Simplifying Fractions Sheet 3 - Practice reducing fractions to their simplest form.
Simplifying Fractions Sheet 3 worksheet with math problems for reducing fractions to simplest form.
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Show Answer Key & Explanations
Step-by-step solution for: Simplifying Fractions Worksheet
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Show Answer Key & Explanations
Step-by-step solution for: Simplifying Fractions Worksheet
Let’s simplify each fraction step by step. To simplify a fraction, we find the greatest common factor (GCF) of the numerator and denominator, then divide both by that number.
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1) 38/42
Factors of 38: 1, 2, 19, 38
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
GCF = 2
→ 38 ÷ 2 = 19
→ 42 ÷ 2 = 21
✔ 19/21
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2) 25/27
Factors of 25: 1, 5, 25
Factors of 27: 1, 3, 9, 27
GCF = 1 → already simplified
✔ 25/27
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3) 25/63
Factors of 25: 1, 5, 25
Factors of 63: 1, 3, 7, 9, 21, 63
GCF = 1 → already simplified
✔ 25/63
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4) 35/28
Factors of 35: 1, 5, 7, 35
Factors of 28: 1, 2, 4, 7, 14, 28
GCF = 7
→ 35 ÷ 7 = 5
→ 28 ÷ 7 = 4
✔ 5/4 (or 1¼ if mixed number allowed — but since it says “simplest form”, improper fraction is fine unless specified)
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5) 38/22
Factors of 38: 1, 2, 19, 38
Factors of 22: 1, 2, 11, 22
GCF = 2
→ 38 ÷ 2 = 19
→ 22 ÷ 2 = 11
✔ 19/11
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6) 88/77
Factors of 88: 1, 2, 4, 8, 11, 22, 44, 88
Factors of 77: 1, 7, 11, 77
GCF = 11
→ 88 ÷ 11 = 8
→ 77 ÷ 11 = 7
✔ 8/7
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7) 28/64
Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 64: 1, 2, 4, 8, 16, 32, 64
GCF = 4
→ 28 ÷ 4 = 7
→ 64 ÷ 4 = 16
✔ 7/16
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8) 77/44
Factors of 77: 1, 7, 11, 77
Factors of 44: 1, 2, 4, 11, 22, 44
GCF = 11
→ 77 ÷ 11 = 7
→ 44 ÷ 11 = 4
✔ 7/4
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9) 35/53
35: 1, 5, 7, 35
53: prime → only 1 and 53
GCF = 1 → already simplified
✔ 35/53
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10) 27/45
Factors of 27: 1, 3, 9, 27
Factors of 45: 1, 3, 5, 9, 15, 45
GCF = 9
→ 27 ÷ 9 = 3
→ 45 ÷ 9 = 5
✔ 3/5
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11) 96/60
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
GCF = 12
→ 96 ÷ 12 = 8
→ 60 ÷ 12 = 5
✔ 8/5
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12) 32/20
Factors of 32: 1, 2, 4, 8, 16, 32
Factors of 20: 1, 2, 4, 5, 10, 20
GCF = 4
→ 32 ÷ 4 = 8
→ 20 ÷ 4 = 5
✔ 8/5
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13) 45/54
Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
GCF = 9
→ 45 ÷ 9 = 5
→ 54 ÷ 9 = 6
✔ 5/6
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14) 72/64
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Factors of 64: 1, 2, 4, 8, 16, 32, 64
GCF = 8
→ 72 ÷ 8 = 9
→ 64 ÷ 8 = 8
✔ 9/8
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15) 20/56
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
GCF = 4
→ 20 ÷ 4 = 5
→ 56 ÷ 4 = 14
✔ 5/14
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16) 48/64
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 64: 1, 2, 4, 8, 16, 32, 64
GCF = 16
→ 48 ÷ 16 = 3
→ 64 ÷ 16 = 4
✔ 3/4
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17) 63/64
63: 1, 3, 7, 9, 21, 63
64: powers of 2 → no common factors except 1
GCF = 1 → already simplified
✔ 63/64
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18) 72/81
