How to Simplify Ratios

Simplifying a Ratio

To simplify a ratio, divide both numbers by their greatest common factor (GCF) — the largest number that divides evenly into both.

Simplify 12:8

Find the GCF of 12 and 8 → 4

Divide both: 12 ÷ 4 = 3, 8 ÷ 4 = 2

Simplified: 3:2

More Examples

Simplify 20:35

GCF of 20 and 35 → 5

20 ÷ 5 = 4, 35 ÷ 5 = 7

Simplified: 4:7

Simplify a ratio with decimals: 1.5:2.5

Multiply both by 10 to remove decimals: 15:25

GCF of 15 and 25 → 5

15 ÷ 5 = 3, 25 ÷ 5 = 5

Simplified: 3:5

How to Find the GCF

List the factors of each number, then pick the largest one they share.

GCF of 18 and 24

Factors of 18: 1, 2, 3, 6, 9, 18

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Largest shared factor: 6

💡 Shortcut: If you can't spot the GCF immediately, just keep dividing both numbers by any common factor (2, 3, 5…) until nothing works. You'll get to the simplest form.

🎯 Practice Problems

1. Simplify the ratio 10:15.

A) 1:5

B) 5:3

C) 2:3

D) 10:15

2. Simplify 24:36.

A) 4:6

B) 12:18

C) 2:3

D) 6:9

3. Simplify 9:9.

A) 9:9

B) 0:0

C) 1:1

D) 9:1

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🎯 Bonus Practice

1. Simplify 45:30.

A) 9:6

B) 3:2

C) 15:10

D) 45:30

2. Simplify the ratio 2.4:1.6.

A) 24:16

B) 6:4

C) 3:2

D) 2:1

3. Simplify 100:250.

A) 1:25

B) 10:25

C) 2:5

D) 4:10

4. Is 4:6 fully simplified?

A) Yes

B) No — simplify to 2:3

C) No — simplify to 1:1.5

D) No — simplify to 4:3

5. Simplify 7:21.

A) 7:21

B) 1:3

C) 7:3

D) 1:7