Equivalent Ratios

Different numbers, same relationship

What Are Equivalent Ratios?

Equivalent ratios have the same relationship between their parts, even though the numbers are different. They simplify to the same ratio.
These are all equivalent

1:2 = 2:4 = 3:6 = 5:10 = 50:100

They all simplify to 1:2.

How to Find Equivalent Ratios

Multiply or divide both parts by the same number. This is the golden rule. As long as you do the same thing to both sides, the ratio stays equivalent.
Start with 3:4
× 2 → 6:8
× 3 → 9:12
× 5 → 15:20
× 10 → 30:40

All equivalent to 3:4.

How to Check If Two Ratios Are Equivalent

Two methods:

Method 1: Simplify both

Are 8:12 and 10:15 equivalent?

8:12 → ÷4 → 2:3
10:15 → ÷5 → 2:3
Same simplified form → Yes, equivalent
Method 2: Cross multiply

Are 3:5 and 9:15 equivalent?

3 × 15 = 45
5 × 9 = 45
Cross products are equal → Yes, equivalent
💡 Key insight: Equivalent ratios are the foundation of proportions. When you write 3:5 = 9:15, that's a proportion — two equivalent ratios set equal.

🎯 Practice Problems

1. Which ratio is equivalent to 2:5?
A) 4:7
B) 6:15
C) 4:25
D) 10:20
2. Are 4:6 and 10:15 equivalent?
A) Yes
B) No
3. Find the missing number: 3:7 = 9:?
A) 14
B) 21
C) 63
D) 7

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🎯 Bonus Practice

1. Which ratio is NOT equivalent to 5:2?
A) 10:4
B) 15:6
C) 25:10
D) 20:10
2. Find the missing number: ?:12 = 5:6
A) 10
B) 7
C) 24
D) 2
3. Are 3:8 and 9:20 equivalent?
A) Yes
B) No
4. Write three equivalent ratios for 1:4.
A) 2:8, 3:12, 4:16
B) 2:5, 3:6, 4:7
C) 1:8, 1:12, 1:16
D) 4:1, 8:2, 12:3
5. If 6:9 is equivalent to 2:x, what is x?
A) 6
B) 3
C) 9
D) 4