# Fraction calculator

> A fraction calculator adds, subtracts, multiplies, divides, and simplifies fractions, and returns the answer in lowest terms. For 1/2 + 1/3, the common denominator is 6, the problem becomes 3/6 + 2/6, and the answer is 5/6, or 0.8333 as a decimal. Improper fractions also show as a mixed number.

Source: https://www.calterix.com/en-us/calculator/fraction/ · Updated 11/06/2026 · en-US

## How to do math with fractions

Each operation has its own rule. To add or subtract, the fractions need the same denominator. To multiply, multiply the numerators and the denominators. To divide, multiply by the flipped fraction. In every case, simplify the answer with the greatest common factor (GCF).

```
a/b + c/d = (a·d + c·b) ÷ (b·d)
a/b − c/d = (a·d − c·b) ÷ (b·d)
a/b × c/d = (a·c) ÷ (b·d)
a/b ÷ c/d = (a·d) ÷ (b·c)
```
The calculator finds the least common multiple of the denominators and simplifies at the end.

Simplifying depends on the greatest common factor. To see that step by step, use the [LCM and GCF calculator](https://www.calterix.com/en-us/calculator/lcm-gcf/).

## Worked examples

| Problem | Steps | Answer |
| --- | --- | --- |
| 1/2 + 1/3 | 3/6 + 2/6 | 5/6 |
| 3/4 − 1/4 | 2/4, simplified by 2 | 1/2 |
| 2/3 × 9/4 | 18/12, simplified by 6 | 3/2, or 1 1/2 |
| 1/2 ÷ 3/4 | 1/2 × 4/3 = 4/6 | 2/3 |
| 1/3 − 1/2 | 2/6 − 3/6 | −1/6 |
| 18/24 | GCF = 6 | 3/4 |

Problems checked by hand.

Fractions show up in the kitchen all the time. If a recipe calls for 3/4 cup of flour and you want half the batch, multiply 3/4 × 1/2 = 3/8 cup. To see a fraction as a decimal and a percent, try the [percentage calculator](https://www.calterix.com/en-us/calculator/percentage/): 3/4 is 0.75, or 75%.

## Special cases and common mistakes

- A denominator of zero does not exist, so the calculator rejects it.
- Dividing by a fraction that equals zero (numerator 0) is also impossible.
- Negative fractions: the sign moves to the numerator, so −1/6 is the same as 1/(−6).
- Adding numerators and denominators straight across (1/2 + 1/3 = 2/5) is the most common mistake. The right answer is 5/6.
- Improper fractions (numerator larger than denominator) become mixed numbers: 7/4 = 1 3/4.

> The fields accept whole numbers up to 1 trillion. For fractions with decimals, multiply the numerator and denominator by 10 until the decimals disappear: 0.5/2 becomes 5/20, which simplifies to 1/4.

To compare quantities, the [proportion calculator](https://www.calterix.com/en-us/calculator/proportion/) uses equivalent fractions.

## Frequently asked questions

### How do you add fractions with different denominators?

Find the least common multiple of the denominators, convert each fraction, and add the numerators. For 1/2 + 1/3, the common denominator is 6, the problem becomes 3/6 + 2/6, and the answer is 5/6.

### How do you multiply fractions?

Multiply numerator by numerator and denominator by denominator, then simplify. For 2/3 × 9/4, the product is 18/12, which simplifies to 3/2.

### How do you divide fractions?

Multiply the first fraction by the reciprocal of the second. For 1/2 ÷ 3/4, the problem becomes 1/2 × 4/3 = 4/6, which simplifies to 2/3.

### How do you simplify a fraction?

Divide the numerator and denominator by their greatest common factor. For 18/24, the GCF is 6, so the fraction in lowest terms is 3/4. If the GCF is 1, the fraction is already simplified.

### How do you turn a fraction into a decimal?

Divide the numerator by the denominator. 3/4 = 3 ÷ 4 = 0.75. The calculator shows the decimal for every result, up to 6 places.

### What is an improper fraction and a mixed number?

An improper fraction has a numerator larger than its denominator, like 7/4. A mixed number pulls out the whole part: 7/4 = 1 3/4. The calculator shows both forms.