Fraction Calculator
Three fraction tools in one place, all live as you type: add, subtract, multiply or divide two fractions with the steps shown; simplify any single fraction to lowest terms; and convert freely between a fraction, a decimal and a percent by editing any one of the three.
How fractions are combined
Add: a/b + c/d = (ad + cb) ÷ (bd)
Subtract: a/b − c/d = (ad − cb) ÷ (bd)
Multiply: a/b × c/d = (ac) ÷ (bd)
Divide: a/b ÷ c/d = (ad) ÷ (bc)
Adding and subtracting find a common denominator by cross-multiplying, the way it is taught on paper. Multiplying multiplies straight across. Dividing multiplies by the reciprocal of the second fraction. The result is then simplified by dividing the numerator and denominator by their greatest common divisor.
Worked example
Adding 1/2 and 1/3:
| Common denominator | 1×3 + 1×2 = 5, over 2×3 = 6 |
|---|---|
| Unsimplified result | 5/6 |
| Simplified fraction | 5/6 (already in lowest terms) |
| Decimal | 0.833333 |
Multiplying the same two fractions instead gives 1/2 × 1/3 = 1/6, a smaller result, since multiplying proper fractions always shrinks the value.
Reading the result
A fraction is in lowest terms when the numerator and denominator share no common factor other than 1. The calculator always simplifies automatically, so 4/8 is returned as 1/2. When the numerator is larger than the denominator, the mixed-number form (a whole number plus a proper fraction) is often easier to read than the improper fraction, and the calculator shows both.
The fraction, decimal and percent converter above stays in sync in both directions: type a fraction and the decimal and percent update, or type a decimal or a percent and the equivalent fraction appears. For a broader set of percentage questions, such as percent change or increasing a number by a percentage, see the percentage calculator.
Frequently asked questions
How do I add two fractions with different denominators?
Cross-multiply to get a common denominator: a/b + c/d = (ad + cb) ÷ (bd). For 1/4 + 1/6, that is (1×6 + 1×4) ÷ (4×6) = 10/24, which simplifies to 5/12.
How do I simplify a fraction?
Find the greatest common divisor of the numerator and denominator and divide both by it. 8/12 has a greatest common divisor of 4, so it simplifies to 2/3. The calculator does this for every result automatically.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. 3/4 = 3 ÷ 4 = 0.75. The calculator shows the decimal form alongside the simplified fraction for every operation.
What does the mixed number mean?
A mixed number writes an improper fraction (numerator larger than denominator) as a whole number plus a proper fraction. 7/2 is the same value as the mixed number 3 1/2. Both are shown when they apply.
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Last updated . Formulas are shown on the page and checked against the worked example.
This calculator is for general information and education only. It is not professional advice. Confirm important decisions with a qualified adviser.