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Factors of 81: 1, 3, 9, 27, 81
GCF = 9
→ 72 ÷ 9 = 8
→ 81 ÷ 9 = 9
✔ 8/9
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Final Answer:
1) 19/21
2) 25/27
3) 25/63
4) 5/4
5) 19/11
6) 8/7
7) 7/16
8) 7/4
9) 35/53
10) 3/5
11) 8/5
12) 8/5
13) 5/6
14) 9/8
15) 5/14
16) 3/4
17) 63/64
18) 8/9
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1) 38/42
Factors of 38: 1, 2, 19, 38
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
GCF = 2
→ 38 ÷ 2 = 19
→ 42 ÷ 2 = 21
✔ 19/21
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2) 25/27
Factors of 25: 1, 5, 25
Factors of 27: 1, 3, 9, 27
GCF = 1 → already simplified
✔ 25/27
---
3) 25/63
Factors of 25: 1, 5, 25
Factors of 63: 1, 3, 7, 9, 21, 63
GCF = 1 → already simplified
✔ 25/63
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4) 35/28
Factors of 35: 1, 5, 7, 35
Factors of 28: 1, 2, 4, 7, 14, 28
GCF = 7
→ 35 ÷ 7 = 5
→ 28 ÷ 7 = 4
✔ 5/4 (or 1¼ if mixed number allowed — but since it says “simplest form”, improper fraction is fine unless specified)
---
5) 38/22
Factors of 38: 1, 2, 19, 38
Factors of 22: 1, 2, 11, 22
GCF = 2
→ 38 ÷ 2 = 19
→ 22 ÷ 2 = 11
✔ 19/11
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6) 88/77
Factors of 88: 1, 2, 4, 8, 11, 22, 44, 88
Factors of 77: 1, 7, 11, 77
GCF = 11
→ 88 ÷ 11 = 8
→ 77 ÷ 11 = 7
✔ 8/7
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7) 28/64
Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 64: 1, 2, 4, 8, 16, 32, 64
GCF = 4
→ 28 ÷ 4 = 7
→ 64 ÷ 4 = 16
✔ 7/16
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8) 77/44
Factors of 77: 1, 7, 11, 77
Factors of 44: 1, 2, 4, 11, 22, 44
GCF = 11
→ 77 ÷ 11 = 7
→ 44 ÷ 11 = 4
✔ 7/4
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9) 35/53
35: 1, 5, 7, 35
53: prime → only 1 and 53
GCF = 1 → already simplified
✔ 35/53
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10) 27/45
Factors of 27: 1, 3, 9, 27
Factors of 45: 1, 3, 5, 9, 15, 45
GCF = 9
→ 27 ÷ 9 = 3
→ 45 ÷ 9 = 5
✔ 3/5
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11) 96/60
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
GCF = 12
→ 96 ÷ 12 = 8
→ 60 ÷ 12 = 5
✔ 8/5
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12) 32/20
Factors of 32: 1, 2, 4, 8, 16, 32
Factors of 20: 1, 2, 4, 5, 10, 20
GCF = 4
→ 32 ÷ 4 = 8
→ 20 ÷ 4 = 5
✔ 8/5
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13) 45/54
Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
GCF = 9
→ 45 ÷ 9 = 5
→ 54 ÷ 9 = 6
✔ 5/6
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14) 72/64
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Factors of 64: 1, 2, 4, 8, 16, 32, 64
GCF = 8
→ 72 ÷ 8 = 9
→ 64 ÷ 8 = 8
✔ 9/8
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15) 20/56
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
GCF = 4
→ 20 ÷ 4 = 5
→ 56 ÷ 4 = 14
✔ 5/14
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16) 48/64
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 64: 1, 2, 4, 8, 16, 32, 64
GCF = 16
→ 48 ÷ 16 = 3
→ 64 ÷ 16 = 4
✔ 3/4
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17) 63/64
63: 1, 3, 7, 9, 21, 63
64: powers of 2 → no common factors except 1
GCF = 1 → already simplified
✔ 63/64
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18) 72/81
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Factors of 81: 1, 3, 9, 27, 81
GCF = 9
→ 72 ÷ 9 = 8
→ 81 ÷ 9 = 9
✔ 8/9
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Final Answer:
1) 19/21
2) 25/27
3) 25/63
4) 5/4
5) 19/11
6) 8/7
7) 7/16
8) 7/4
9) 35/53
10) 3/5
11) 8/5
12) 8/5
13) 5/6
14) 9/8
15) 5/14
16) 3/4
17) 63/64
18) 8/9
Parent Tip: Review the logic above to help your child master the concept of simplifying fractions worksheet.
