7 \div 7}{49 \div 7} = \frac{1}{7}
$$
- Answer: $\frac{1}{7}$

6. Simplify $\frac{12}{30}$

- Numerator: 12
- Denominator: 30
- GCD of 12 and 30: 6
- Divide both numerator and denominator by 6:
$$
\frac{12 \div 6}{30 \div 6} = \frac{2}{5}
$$
- Answer: $\frac{2}{5}$

7. Simplify $\frac{14}{56}$

- Numerator: 14
- Denominator: 56
- GCD of 14 and 56: 14
- Divide both numerator and denominator by 14:
$$
\frac{14 \div 14}{56 \div 14} = \frac{1}{4}
$$
- Answer: $\frac{1}{4}$

8. Simplify $\frac{36}{40}$

- Numerator: 36
- Denominator: 40
- GCD of 36 and 40: 4
- Divide both numerator and denominator by 4:
$$
\frac{36 \div 4}{40 \div 4} = \frac{9}{10}
$$
- Answer: $\frac{9}{10}$

9. Simplify $\frac{18}{38}$

- Numerator: 18
- Denominator: 38
- GCD of 18 and 38: 2
- Divide both numerator and denominator by 2:
$$
\frac{18 \div 2}{38 \div 2} = \frac{9}{19}
$$
- Answer: $\frac{9}{19}$

10. Simplify $\frac{25}{40}$

- Numerator: 25
- Denominator: 40
- GCD of 25 and 40: 5
- Divide both numerator and denominator by 5:
$$
\frac{25 \div 5}{40 \div 5} = \frac{5}{8}
$$
- Answer: $\frac{5}{8}$

Final Answers:

$$
\boxed{
\begin{array}{ll}
1. \frac{2}{5} & 6. \frac{2}{5} \\
2. \frac{1}{3} & 7. \frac{1}{4} \\
3. \frac{3}{4} & 8. \frac{9}{10} \\
4. \frac{2}{3} & 9. \frac{9}{19} \\
5. \frac{1}{7} & 10. \frac{5}{8} \\
\end{array}
}
$$