About the Fraction Calculator
What is the Fraction Calculator?
A fraction a/b represents a parts out of b equal parts. The top number is the numerator and the bottom number is the denominator, which can never be zero. Fractions appear everywhere, from recipes (¾ cup) and measurements (5/8 inch) to probability and ratios.
Enter two fractions and choose an operation. The calculator uses exact whole-number arithmetic (so there is no rounding error), then reduces the answer to lowest terms by dividing the numerator and denominator by their greatest common divisor. It also shows the answer as a mixed number and as a decimal.
How to use the Fraction Calculator
- First Numerator — a whole number; put a minus sign here for a negative fraction. (sample: 1)
- First Denominator — a non-zero whole number. (sample: 2)
- Operation (sample: Add (+))
- Second Numerator (sample: 1)
- Second Denominator — a non-zero whole number. (sample: 3)
- Press Calculate Fraction (results also refresh as you type). The result card shows the Result, along with Decimal value, Mixed number and Before simplifying.
Formula used
a/b + c/d = (a × d + b × c) ÷ (b × d)
- a, c = the numerators
- b, d = the denominators (not zero)
Subtraction: (ad − bc) ÷ bd. Multiplication: ac ÷ bd. Division: a/b ÷ c/d = ad ÷ bc, i.e. multiply by the reciprocal. The result is then simplified by dividing top and bottom by their GCD.
Worked example
These are the sample values already filled in the calculator above, and the result it returns for them:
| Input | Sample value |
|---|---|
| First Numerator | 1 |
| First Denominator | 2 |
| Operation | Add (+) |
| Second Numerator | 1 |
| Second Denominator | 3 |
| Result | Value |
|---|---|
| Result (simplified) | 5/6 |
| Decimal value | 0.833333 |
| Mixed number | 5/6 |
| Before simplifying | 5/6 |
Mixed numbers, improper fractions and decimals
To turn an improper fraction into a mixed number, divide the numerator by the denominator: 17/5 = 3 remainder 2, so 17/5 = 3 2/5. To go back, multiply the whole part by the denominator and add the numerator: 3 × 5 + 2 = 17, giving 17/5.
To turn a terminating decimal into a fraction, write it over the matching power of ten and simplify: 0.375 = 375/1000 = 3/8 (dividing both by 125).
Tips for using the Fraction Calculator
- To enter a mixed number such as 2 ¾, convert it to an improper fraction first: 2 × 4 + 3 = 11, so enter 11/4.
- A whole number is a fraction with denominator 1 — enter 5 as 5/1.
- Dividing by a fraction whose numerator is 0 is undefined, so the calculator shows an error instead of a result.