Sure! Let’s simplify each of the given ratios step by step.
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1) 4 : 6
Find the
Greatest Common Divisor (GCD) of 4 and 6 → GCD = 2
Divide both numbers by 2:
> 4 ÷ 2 = 2
> 6 ÷ 2 = 3
✔ Simplified ratio: 2 : 3
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2) 16 : 40
GCD of 16 and 40 → 8
> 16 ÷ 8 = 2
> 40 ÷ 8 = 5
✔ Simplified ratio: 2 : 5
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3) 30 : 50 : 60
Find GCD of 30, 50, and 60 → GCD = 10
> 30 ÷ 10 = 3
> 50 ÷ 10 = 5
> 60 ÷ 10 = 6
✔ Simplified ratio: 3 : 5 : 6
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4) 12 : 20 : 32
GCD of 12, 20, 32 → GCD = 4
> 12 ÷ 4 = 3
> 20 ÷ 4 = 5
> 32 ÷ 4 = 8
✔ Simplified ratio: 3 : 5 : 8
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5) ³/₅ : ⁸/₁₀
First, simplify ⁸/₁₀ → ⁴/₅
Now we have:
³/₅ : ⁴/₅
Since denominators are same, compare numerators:
→ 3 : 4
✔ Simplified ratio: 3 : 4
*(Alternatively, multiply both parts by 5 to eliminate denominators: 3 : 4)*
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6) ³/₅ : ¹/₂
To simplify a ratio of fractions, multiply both parts by the
LCM of denominators (LCM of 5 and 2 is 10):
> (³/₅ × 10) : (¹/₂ × 10) = 6 : 5
✔ Simplified ratio: 6 : 5
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7) 250 : 300 : 350
GCD of 250, 300, 350 → 50
> 250 ÷ 50 = 5
> 300 ÷ 50 = 6
> 350 ÷ 50 = 7
✔ Simplified ratio: 5 : 6 : 7
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8) 1 ¹/₃ : ³/₅
Convert mixed number to improper fraction:
1 ¹/₃ = ⁴/₃
So now:
⁴/₃ : ³/₅
Multiply both parts by LCM of 3 and 5 → 15
> (⁴/₃ × 15) = 20
> (³/₅ × 15) = 9
✔ Simplified ratio: 20 : 9
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9) 33 : 121
GCD of 33 and 121 → 11
> 33 ÷ 11 = 3
> 121 ÷ 11 = 11
✔ Simplified ratio: 3 : 11
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10) 27 : 63
GCD of 27 and 63 → 9
> 27 ÷ 9 = 3
> 63 ÷ 9 = 7
✔ Simplified ratio: 3 : 7
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11) 8 : ²/₃
Multiply both parts by 3 to eliminate the fraction:
> 8 × 3 = 24
> (²/₃) × 3 = 2
So: 24 : 2 → Simplify by dividing by 2 → 12 : 1
✔ Simplified ratio: 12 : 1
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12) 84 : 156
GCD of 84 and 156 → 12
> 84 ÷ 12 = 7
> 156 ÷ 12 = 13
✔ Simplified ratio: 7 : 13
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##
✔ Final Answers:
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
Let me know if you’d like to see any step explained in more detail!
Parent Tip: Review the logic above to help your child master the concept of simplifying ratio worksheet for grade 7.
