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Fraction calculator
Add, subtract, multiply and divide fractions, simplified.
Quick answer
Fractions are added, subtracted, multiplied or divided, and the answer is reduced to lowest terms. Formula: a/b + c/d = (ad + bc) ÷ bd, a/b − c/d = (ad − bc) ÷ bd. 1/2 + 1/3 = 5/6, which is 0.8333 as a decimal.
Read the guide: How to simplify a ratio and solve proportions
Answer
5/6
- Mixed number
- 5/6
- Decimal
- 0.833333
How is fraction sums calculated?
To add or subtract fractions, give them the same denominator first; the calculator does this by cross-multiplying.
To multiply, multiply the tops and the bottoms. To divide, flip the second fraction and multiply.
The answer is always reduced to lowest terms and also shown as a mixed number.
What is the formula for fraction sums?
- a/b + c/d = (ad + bc) ÷ bd, a/b − c/d = (ad − bc) ÷ bd
- a/b × c/d = ac ÷ bd, a/b ÷ c/d = ad ÷ bc
- Then divide top and bottom by their greatest common divisor
Can you show a worked example of fraction sums?
1/2 + 1/3 = (1 × 3 + 1 × 2) ÷ (2 × 3) = 5/6. The decimal is 0.833333.
What are common fractions as decimals and percentages?
Each fraction in lowest terms, as a decimal and as a percentage.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/8 | 0.125 | 12.5% |
| 1/5 | 0.2 | 20% |
| 1/4 | 0.25 | 25% |
| 1/3 | 0.3333 | 33.3% |
| 3/8 | 0.375 | 37.5% |
| 1/2 | 0.5 | 50% |
| 2/3 | 0.6667 | 66.7% |
| 3/4 | 0.75 | 75% |
Common questions
How do I add fractions with different denominators?
Rewrite them over a common denominator, add the numerators, then simplify. 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common divisor. 6/8 becomes 3/4.
How do I divide by a fraction?
Multiply by its reciprocal. 1/2 ÷ 1/4 = 1/2 × 4/1 = 2.
What is a mixed number?
A whole number with a fraction, such as 1 1/2, which equals 3/2.