Fraction Worksheets - Free Printable

Problem: Reducing Fractions

The task is to simplify each fraction to its lowest terms. To do this, 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:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

#### 23) $\frac{10}{20}$
- GCD of 10 and 20 is 10.
- Simplify: $\frac{10 \div 10}{20 \div 10} = \frac{1}{2}$.
- Answer: $\frac{1}{2}$

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

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

#### 26) $\frac{9}{15}$
- GCD of 9 and 15 is 3.
- Simplify: $\frac{9 \div 3}{15 \div 3} = \frac{3}{5}$.
- Answer: $\frac{3}{5}$

#### 27) $\frac{10}{40}$
- GCD of 10 and 40 is 10.
- Simplify: $\frac{10 \div 10}{40 \div 10} = \frac{1}{4}$.
- Answer: $\frac{1}{4}$

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

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

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

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Final Answers:

\[
\boxed{
\begin{array}{ccc}
1) \frac{1}{2} & 11) \frac{1}{2} & 21) \frac{1}{4} \\
2) \frac{2}{7} & 12) \frac{3}{4} & 22) \frac{1}{2} \\
3) \frac{1}{4} & 13) \frac{3}{4} & 23) \frac{1}{2} \\
4) \frac{2}{9} & 14) \frac{1}{6} & 24) \frac{2}{7} \\
5) \frac{1}{5} & 15) \frac{1}{7} & 25) \frac{7}{9} \\
6) \frac{5}{6} & 16) \frac{3}{5} & 26) \frac{3}{5} \\
7) \frac{8}{9} & 17) \frac{2}{3} & 27) \frac{1}{4} \\
8) \frac{2}{3} & 18) \frac{1}{2} & 28) \frac{2}{3} \\
9) \frac{1}{5} & 19) \frac{7}{8} & 29) \frac{1}{2} \\
10) \frac{3}{5} & 20) \frac{7}{10} & 30) \frac{5}{7} \\
\end{array}
}
\]