Fraction Calculator
Fractions follow different rules for each operation, which is why they cause more trouble than the numbers involved deserve. This calculator handles all four and simplifies the result.
Formula
a/b + c/d = (ad + cb) ÷ bd · a/b × c/d = ac ÷ bd
- Dividing flips the second fraction: a/b ÷ c/d = a/b × d/c
- Simplify by dividing both parts by their greatest common divisor
1/2 + 1/3 = (3 + 2) ÷ 6 = 5/6
The Rules, Operation by Operation
- Multiplying is the easy one: multiply the tops, multiply the bottoms. 2/3 × 3/4 = 6/12 = 1/2.
- Dividing means flipping the second fraction and multiplying. 1/2 ÷ 1/4 = 1/2 × 4/1 = 2.
- Adding and subtracting need a common denominator first. 1/3 + 1/4 becomes 4/12 + 3/12 = 7/12.
The common trap is adding tops and bottoms straight across. 1/2 + 1/2 is 1, not 2/4.
Simplifying to Lowest Terms
Divide the numerator and denominator by their greatest common divisor.
18/24: the GCD is 6, so it reduces to 3/4.
An answer left as 6/12 is not wrong, but it is unfinished, and most marking schemes expect the simplified form.
Fractions and Decimals
A fraction is a division waiting to happen: 3/8 is 3 ÷ 8 = 0.375.
Denominators built only from 2s and 5s give terminating decimals; anything else recurs. 1/3 = 0.333... and 1/7 = 0.142857 repeating. This is why 1/3 cannot be written exactly as a decimal, and why keeping the fraction is often the more accurate choice.
Quick Reference
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/8 | 0.125 | 12.5% |
| 1/4 | 0.25 | 25% |
| 1/3 | 0.3333… | 33.33% |
| 3/8 | 0.375 | 37.5% |
| 1/2 | 0.5 | 50% |
| 5/8 | 0.625 | 62.5% |
| 2/3 | 0.6667… | 66.67% |
| 3/4 | 0.75 | 75% |
| 7/8 | 0.875 | 87.5% |
Frequently Asked Questions
- How do I add fractions with different denominators?
- Convert both to a common denominator first, then add the numerators. For 1/3 + 1/4, use twelfths: 4/12 + 3/12 = 7/12.
- Why do you flip the second fraction when dividing?
- Dividing by a number is the same as multiplying by its reciprocal. Dividing by 1/4 is multiplying by 4, which is why 1/2 ÷ 1/4 equals 2.
- How do I convert a fraction to a decimal?
- Divide the top by the bottom. 3/8 is 3 ÷ 8 = 0.375.
- What is an improper fraction?
- One where the numerator exceeds the denominator, such as 7/4. It can be written as the mixed number 1 3/4; both are correct.