Grade 6 Simplifying and converting fractions worksheets - free ... - Free Printable

Sure! Let’s solve each of the 14 fraction simplification problems step by step. The goal is to reduce each fraction to its lowest terms — meaning we divide both numerator and denominator by their greatest common divisor (GCD).

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1. \( \frac{395}{500} \)

- Find GCD of 395 and 500.
- 395 = 5 × 79
- 500 = 2² × 5³
- GCD = 5
- Divide numerator and denominator by 5:
\[
\frac{395 ÷ 5}{500 ÷ 5} = \frac{79}{100}
\]

✔ Answer: \( \frac{79}{100} \)

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2. \( \frac{9}{15} \)

- GCD of 9 and 15 is 3.
- \( \frac{9 ÷ 3}{15 ÷ 3} = \frac{3}{5} \)

✔ Answer: \( \frac{3}{5} \)

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3. \( \frac{520}{105} \)

- GCD of 520 and 105.
- 520 = 2³ × 5 × 13
- 105 = 3 × 5 × 7
- GCD = 5
- \( \frac{520 ÷ 5}{105 ÷ 5} = \frac{104}{21} \)
- This is an improper fraction, but it’s already simplified.

✔ Answer: \( \frac{104}{21} \)

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4. \( \frac{33}{45} \)

- GCD of 33 and 45 is 3.
- \( \frac{33 ÷ 3}{45 ÷ 3} = \frac{11}{15} \)

✔ Answer: \( \frac{11}{15} \)

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5. \( \frac{132}{26} \)

- GCD of 132 and 26.
- 132 = 2² × 3 × 11
- 26 = 2 × 13
- GCD = 2
- \( \frac{132 ÷ 2}{26 ÷ 2} = \frac{66}{13} \)

✔ Answer: \( \frac{66}{13} \)

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6. \( \frac{416}{80} \)

- GCD of 416 and 80.
- 416 = 2⁵ × 13
- 80 = 2⁴ × 5
- GCD = 16 (2⁴)
- \( \frac{416 ÷ 16}{80 ÷ 16} = \frac{26}{5} \)

✔ Answer: \( \frac{26}{5} \)

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7. \( \frac{68}{16} \)

- GCD of 68 and 16 is 4.
- \( \frac{68 ÷ 4}{16 ÷ 4} = \frac{17}{4} \)

✔ Answer: \( \frac{17}{4} \)

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8. \( \frac{342}{60} \)

- GCD of 342 and 60.
- 342 = 2 × 3² × 19
- 60 = 2² × 3 × 5
- GCD = 6
- \( \frac{342 ÷ 6}{60 ÷ 6} = \frac{57}{10} \)

✔ Answer: \( \frac{57}{10} \)

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9. \( \frac{8}{24} \)

- GCD of 8 and 24 is 8.
- \( \frac{8 ÷ 8}{24 ÷ 8} = \frac{1}{3} \)

✔ Answer: \( \frac{1}{3} \)

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10. \( \frac{68}{32} \)

- GCD of 68 and 32 is 4.
- \( \frac{68 ÷ 4}{32 ÷ 4} = \frac{17}{8} \)

✔ Answer: \( \frac{17}{8} \)

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11. \( \frac{46}{8} \)

- GCD of 46 and 8 is 2.
- \( \frac{46 ÷ 2}{8 ÷ 2} = \frac{23}{4} \)

✔ Answer: \( \frac{23}{4} \)

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12. \( \frac{120}{150} \)

- GCD of 120 and 150 is 30.
- \( \frac{120 ÷ 30}{150 ÷ 30} = \frac{4}{5} \)

✔ Answer: \( \frac{4}{5} \)

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13. \( \frac{230}{50} \)

- GCD of 230 and 50 is 10.
- \( \frac{230 ÷ 10}{50 ÷ 10} = \frac{23}{5} \)

✔ Answer: \( \frac{23}{5} \)

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14. \( \frac{18}{90} \)

- GCD of 18 and 90 is 18.
- \( \frac{18 ÷ 18}{90 ÷ 18} = \frac{1}{5} \)

✔ Answer: \( \frac{1}{5} \)

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## ✔ Final Answers:

1. \( \frac{79}{100} \)
2. \( \frac{3}{5} \)
3. \( \frac{104}{21} \)
4. \( \frac{11}{15} \)
5. \( \frac{66}{13} \)
6. \( \frac{26}{5} \)
7. \( \frac{17}{4} \)
8. \( \frac{57}{10} \)
9. \( \frac{1}{3} \)
10. \( \frac{17}{8} \)
11. \( \frac{23}{4} \)
12. \( \frac{4}{5} \)
13. \( \frac{23}{5} \)
14. \( \frac{1}{5} \)

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Let me know if you’d like these converted to mixed numbers or decimals too!