How to Find Equivalent Fractions
Multiply or divide both the numerator and denominator by the same non-zero number:
1/2 × 3/3 = 3/6 (equivalent)
1/2 × 5/5 = 5/10 (equivalent)
1/2 × 5/5 = 5/10 (equivalent)
The key rule: whatever you do to the bottom, do to the top.
Simplifying Fractions
Divide both numerator and denominator by their Greatest Common Factor (GCF):
12/18 → GCF(12,18) = 6 → 12÷6 / 18÷6 = 2/3
A fraction is in simplest form (or lowest terms) when the GCF of numerator and denominator is 1.
Comparing Fractions
To compare fractions, convert them to equivalent fractions with a common denominator:
Which is greater, 2/3 or 3/4?
2/3 = 8/12 | 3/4 = 9/12
9/12 > 8/12, so 3/4 > 2/3
2/3 = 8/12 | 3/4 = 9/12
9/12 > 8/12, so 3/4 > 2/3
Adding Fractions Using Equivalents
You must have the same denominator before adding:
1/3 + 1/4 = 4/12 + 3/12 = 7/12
Common Equivalent Fraction Pairs
| Fraction | Equivalent | Simplified |
|---|---|---|
| 2/4 | 4/8, 6/12, 8/16 | 1/2 |
| 3/9 | 6/18, 9/27 | 1/3 |
| 4/6 | 8/12, 10/15 | 2/3 |
| 6/8 | 9/12, 12/16 | 3/4 |
| 10/20 | 5/10, 2/4 | 1/2 |