Equivalent fractions
Generate a list of fractions equal to any fraction, check whether two fractions are the same amount, or fill in a missing numerator.
List equivalent fractions
Simplest form: 2/3. Every fraction below equals it.
- ×1
- ×2
- ×3
- ×4
- ×5
- ×6
- ×7
- ×8
- ×9
- ×10
- ×11
- ×12
Are these equivalent?
Yes — equivalent
Cross products: 4 × 15 = 60 and 10 × 6 = 60 — equal. In lowest terms they are 2/3 and 2/3.
Find the missing number
Multiply by 5: the missing numerator is 15.
See why 3/4 = 6/8 = 9/12
Multiplying top and bottom by the same number is the same as slicing every piece into that many thinner slices. You get more pieces, each smaller, and the shaded amount stays exactly the same.
3/4 × 1/1 = 3/4. Multiplying by 1/1 is multiplying by 1, which is why the value doesn't move.
How to find equivalent fractions
Multiply the numerator and denominator by the same number: 2/3 × 4/4 = 8/12. Divide both by a common factor to go the other way: 8/12 ÷ 4/4 = 2/3 — that's simplifying.
Equivalent fractions are what make adding and comparing possible: to add 2/3 and 1/4 you swap them for 8/12 and 3/12. The LCD calculator picks the best common denominator.
Common equivalent fractions
| Fraction | Equivalent fractions | Decimal |
|---|---|---|
| 1/2 | 2/4, 3/6, 4/8, 5/10 | 0.5 |
| 1/3 | 2/6, 3/9, 4/12, 5/15 | 0.3333 |
| 2/3 | 4/6, 6/9, 8/12, 10/15 | 0.6667 |
| 1/4 | 2/8, 3/12, 4/16, 5/20 | 0.25 |
| 3/4 | 6/8, 9/12, 12/16, 15/20 | 0.75 |
| 1/5 | 2/10, 3/15, 4/20, 5/25 | 0.2 |
| 2/5 | 4/10, 6/15, 8/20, 10/25 | 0.4 |
| 1/6 | 2/12, 3/18, 4/24, 5/30 | 0.1667 |
| 1/8 | 2/16, 3/24, 4/32, 5/40 | 0.125 |
| 3/8 | 6/16, 9/24, 12/32, 15/40 | 0.375 |
Questions people ask
What are equivalent fractions?
Fractions that name the same amount, like 1/2, 2/4 and 50/100. You get them by multiplying or dividing the top and bottom by the same non-zero number.
What fractions are equivalent to 1/2?
2/4, 3/6, 4/8, 5/10, 6/12, 50/100 — any fraction whose numerator is exactly half its denominator.
How do I check if two fractions are equivalent?
Cross-multiply. 4/6 and 10/15 are equivalent because 4 × 15 = 60 and 10 × 6 = 60. Or simplify both: each becomes 2/3.
How do I find a missing number in equivalent fractions?
Work out what the known denominator was multiplied by and do the same to the numerator. 3/4 = ?/20: 4 × 5 = 20, so the top is 3 × 5 = 15.
What fractions are equivalent to 2/3?
4/6, 6/9, 8/12, 10/15, 12/18, 14/21, 16/24 and so on.