Quick answer: To add or subtract fractions, give them a common denominator. To multiply, multiply tops and bottoms. To divide, flip the second fraction and multiply. Then simplify by dividing top and bottom by their greatest common divisor. For example, 1 1/2 + 2 3/4 = 17/4, which is 4 1/4 or 4.25.
Fractions turn up in recipes, woodworking, homework and money, and the arithmetic is fiddly: common denominators, flipping fractions, simplifying. This calculator handles all of it, including mixed numbers such as 1½ or 2¾.
Put a whole number in the left box if you have one, and the numerator over the denominator in the right box. Pick an operation, and the result appears as a simplified fraction, a mixed number and a decimal.
The rules
a/b − c/d = (a×d − c×b) ÷ (b×d)
a/b × c/d = (a×c) ÷ (b×d)
a/b ÷ c/d = (a×d) ÷ (b×c)
A mixed number such as 1 1/2 is first turned into an improper fraction: 1 × 2 + 1 = 3, so it is 3/2. After the operation, the result is simplified by dividing the top and bottom by their greatest common divisor, and rewritten as a mixed number when the top is larger than the bottom.
The calculation uses exact whole-number arithmetic, so there are no rounding errors in the fraction. The decimal is shown to 10 significant digits, and repeating decimals such as 1/3 are rounded.
A worked example
Example. 1 1/2 + 2 3/4: convert to 3/2 + 11/4 = 6/4 + 11/4 = 17/4, which is 4 1/4 or 4.25. And 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2, which is 1 1/2.
Common fractions as decimals and percents
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.3333 | 33.3% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 2/3 | 0.6667 | 66.7% |
| 3/4 | 0.75 | 75% |
| 5/8 | 0.625 | 62.5% |
Repeating decimals such as 1/3 are rounded.
Common mistakes to avoid
- Adding the denominators. 1/2 + 1/3 is 5/6, not 2/5: only the numerators are added after the denominators match.
- Forgetting to flip when dividing. 3/4 ÷ 1/2 is 3/4 × 2/1 = 3/2, not 3/8.
- Leaving an answer unsimplified. Divide top and bottom by their greatest common divisor, so 6/8 becomes 3/4.
Go deeper: read our guide Cups to Grams: A Baking Conversion Guide.
Frequently asked questions
How do I add fractions with different denominators?
Convert both to a common denominator, usually by multiplying the denominators, then add the numerators. For 1/2 + 1/3 use 3/6 + 2/6 = 5/6. The calculator does this and simplifies the result.
How do I divide fractions?
Flip the second fraction and multiply. 3/4 ÷ 1/2 becomes 3/4 × 2/1 = 6/4, which simplifies to 3/2.
How do I enter a negative fraction?
Put the minus sign on the whole number or, for a simple fraction with no whole number, on the numerator. For −1 1/2, enter −1 in the whole-number box and 1 over 2.
What is a mixed number?
A whole number and a fraction together, such as 2 3/4. It is the same as the improper fraction 11/4.
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Sources and further reading
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