What this calculator does
A fraction calculator takes the tedious part out of fraction arithmetic: finding a common denominator, multiplying across, and then simplifying back down. Enter two fractions, or two mixed numbers such as 2 3/4, choose an operation, and the simplified result comes out directly.
This version accepts a whole-number part alongside the numerator and denominator for each fraction, so a mixed number like 1 1/2 can be entered exactly as written, rather than having to convert it to an improper fraction (3/2) by hand first.
The formula
To add or subtract two fractions, convert both to a common denominator (multiply the two denominators together), combine the numerators, then divide both the numerator and denominator by their greatest common divisor to simplify. To multiply, multiply the numerators together and the denominators together. To divide, multiply by the reciprocal of the second fraction.
| Term | Meaning |
|---|---|
| Numerator | The top number of a fraction, showing how many parts are taken. |
| Denominator | The bottom number of a fraction, showing how many equal parts the whole is divided into. |
| Mixed number | A whole number and a fraction written together, such as 2 3/4, equal to the improper fraction 11/4. |
The inputs explained
| Field | What to enter |
|---|---|
| Sign of first number | Whether the first number is positive or negative. |
| Whole number part 1 (0 if none) | The whole-number part of the first number, if it is a mixed number; enter 0 if it is a plain fraction. |
| Numerator 1 | The numerator of the first fraction. |
| Denominator 1 | The denominator of the first fraction. |
| Operation | The operation to perform between the two numbers. |
| Sign of second number | Whether the second number is positive or negative. |
| Whole number part 2 (0 if none) | The whole-number part of the second number, if it is a mixed number; enter 0 if it is a plain fraction. |
| Numerator 2 | The numerator of the second fraction. |
| Denominator 2 | The denominator of the second fraction. |
When to use it
Adjusting a recipe with fractional measurements
Combining 3/4 cup and 1/3 cup, or halving a recipe that calls for 2 1/2 cups of an ingredient, needs exact fraction arithmetic rather than a rough decimal guess.
Working through fraction homework
Checking an add, subtract, multiply or divide fraction problem against the correct simplified answer catches an arithmetic slip before it compounds into a wrong final answer.
Converting a mixed measurement to a single fraction
A carpentry or sewing measurement like 3 5/8 inches is easier to work with as a single simplified fraction once combined with another measurement.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Adding a fixed fraction to a range of other fractions
1/2 added to a range of other fractions, each result shown in simplest form.
| Denominator of second fraction (numerator fixed at 1) | Result (simplest form) | Decimal |
|---|---|---|
| 3 | 5/6 | 0.8333 |
| 4 | 3/4 | 0.7500 |
| 5 | 7/10 | 0.7000 |
| 6 | 2/3 | 0.6667 |
| 8 | 5/8 | 0.6250 |
| 10 | 3/5 | 0.6000 |
The four operations applied to the same two fractions
The fractions 3/4 and 1/2, combined with each of the four basic operations.
| Operation | Result (simplest form) | As a mixed number | Decimal |
|---|---|---|---|
| Add | 5/4 | 1 1/4 | 1.250 |
| Subtract | 1/4 | 1/4 | 0.2500 |
| Multiply | 3/8 | 3/8 | 0.3750 |
| Divide | 3/2 | 1 1/2 | 1.500 |
Questions
How do you add two fractions?
Find a common denominator (multiplying the two denominators together always works), rewrite both fractions over it, add the numerators, then simplify by dividing both numbers by their greatest common divisor.
How do you divide fractions?
Multiply the first fraction by the reciprocal of the second: flip the second fraction upside down and multiply straight across, numerator by numerator and denominator by denominator.
Can this calculator handle mixed numbers?
Yes. Enter the whole-number part in the whole-number field and the fractional part as usual; the calculator converts the mixed number to an improper fraction internally before doing the arithmetic.
What does it mean to simplify a fraction?
Dividing both the numerator and denominator by their greatest common divisor, so the fraction is expressed with the smallest possible whole numbers. 6/8 and 3/4 represent the same value, but 3/4 is the simplified form.
For turning a decimal into its closest fraction, see the decimal to fraction calculator. For a single two-term ratio problem instead of fraction arithmetic, use the ratio & proportion calculator.