What is a fraction calculator?
A fraction calculator does arithmetic on fractions without converting them to decimals first, so the answer stays exact. Enter two fractions as numerator and denominator, pick add, subtract, multiply or divide, and this calculator returns the result reduced to lowest terms, plus the same value as a decimal rounded to six places.
How to use it
- Enter the numerator (top number) and denominator (bottom number) of the first fraction.
- Choose an operator: +, −, × or ÷.
- Enter the second fraction.
- Click Calculate to see the simplified fraction and the decimal.
Whole numbers can be entered as fractions over 1: 3 is 3/1. A denominator of 0 is rejected, and so is dividing by a fraction equal to zero.
The rules for each operation
For two fractions a/b and c/d, the calculator applies these formulas, then simplifies:
| Operation | Formula | Example | Result |
|---|---|---|---|
| Add | (a × d + c × b) / (b × d) | 1/2 + 1/3 | 5/6 |
| Subtract | (a × d − c × b) / (b × d) | 3/4 − 5/6 | -1/12 |
| Multiply | (a × c) / (b × d) | 2/3 × 9/4 | 3/2 |
| Divide | (a × d) / (b × c) | 5/8 ÷ 3/4 | 5/6 |
Division is multiplication by the reciprocal: flip the second fraction and multiply. That's why 5/8 ÷ 3/4 becomes 5/8 × 4/3 = 20/24.
The calculator always multiplies the two denominators together rather than hunting for the lowest common denominator. The intermediate numbers are bigger, but the final answer is the same once it's simplified.
How simplifying works
To reduce a fraction to lowest terms, divide the top and bottom by their greatest common divisor (GCD), the largest whole number that divides both evenly. The calculator finds it with Euclid's algorithm: divide the larger number by the smaller, replace the larger with the remainder, and repeat until the remainder is 0. The last non-zero divisor is the GCD.
For 20/24: 24 ÷ 20 leaves 4, then 20 ÷ 4 leaves 0, so the GCD is 4, and 20/24 = 5/6.
Worked examples
Subtracting with unlike denominators: 3/4 − 5/6
- Cross-multiply the numerators: 3 × 6 = 18 and 5 × 4 = 20.
- Subtract: 18 − 20 = −2.
- Multiply the denominators: 4 × 6 = 24, giving −2/24.
- The GCD of 2 and 24 is 2, so the answer is −1/12, or −0.083333 as a decimal.
Adding into an improper fraction: 7/4 + 5/6
- 7 × 6 + 5 × 4 = 42 + 20 = 62.
- 4 × 6 = 24, giving 62/24.
- The GCD is 2, so the result is 31/12 (2.583333).
- As a mixed number, 31 ÷ 12 = 2 remainder 7, so 2 7/12.
Dividing to a whole number: 3/4 ÷ 1/8
3/4 × 8/1 = 24/4, which simplifies to 6/1, displayed as 6/1. Read it as 6.
Reading the output
- Result (Fraction) is always in lowest terms with a positive denominator. A whole-number answer is shown over 1, and zero is shown as
0/1. - Result (Decimal) is rounded to six decimal places with trailing zeros removed. Repeating decimals are cut off, so 2/3 shows as 0.666667. Use the fraction when you need the exact value.
- Mixed numbers aren't produced. Convert improper fractions yourself as shown above.
Where fractions come up
Recipes, measurements in inches (5/8 in, 3/16 in), and probabilities all use fractions, and adding them by hand is where most mistakes happen. If your fractions represent parts of a whole that you'd rather compare as percentages, the percentage calculator is the better fit. For proportions such as 3:4 = 9:?, try the ratio calculator.
Related calculators
- Basic calculator: type a full expression such as (3/4 - 5/6) * 2 and get a decimal.
- Ratio calculator: simplify a ratio or solve a proportion for the missing term.
- Algebra solver: solve a linear equation for x.
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