Finding an Equivalent Fraction
The method is straightforward: multiply, or divide, the numerator and denominator by the same nonzero number. Because you're applying the same change to both parts, the fraction's actual value stays put - only its appearance changes.
1/2 × 5/5 = 5/10 (same value)
There's one rule worth holding onto: whatever you do to the denominator, do it to the numerator too. Skip that, and you've quietly turned it into a different fraction altogether.
Simplifying a Fraction to Lowest Terms
Simplifying is the same process run backward - dividing instead of multiplying. Find the Greatest Common Factor (GCF) of the numerator and denominator, then divide both by it:
Once the only number that divides evenly into both the top and bottom is 1, you're finished - that's what mathematicians call simplest form, or lowest terms.
Using Equivalent Fractions to Compare Sizes
Fractions with different denominators are tough to size up at a glance. Rewrite them with a shared denominator first, and the comparison becomes obvious:
2/3 = 8/12 | 3/4 = 9/12
9/12 > 8/12, so 3/4 is the larger fraction
Adding Fractions With Different Denominators
That same trick unlocks addition. Fractions can't be combined until they share a denominator, so convert each one into an equivalent fraction that does:
A Quick Reference Table
| 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 |