Equivalent fractions of 2/3 are fractions that simplify back to two-thirds. You build them by scaling the numerator and denominator together.
2/3 = 4/6 = 6/9 = 8/12 = 10/15 = 20/30
How to find fractions equivalent to 2/3
Multiply the top and bottom by the same number:
2/3 × 2/2 = 4/6
2/3 × 3/3 = 6/9
2/3 × 4/4 = 8/12
2/3 × 5/5 = 10/15
A table of equivalents
| Multiply by | Equivalent fraction |
|---|---|
| 2 | 4/6 |
| 3 | 6/9 |
| 4 | 8/12 |
| 5 | 10/15 |
| 10 | 20/30 |
| 100 | 200/300 |
How to check a fraction equals 2/3
Cross-multiply: to test if c/d equals 2/3, check whether 2 × d = 3 × c. For 8/12: 2 × 12 = 24 and 3 × 8 = 24 — equal, so 8/12 = 2/3. ✓
Divide: 2/3 as a decimal is 2 ÷ 3 = 0.6666…, a repeating decimal of about 66.67%. Any equivalent fraction gives the same 0.666… You can verify on the scientific calculator.
Simplifying to 2/3
Divide top and bottom by their greatest common factor. 10/15 → divide by 5 → 2/3. Two-thirds is already in lowest terms because 2 and 3 share no common factor besides 1.
2/3 as a decimal and percent
Because the denominator (3) isn't made only of 2s and 5s, 2/3 is a repeating decimal — the same reason 1/3 repeats. For converting fractions to percentages with steps shown, use our percentage calculator. See also what's equivalent to 1/2.
Frequently asked questions
What fractions are equivalent to 2/3?
Is 2/3 the same as 0.67?
How do you find a fraction equivalent to 2/3?
How do you check that a fraction equals 2/3?
Is 2/3 already in simplest form?
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