Date Name: Ande Simplifying Fractions Simplify the fractions. Show work. $$ \frac{4}{8}= $$ $$ \qquad $$ 2) $$ \frac{9}{15}-\frac{3}{=} \frac{3}{5} $$ $$ \frac{28}{42}= $$ $$ \qquad $$ 4) $$ \frac{9}{24}= $$ $$ \qquad $$ $$ \frac{10}{20}= $$ $$ \qquad $$ 8) $$ \frac{16}{40}= $$ $$ \qquad $$ 142 $$ \frac{25}{40}= $$ $$ \qquad $$ 12) $$ \frac{4}{12}= $$ $$ \qquad $$ $$ \frac{12}{15}= $$ $$ \qquad $$ 14) $$ \frac{2}{8}= $$ $$ \qquad $$ 7) $$ \frac{7}{42}= $$ $$ \qquad $$ 16) $$ \frac{45}{72}= $$ $$ \qquad $$ $$ \frac{18}{36}= $$ $$ \qquad $$ 20) $$ \frac{18}{30}= $$ $$ \qquad $$ 2+1 $$ \frac{12}{24}= $$ $$ \qquad $$ 22) $$ \frac{9}{36}= $$ $$ \qquad $$ 123) $$ \frac{30}{36}= $$ $$ \qquad $$ 24) $$ \frac{54}{72}= $$ $$ \qquad $$

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

1) $$ \frac{4}{8} $$

- The GCD of 4 and 8 is 4.
- Divide both the numerator and the denominator by 4:
  $$
  \frac{4 \div 4}{8 \div 4} = \frac{1}{2}
  $$

2) $$ \frac{9}{15} $$

- The GCD of 9 and 15 is 3.
- Divide both by 3:
  $$
  \frac{9 \div 3}{15 \div 3} = \frac{3}{5}
  $$

3) $$ \frac{28}{42} $$

- The GCD of 28 and 42 is 14.
- Divide both by 14:
  $$
  \frac{28 \div 14}{42 \div 14} = \frac{2}{3}
  $$

4) $$ \frac{9}{24} $$

- The GCD of 9 and 24 is 3.
- Divide both by 3:
  $$
  \frac{9 \div 3}{24 \div 3} = \frac{3}{8}
  $$

5) $$ \frac{10}{20} $$

- The GCD of 10 and 20 is 10.
- Divide both by 10:
  $$
  \frac{10 \div 10}{20 \div 10} = \frac{1}{2}
  $$

6) $$ \frac{16}{40} $$

- The GCD of 16 and 40 is 8.
- Divide both by 8:
  $$
  \frac{16 \div 8}{40 \div 8} = \frac{2}{5}
  $$

7) $$ \frac{25}{40} $$

- The GCD of 25 and 40 is 5.
- Divide both by 5:
  $$
  \frac{25 \div 5}{40 \div 5} = \frac{5}{8}
  $$

8) $$ \frac{4}{12} $$

- The GCD of 4 and 12 is 4.
- Divide both by 4:
  $$
  \frac{4 \div 4}{12 \div 4} = \frac{1}{3}
  $$

9) $$ \frac{12}{15} $$

- The GCD of 12 and 15 is 3.
- Divide both by 3:
  $$
  \frac{12 \div 3}{15 \div 3} = \frac{4}{5}
  $$

10) $$ \frac{2}{8} $$

- The GCD of 2 and 8 is 2.
- Divide both by 2:
  $$
  \frac{2 \div 2}{8 \div 2} = \frac{1}{4}
  $$

11) $$ \frac{7}{42} $$

- The GCD of 7 and 42 is 7.
- Divide both by 7:
  $$
  \frac{7 \div 7}{42 \div 7} = \frac{1}{6}
  $$

12) $$ \frac{45}{72} $$

- The GCD of 45 and 72 is 9.
- Divide both by 9:
  $$
  \frac{45 \div 9}{72 \div 9} = \frac{5}{8}
  $$

13) $$ \frac{18}{36} $$

- The GCD of 18 and 36 is 18.
- Divide both by 18:
  $$
  \frac{18 \div 18}{36 \div 18} = \frac{1}{2}
  $$

14) $$ \frac{18}{30} $$

- The GCD of 18 and 30 is 6.
- Divide both by 6:
  $$
  \frac{18 \div 6}{30 \div 6} = \frac{3}{5}
  $$

15) $$ \frac{12}{24} $$

- The GCD of 12 and 24 is 12.
- Divide both by 12:
  $$
  \frac{12 \div 12}{24 \div 12} = \frac{1}{2}
  $$

16) $$ \frac{9}{36} $$

- The GCD of 9 and 36 is 9.
- Divide both by 9:
  $$
  \frac{9 \div 9}{36 \div 9} = \frac{1}{4}
  $$

17) $$ \frac{30}{36} $$

- The GCD of 30 and 36 is 6.
- Divide both by 6:
  $$
  \frac{30 \div 6}{36 \div 6} = \frac{5}{6}
  $$

18) $$ \frac{54}{72} $$

- The GCD of 54 and 72 is 18.
- Divide both by 18:
  $$
  \frac{54 \div 18}{72 \div 18} = \frac{3}{4}
  $$

Now, let's summarize the simplified fractions:

1) $$ \frac{4}{8} = \frac{1}{2} $$

2) $$ \frac{9}{15} = \frac{3}{5} $$

3) $$ \frac{28}{42} = \frac{2}{3} $$

4) $$ \frac{9}{24} = \frac{3}{8} $$

5) $$ \frac{10}{20} = \frac{1}{2} $$

6) $$ \frac{16}{40} = \frac{2}{5} $$

7) $$ \frac{25}{40} = \frac{5}{8} $$

8) $$ \frac{4}{12} = \frac{1}{3} $$

9) $$ \frac{12}{15} = \frac{4}{5} $$

10) $$ \frac{2}{8} = \frac{1}{4} $$

11) $$ \frac{7}{42} = \frac{1}{6} $$

12) $$ \frac{45}{72} = \frac{5}{8} $$

13) $$ \frac{18}{36} = \frac{1}{2} $$

14) $$ \frac{18}{30} = \frac{3}{5} $$

15) $$ \frac{12}{24} = \frac{1}{2} $$

16) $$ \frac{9}{36} = \frac{1}{4} $$

17
Here are the simplified fractions: 1) $$ \frac{4}{8} = \frac{1}{2} $$ 2) $$ \frac{9}{15} = \frac{3}{5} $$ 3) $$ \frac{28}{42} = \frac{2}{3} $$ 4) $$ \frac{9}{24} = \frac{3}{8} $$ 5) $$ \frac{10}{20} = \frac{1}{2} $$ 6) $$ \frac{16}{40} = \frac{2}{5} $$ 7) $$ \frac{25}{40} = \frac{5}{8} $$ 8) $$ \frac{4}{12} = \frac{1}{3} $$ 9) $$ \frac{12}{15} = \frac{4}{5} $$ 10) $$ \frac{2}{8} = \frac{1}{4} $$ 11) $$ \frac{7}{42} = \frac{1}{6} $$ 12) $$ \frac{45}{72} = \frac{5}{8} $$ 13) $$ \frac{18}{36} = \frac{1}{2} $$ 14) $$ \frac{18}{30} = \frac{3}{5} $$ 15) $$ \frac{12}{24} = \frac{1}{2} $$ 16) $$ \frac{9}{36} = \frac{1}{4} $$ 17) $$ \frac{30}{36} = \frac{5}{6} $$ 18) $$ \frac{54}{72} = \frac{3}{4} $$

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