How the Fraction Calculator Works
A fraction shows part of a whole, such as 3/4: three parts out of four. Adding or dividing fractions by hand means finding common denominators, flipping and simplifying. The Fraction Calculator does it all. It adds, subtracts, multiplies and divides two fractions, and gives the answer as a simplified fraction, a decimal and (when it applies) a mixed number.
What you enter
- Numerator 1 and Denominator 1: the top and bottom of the first fraction (the default is 1/2).
- Operation: add, subtract, multiply or divide.
- Numerator 2 and Denominator 2: the second fraction (the default is 3/4).
The numbers must be whole numbers, and a denominator cannot be 0.
What you get
- Result: the answer as a fraction in its simplest form.
- Decimal: the same value, to 4 decimal places.
- Mixed number: shown when the answer is bigger than 1, such as 1 1/4.
The rules
| Operation | Rule |
|---|---|
| Add | a/b + c/d = (a x d + c x b) / (b x d) |
| Subtract | a/b - c/d = (a x d - c x b) / (b x d) |
| Multiply | a/b x c/d = (a x c) / (b x d) |
| Divide | a/b / c/d = (a x d) / (b x c) |
Then the answer is simplified by dividing the top and the bottom by their greatest common divisor (GCD). A negative sign is always kept on the top.
A worked example
The default is 1/2 + 3/4:
| Step | Value |
|---|---|
| Top: 1 x 4 + 3 x 2 | 10 |
| Bottom: 2 x 4 | 8 |
| Simplify (divide by the GCD, 2) | 5/4 |
| Decimal | 1.25 |
| Mixed number | 1 1/4 |
More examples
| Calculation | Result | Decimal |
|---|---|---|
| 2/3 x 3/5 | 2/5 | 0.4 |
| 3/4 - 5/6 | -1/12 | -0.0833 |
| 1/2 / 1/4 | 2 | 2 |
| 7/3 + 0/1 | 7/3 (2 1/3) | 2.3333 |
Chart: the example
The bars show the size of each fraction in the default example:
1/2 ████████████████ 0.5 3/4 ████████████████████████ 0.75 1/2 + 3/4 ████████████████████████████████████████ 1.25
Chart: unit fractions
The bigger the bottom number, the smaller the fraction:
1/2 ████████████████████████████████████████ 0.5 1/3 ███████████████████████████ 0.3333 1/4 ████████████████████ 0.25 1/5 ████████████████ 0.2 1/8 ██████████ 0.125
Doing it by hand
- Simplify: divide the top and bottom by the same number until you cannot. 10/8 becomes 5/4.
- Improper to mixed: divide the top by the bottom. 7/3 is 2 with a remainder of 1, so it is 2 1/3.
- Divide by a fraction: multiply by its flip. 1/2 divided by 1/4 is 1/2 x 4/1 = 2.
- Fraction to decimal: divide the top by the bottom. 3/4 = 0.75.
Tips
- The result is always in its simplest form, so you may see a smaller fraction than you expected.
- You cannot divide by a fraction that equals zero (such as 0/5).
- Decimals are not accepted in the boxes. To use 0.5, enter it as 1/2.
- Very large numbers are rejected, because the answer could not be exact.
This tool gives an estimate for general information only. Always check homework answers against your own working.