To simplify ratios, we divide all parts by their greatest common divisor (GCD). Let’s go step by step for each problem:
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1) 4 : 6
GCD of 4 and 6 is 2.
Divide both by 2 → 4÷2 = 2, 6÷2 = 3
→
2 : 3
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2) 16 : 40
GCD of 16 and 40 is 8.
16÷8 = 2, 40÷8 = 5
→
2 : 5
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3) 30 : 50 : 60
GCD of 30, 50, 60 is 10.
30÷10=3, 50÷10=5, 60÷10=6
→
3 : 5 : 6
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4) 12 : 20 : 32
GCD of 12, 20, 32 is 4.
12÷4=3, 20÷4=5, 32÷4=8
→
3 : 5 : 8
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5) 3/5 : 8/10
First, simplify 8/10 to 4/5.
Now we have 3/5 : 4/5
Since denominators are same, compare numerators: 3 : 4
→
3 : 4
*(Alternatively, multiply both by 10 to eliminate denominators: 3/5×10=6, 8/10×10=8 → 6:8 → divide by 2 → 3:4)*
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6) 3/5 : 1/2
Multiply both parts by 10 (LCM of 5 and 2) to clear denominators:
3/5 × 10 = 6, 1/2 × 10 = 5
→
6 : 5
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7) 250 : 300 : 350
GCD of 250, 300, 350 is 50.
250÷50=5, 300÷50=6, 350÷50=7
→
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 by 15 (LCM of 3 and 5):
4/3 × 15 = 20, 3/5 × 15 = 9
→
20 : 9
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9) 33 : 121
GCD of 33 and 121 is 11.
33÷11=3, 121÷11=11
→
3 : 11
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10) 27 : 63
GCD of 27 and 63 is 9.
27÷9=3, 63÷9=7
→
3 : 7
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11) 8 : 2/3
Multiply both by 3 to eliminate denominator:
8×3 = 24, (2/3)×3 = 2
→ 24 : 2 → divide by 2 →
12 : 1
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12) 84 : 156
Find GCD 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
GCD is 12.
84÷12=7, 156÷12=13
→
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 simplifying ratios worksheet.
