Simplifying Fractions Worksheets - Math Monks - Free Printable

Let’s go through each fraction one by one and reduce it to its simplest form. To do this, we find the greatest common factor (GCF) of the numerator and denominator, then divide both by that number.

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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 → 7/11

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 → 4/9

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 → 1/2

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 → 1/14

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 → 5/9

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 → 5/2 (or 2½ if mixed number is allowed — but since not specified, leave as improper fraction)

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 → 11/3

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 → 25/3

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 → 44/9

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 → 7/1 or just 7

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 → 5/12

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 → 8/13

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 → 7/10

14) 418/80
Let’s find GCF of 418 and 80.
First, factor 80: 2×2×2×2×5
Check if 418 divisible by 2? Yes → 418 ÷ 2 = 209
80 ÷ 2 = 40
Now check 209 and 40.
209 factors: 11 × 19
40 factors: 2×2×2×5 → no common factors with 209
So GCF was 2
→ 418 ÷ 2 = 209, 80 ÷ 2 = 40 → 209/40

15) 230/180
Both end in 0 → divisible by 10
230 ÷ 10 = 23, 180 ÷ 10 = 18
Now check 23 and 18 → 23 is prime, doesn’t divide 18
So GCF = 10
→ 23/18

Wait — let me double-check #14 and #15 for accuracy.

For #14: 418 ÷ 2 = 209, 80 ÷ 2 = 40 → 209 and 40 share no common factors → correct.

For #15: 230 and 180 → GCF is actually 10? Let’s see:

230 = 23 × 10
180 = 18 × 10
But 23 and 18 have no common factors → yes, GCF=10 → 23/18 ✔️

Actually, wait — can we simplify 230/180 more?

Let’s try dividing by 10 first: 23/18 — that’s already simplified.

Alternatively, GCF of 230 and 180:

Prime factors:

230 = 2 × 5 × 23
180 = 2² × 3² × 5
Common: 2 × 5 = 10 → same result → 23/18 ✔️

All done!

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