What Are Equivalent Fractions?
Equivalent fractions are fractions that have different numerators and denominators but represent the same value or proportion of a whole. They are equal in value even though they look different.
How to Find Equivalent Fractions
You can create equivalent fractions by:
- Multiplying both the numerator and denominator by the same number
- Dividing both the numerator and denominator by a common factor (simplifying)
Visual Representation
Think of equivalent fractions like different ways to slice the same pizza:
- 1/2 = one half of a pizza (1 slice out of 2)
- 2/4 = two quarters of the same pizza (2 slices out of 4)
- 4/8 = four eighths of the same pizza (4 slices out of 8)
All represent exactly half the pizza!
Examples
Example 1: Equivalent Fractions for 1/2
Original:
1/2
Multiply by 2: 1/2 = (1×2)/(2×2) = 2/4
Multiply by 3: 1/2 = (1×3)/(2×3) = 3/6
Multiply by 4: 1/2 = (1×4)/(2×4) = 4/8
Multiply by 5: 1/2 = (1×5)/(2×5) = 5/10
Equivalent fractions: 2/4, 3/6, 4/8, 5/10, 6/12, ...
Example 2: Equivalent Fractions for 2/3
Original:
2/3
Multiply by 2: 2/3 = (2×2)/(3×2) = 4/6
Multiply by 3: 2/3 = (2×3)/(3×3) = 6/9
Multiply by 4: 2/3 = (2×4)/(3×4) = 8/12
Multiply by 5: 2/3 = (2×5)/(3×5) = 10/15
Equivalent fractions: 4/6, 6/9, 8/12, 10/15, 12/18, ...
Example 3: Equivalent Fractions for 3/5
Original:
3/5
Multiply by 2: 3/5 = (3×2)/(5×2) = 6/10
Multiply by 3: 3/5 = (3×3)/(5×3) = 9/15
Multiply by 4: 3/5 = (3×4)/(5×4) = 12/20
Multiply by 5: 3/5 = (3×5)/(5×5) = 15/25
Equivalent fractions: 6/10, 9/15, 12/20, 15/25, 18/30, ...
Example 4: Simplifying to Find Equivalents
Problem:
Find simplest form of 12/18
12/18 and all its equivalents share the same simplest form
GCD of 12 and 18 = 6
12/18 = 2/3 (simplest form)
All equivalent: 2/3, 4/6, 6/9, 8/12, 10/15, 12/18, ...
Example 5: Checking if Fractions are Equivalent
Question:
Are 3/4 and 15/20 equivalent?
Method 1: Cross multiply
3 × 20 = 60 and 4 × 15 = 60
Since both products are equal, they are equivalent
Method 2: Simplify both
3/4 is already in simplest form
15/20 = 3/4 (divide by 5)
Yes! 3/4 = 15/20