Simplifying Fractions Worksheets - Math Monks - Free Printable

Let's solve each fraction by reducing it to its simplest form. To do this, we find the greatest common divisor (GCD) of the numerator and denominator and divide both by that number.

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1) $\frac{14}{22}$

- GCD of 14 and 22 is 2
- $\frac{14 \div 2}{22 \div 2} = \frac{7}{11}$
✔ Answer: $\frac{7}{11}$

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2) $\frac{8}{18}$

- GCD of 8 and 18 is 2
- $\frac{8 \div 2}{18 \div 2} = \frac{4}{9}$
✔ Answer: $\frac{4}{9}$

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3) $\frac{14}{28}$

- GCD of 14 and 28 is 14
- $\frac{14 \div 14}{28 \div 14} = \frac{1}{2}$
✔ Answer: $\frac{1}{2}$

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4) $\frac{4}{56}$

- GCD of 4 and 56 is 4
- $\frac{4 \div 4}{56 \div 4} = \frac{1}{14}$
✔ Answer: $\frac{1}{14}$

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5) $\frac{15}{27}$

- GCD of 15 and 27 is 3
- $\frac{15 \div 3}{27 \div 3} = \frac{5}{9}$
✔ Answer: $\frac{5}{9}$

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

- GCD of 40 and 16 is 8
- $\frac{40 \div 8}{16 \div 8} = \frac{5}{2}$
✔ Answer: $\frac{5}{2}$ (or $2\frac{1}{2}$)

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7) $\frac{22}{6}$

- GCD of 22 and 6 is 2
- $\frac{22 \div 2}{6 \div 2} = \frac{11}{3}$
✔ Answer: $\frac{11}{3}$ (or $3\frac{2}{3}$)

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8) $\frac{50}{6}$

- GCD of 50 and 6 is 2
- $\frac{50 \div 2}{6 \div 2} = \frac{25}{3}$
✔ Answer: $\frac{25}{3}$ (or $8\frac{1}{3}$)

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9) $\frac{88}{18}$

- GCD of 88 and 18 is 2
- $\frac{88 \div 2}{18 \div 2} = \frac{44}{9}$
✔ Answer: $\frac{44}{9}$ (or $4\frac{8}{9}$)

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10) $\frac{56}{8}$

- GCD of 56 and 8 is 8
- $\frac{56 \div 8}{8 \div 8} = \frac{7}{1} = 7$
✔ Answer: $7$

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11) $\frac{25}{60}$

- GCD of 25 and 60 is 5
- $\frac{25 \div 5}{60 \div 5} = \frac{5}{12}$
✔ Answer: $\frac{5}{12}$

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12) $\frac{16}{26}$

- GCD of 16 and 26 is 2
- $\frac{16 \div 2}{26 \div 2} = \frac{8}{13}$
✔ Answer: $\frac{8}{13}$

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13) $\frac{21}{30}$

- GCD of 21 and 30 is 3
- $\frac{21 \div 3}{30 \div 3} = \frac{7}{10}$
✔ Answer: $\frac{7}{10}$

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14) $\frac{418}{80}$

- GCD of 418 and 80:
- Factors:
- 418 ÷ 2 = 209
- 80 ÷ 2 = 40
- Now check GCD of 209 and 40:
- 209 = 11 × 19
- 40 = 2³ × 5 → no common factors
- So GCD is 2
- $\frac{418 \div 2}{80 \div 2} = \frac{209}{40}$
✔ Answer: $\frac{209}{40}$ (or $5\frac{9}{40}$)

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15) $\frac{230}{180}$

- GCD of 230 and 180:
- Both divisible by 10 → $\frac{23}{18}$
- Now check if 23 and 18 have common factors:
- 23 is prime, doesn't divide 18
- So GCD is 10
- $\frac{230 \div 10}{180 \div 10} = \frac{23}{18}$
✔ Answer: $\frac{23}{18}$ (or $1\frac{5}{18}$)

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✔ Final Answers:

1) $\frac{7}{11}$
2) $\frac{4}{9}$
3) $\frac{1}{2}$
4) $\frac{1}{14}$
5) $\frac{5}{9}$
6) $\frac{5}{2}$
7) $\frac{11}{3}$
8) $\frac{25}{3}$
9) $\frac{44}{9}$
10) $7$
11) $\frac{5}{12}$
12) $\frac{8}{13}$
13) $\frac{7}{10}$
14) $\frac{209}{40}$
15) $\frac{23}{18}$

Let me know if you'd like these as mixed numbers!