Math worksheet for reducing fractions to their simplest form.

I'll solve each fraction reduction problem step by step, finding the greatest common factor (GCF) for each and simplifying.

Problem 1: 14/22
- Factors of 14: 1, 2, 7, 14
- Factors of 22: 1, 2, 11, 22
- GCF = 2
- 14 ÷ 2 = 7, 22 ÷ 2 = 11
- Answer: 7/11

Problem 2: 8/18
- Factors of 8: 1, 2, 4, 8
- Factors of 18: 1, 2, 3, 6, 9, 18
- GCF = 2
- 8 ÷ 2 = 4, 18 ÷ 2 = 9
- Answer: 4/9

Problem 3: 14/28
- Factors of 14: 1, 2, 7, 14
- Factors of 28: 1, 2, 4, 7, 14, 28
- GCF = 14
- 14 ÷ 14 = 1, 28 ÷ 14 = 2
- Answer: 1/2

Problem 4: 4/56
- Factors of 4: 1, 2, 4
- Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
- GCF = 4
- 4 ÷ 4 = 1, 56 ÷ 4 = 14
- Answer: 1/14

Problem 5: 15/27
- Factors of 15: 1, 3, 5, 15
- Factors of 27: 1, 3, 9, 27
- GCF = 3
- 15 ÷ 3 = 5, 27 ÷ 3 = 9
- Answer: 5/9

Problem 6: 40/16
- Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
- Factors of 16: 1, 2, 4, 8, 16
- GCF = 8
- 40 8 = 5, 16 ÷ 8 = 2
- Answer: 5/2 or 2½

Problem 7: 22/6
- Factors of 22: 1, 2, 11, 22
- Factors of 6: 1, 2, 3, 6
- GCF = 2
- 22 ÷ 2 = 11, 6 ÷ 2 = 3
- Answer: 11/3 or 3

Problem 8: 50/6
- Factors of 50: 1, 2, 5, 10, 25, 50
- Factors of 6: 1, 2, 3, 6
- GCF = 2
- 50 ÷ 2 = 25, 6 ÷ 2 = 3
- Answer: 25/3 or 8⅓

Problem 9: 88/18
- Factors of 88: 1, 2, 4, 8, 11, 22, 44, 88
- Factors of 18: 1, 2, 3, 6, 9, 18
- GCF = 2
- 88 ÷ 2 = 44, 18 ÷ 2 = 9
- Answer: 44/9 or 4⁸/₉

Problem 10: 56/8
- Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
- Factors of 8: 1, 2, 4, 8
- GCF = 8
- 56 ÷ 8 = 7, 8 ÷ 8 = 1
- Answer: 7/1 or 7

Problem 11: 25/60
- Factors of 25: 1, 5, 25
- Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- GCF = 5
- 25 ÷ 5 = 5, 60 ÷ 5 = 12
- Answer: 5/12

Problem 12: 16/26
- Factors of 16: 1, 2, 4, 8, 16
- Factors of 26: 1, 2, 13, 26
- GCF = 2
- 16 ÷ 2 = 8, 26 ÷ 2 = 13
- Answer: 8/13

Problem 13: 21/30
- Factors of 21: 1, 3, 7, 21
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- GCF = 3
- 21 ÷ 3 = 7, 30 ÷ 3 = 10
- Answer: 7/10

Problem 14: 418/80
Let me check this carefully:
- 418 = 2 × 209 = 2 × 11 × 19
- 80 = 2 × 40 = 2 × 2 × 20 = 2 × 2 × 2 × 10 = 2³ × 2 × 5 = 2⁴ × 5
- GCF = 2
- 418 2 = 209, 80 ÷ 2 = 40
- Answer: 209/40 or 5⁹/₄₀

Problem 15: 230/180
- 230 = 10 × 23 = 2 × 5 × 23
- 180 = 10 × 18 = 2 × 5 × 18 = 2 × 5 × 2 × 9 = 2² × 5 × 3²
- GCF = 2 × 5 = 10
- 230 ÷ 10 = 23, 180 ÷ 10 = 18
- Answer: 23/18 or 1⁵/₁₈

Final Answer:
1) 7/11
2) 4/9
3) 1/2
4) 1/14
5) 5/9
6) 5/2
7) 11/3
8) 25/3
9) 44/9
10) 7
11) 5/12
12) 8/13
13) 7/10
14) 209/40
15) 23/18