Equivalent fractions are different-looking fractions that represent the same value. For 1/2, that means any fraction where the numerator is exactly half the denominator.
1/2 = 2/4 = 3/6 = 4/8 = 5/10 = 10/20 = 50/100
How to find fractions equivalent to 1/2
Multiply the top and bottom by the same number. Because you're multiplying by a form of 1 (like 2/2 or 3/3), the value doesn't change:
1/2 × 2/2 = 2/4
1/2 × 3/3 = 3/6
1/2 × 4/4 = 4/8
1/2 × 5/5 = 5/10
A table of equivalents
| Multiply by | Equivalent fraction |
|---|---|
| 2 | 2/4 |
| 3 | 3/6 |
| 4 | 4/8 |
| 5 | 5/10 |
| 10 | 10/20 |
| 50 | 50/100 |
There are infinitely many — you can keep going forever.
How to check two fractions are equivalent
Method 1 — divide: a fraction equals 1/2 when numerator ÷ denominator = 0.5. For 7/14: 7 ÷ 14 = 0.5 ✓. You can confirm divisions on the scientific calculator.
Method 2 — cross-multiply: a/b = c/d when a × d = b × c. Check 4/8 vs 1/2: 4 × 2 = 8 and 8 × 1 = 8 — equal, so they match.
Simplifying back to 1/2
Going the other way, divide top and bottom by their greatest common factor. 6/12 → divide by 6 → 1/2. The simplest form of all these fractions is 1/2.
Why this matters
Equivalent fractions let you add fractions with different denominators, compare sizes, and convert to percentages. In fact 1/2 = 0.5 = 50% — the same idea behind 3/4 as a percent and decimal. Next, see what's equivalent to 2/3.
Frequently asked questions
What fractions are equivalent to 1/2?
How do you check if a fraction equals 1/2?
How do you make an equivalent fraction?
What is the simplest form of these fractions?
Is 1/2 equal to 50%?
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