Let’s solve each ratio step by step. We’ll simplify them just like we simplify fractions — by dividing all parts by their greatest common factor (GCF).
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1) 4 : 6
Both numbers are divisible by 2.
→ 4 ÷ 2 = 2
→ 6 ÷ 2 = 3
✔ Simplified:
2 : 3
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2) 16 : 40
Find GCF of 16 and 40 → it’s 8.
→ 16 ÷ 8 = 2
→ 40 ÷ 8 = 5
✔ Simplified:
2 : 5
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3) 30 : 50 : 60
All three numbers are divisible by 10.
→ 30 ÷ 10 = 3
→ 50 ÷ 10 = 5
→ 60 ÷ 10 = 6
✔ Simplified:
3 : 5 : 6
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4) 12 : 20 : 32
Find GCF of 12, 20, and 32 → it’s 4.
→ 12 ÷ 4 = 3
→ 20 ÷ 4 = 5
→ 32 ÷ 4 = 8
✔ Simplified:
3 : 5 : 8
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5) ³⁄₅ : ⁄₁₀
First, simplify ⁸⁄₁₀ → that’s ⁴⁄₅.
Now we have: ³⁄₅ : ⁄₅
Since denominators are the same, compare numerators: 3 : 4
✔ Simplified:
3 : 4
*(Alternatively, multiply both sides by 10 to eliminate denominators:
(³⁄₅ × 10) : (⁸⁄₁₀ × 10) = 6 : 8 → then divide by 2 → 3 : 4)*
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6) ³⁄₅ : ¹⁄₂
To simplify ratios with fractions, multiply both sides by the least common denominator (LCD). LCD of 5 and 2 is 10.
→ ³⁄₅ × 10 = 6
→ ¹⁄₂ × 10 = 5
✔ Simplified:
6 : 5
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7) 250 : 300 : 350
All divisible by 50.
→ 250 ÷ 50 = 5
→ 300 ÷ 50 = 6
→ 350 ÷ 50 = 7
✔ Simplified:
5 : 6 : 7
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8) 1⅓ : ³⁄₅
Convert mixed number to improper fraction:
1⅓ = ⁴⁄₃
So now: ⁴⁄ : ³⁄₅
Multiply both sides by LCD of 3 and 5 → which is 15.
→ ⁴⁄₃ × 15 = 20
→ ³⁄₅ × 15 = 9
✔ Simplified:
20 : 9
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9) 33 : 121
Find GCF of 33 and 121.
33 = 3 × 11
121 = 11 × 11
→ GCF = 11
→ 33 ÷ 11 = 3
→ 121 ÷ 11 = 11
✔ Simplified:
3 : 11
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10) 27 : 63
GCF of 27 and 63 → 9
→ 27 ÷ 9 = 3
→ 63 ÷ 9 = 7
✔ Simplified:
3 : 7
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11) 8 : ²⁄₃
Multiply both sides by 3 to eliminate denominator.
→ 8 × 3 = 24
→ ²⁄₃ × 3 = 2
Now we have 24 : 2 → divide both by 2 → 12 : 1
✔ Simplified:
12 : 1
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12) 84 : 156
Find GCF of 84 and 156.
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Factors of 156: 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156
→ GCF = 12
→ 84 ÷ 12 = 7
→ 156 ÷ 12 = 13
✔ Simplified:
7 : 13
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Final Answer:
1) 2 : 3
2) 2 : 5
3) 3 : 5 : 6
4) 3 : 5 : 8
5) 3 : 4
6) 6 : 5
7) 5 : 6 : 7
8) 20 : 9
9) 3 : 11
10) 3 : 7
11) 12 : 1
12) 7 : 13
Parent Tip: Review the logic above to help your child master the concept of reducing ratios worksheet.
