How to use the equivalent fractions calculator
- List equivalent fractions – type a fraction to see the first ten fractions equal to it.
- Check if two fractions are equal – type both; the calculator cross-multiplies and compares their simplest forms.
- Find the missing number – solve problems like 3/4 = ?/20.
What are equivalent fractions?
Equivalent fractions name the same amount with different numbers: 1/2, 2/4 and 4/8 all mean half. You get one from another by multiplying (or dividing) the top and bottom by the same number:
\frac{a}{b} = \frac{a \times k}{b \times k} \qquad \frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}How to check if two fractions are equivalent
Cross-multiply: a/b and c/d are equal exactly when a × d = b × c. For 6/8 and 9/12: 6 × 12 = 72 and 8 × 9 = 72, so they are equal. You can also simplify both – 6/8 = 3/4 and 9/12 = 3/4.
How to find a missing number
Example: 3/4 = ?/20. The denominator went from 4 to 20, so it was multiplied by 5. Multiply the numerator by 5 too:
\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}Equivalent fractions chart
| Fraction | Equivalent fractions |
|---|---|
| 1/2 | 2/4, 3/6, 4/8, 5/10, 6/12 |
| 1/3 | 2/6, 3/9, 4/12, 5/15, 6/18 |
| 2/3 | 4/6, 6/9, 8/12, 10/15, 12/18 |
| 1/4 | 2/8, 3/12, 4/16, 5/20, 6/24 |
| 3/4 | 6/8, 9/12, 12/16, 15/20, 18/24 |
| 1/5 | 2/10, 3/15, 4/20, 5/25, 6/30 |
| 2/5 | 4/10, 6/15, 8/20, 10/25, 12/30 |
| 3/5 | 6/10, 9/15, 12/20, 15/25, 18/30 |
| 1/6 | 2/12, 3/18, 4/24, 5/30, 6/36 |
| 5/6 | 10/12, 15/18, 20/24, 25/30, 30/36 |
| 1/8 | 2/16, 3/24, 4/32, 5/40, 6/48 |
| 3/8 | 6/16, 9/24, 12/32, 15/40, 18/48 |
Frequently asked questions
How do you find equivalent fractions?
Multiply or divide the numerator and denominator by the same non-zero number: 2/3 = 4/6 = 6/9 = 8/12.
How can I tell if two fractions are equivalent?
Cross-multiply: a/b and c/d are equal when a × d = b × c. Or simplify both and see if you get the same fraction.
How many equivalent fractions does a fraction have?
Infinitely many – you can multiply the top and bottom by any whole number.
How do I solve 2/5 = ?/15?
15 ÷ 5 = 3, so multiply the numerator by 3 as well: 2 × 3 = 6, giving 6/15.
Why are equivalent fractions useful?
They let you rewrite fractions with a common denominator so you can add, subtract and compare them.