Equivalent Ratios
Equivalent ratios are different ratios that express the same relationship between quantities. Just like equivalent fractions, they have the same value but use different numbers!
What Are Equivalent Ratios?
Equivalent ratios express the same relationship between two quantities using different numbers.
Example: 1:2 = 2:4 = 3:6 = 10:20
All these ratios represent the same relationship: the second number is always twice the first number!
Think of it like this:
- 1 apple for every 2 oranges
- 2 apples for every 4 oranges
- 10 apples for every 20 oranges
The proportion stays the same!
Visual Representation
Interactive visualization — available in the full lesson
Each ratio shows the same 1:2 relationship scaled up!
Creating Equivalent Ratios
Rule: Multiply (or divide) BOTH terms by the SAME number!
Starting with 3:4
| Operation | Result |
|---|---|
| × 2 | 3×2 : 4×2 = 6:8 |
| × 3 | 3×3 : 4×3 = 9:12 |
| × 5 | 3×5 : 4×5 = 15:20 |
| × 10 | 3×10 : 4×10 = 30:40 |
All equivalent to 3:4!
Simplifying Ratios (Reducing)
Rule: Divide BOTH terms by their Greatest Common Divisor (GCD)
24 : 36
GCD = 12
24÷12 : 36÷12
= 2 : 3
50 : 100
GCD = 50
50÷50 : 100÷50
= 1 : 2
Simplest Form: When the GCD of both terms is 1 (they share no common factors except 1)