# Fraction Calculator

> To add fractions, rewrite them over a common denominator and add the numerators: 1 1/2 + 2/3 = 9/6 + 4/6 = 13/6, or 2 1/6. The calculator adds, subtracts, multiplies and divides fractions and mixed numbers exactly, showing every step and the answer in lowest terms and as a decimal.

- Interactive calculator: https://calculatorswithsteps.com/fraction-calculator
- Category: Math & Statistics Calculators
- Last updated: 2026-11-10
- Publisher: Calculators With Steps (calculatorswithsteps.com)

## How to use the fraction calculator

Type the first fraction in box **a** and the second in box **b**, then choose an operation. The answer updates as you type. Each box accepts several formats:

| You type | Read as | Example meaning |
| --- | --- | --- |
| 3/4 | A simple fraction | three quarters |
| 1 1/2 | A mixed number (note the space) | one and a half |
| −2/5 | A negative fraction | minus two fifths |
| 7 | A whole number | 7/1 |
| 0.75 | A decimal | 75/100, which simplifies to 3/4 |

Pick **Simplify a** to reduce a single fraction or turn a decimal into a fraction. Every result is shown four ways: as a simplified fraction, as a mixed number, as a decimal (with any repeating digits marked in brackets) and as a percentage.

## Fraction formulas

For fractions a/b and c/d:

- **Addition:** a/b + c/d = (a × d + c × b) ÷ (b × d), or rewrite both over the least common denominator (LCD) and add the numerators.
- **Subtraction:** a/b − c/d = (a × d − c × b) ÷ (b × d), or use the LCD the same way.
- **Multiplication:** a/b × c/d = (a × c) ÷ (b × d).
- **Division:** a/b ÷ c/d = a/b × d/c = (a × d) ÷ (b × c). This is often called cross-multiplying.

After any operation, divide the numerator and denominator by their **greatest common divisor (GCD)** to get the answer in lowest terms. The calculator uses the LCD for addition and subtraction because it keeps the numbers small and matches how fractions are taught in school.

## Worked examples

**Adding with unlike denominators: 3/4 + 5/6.** The LCD of 4 and 6 is 12. Rewrite: 3/4 = 9/12 and 5/6 = 10/12. Add the numerators: 9 + 10 = 19, so the sum is **19/12**. Since 19 ÷ 12 = 1 remainder 7, that is **1 7/12**, or about 1.583333.

**Subtracting mixed numbers: 5 1/4 − 2 2/3.** Convert to improper fractions: 5 1/4 = 21/4 and 2 2/3 = 8/3. The LCD is 12, so 21/4 = 63/12 and 8/3 = 32/12. Subtract: 63 − 32 = 31, giving **31/12 = 2 7/12**.

**Multiplying mixed numbers: 2 1/3 × 1 1/2.** Convert: 7/3 × 3/2. Multiply across: 21/6. The GCD of 21 and 6 is 3, so the answer simplifies to **7/2 = 3 1/2 = 3.5**.

**Dividing: 3/4 ÷ 2/5.** Flip the second fraction and multiply: 3/4 × 5/2 = **15/8 = 1 7/8 = 1.875**.

| Problem | Exact answer | Mixed number | Decimal |
| --- | --- | --- | --- |
| 3/4 + 5/6 | 19/12 | 1 7/12 | 1.58(3) |
| 5 1/4 − 2 2/3 | 31/12 | 2 7/12 | 2.58(3) |
| 2 1/3 × 1 1/2 | 7/2 | 3 1/2 | 3.5 |
| 3/4 ÷ 2/5 | 15/8 | 1 7/8 | 1.875 |

## How to simplify a fraction

A fraction is in simplest form when the numerator and denominator share no common factor other than 1. To get there in one step, divide both by their GCD. For 18/24, the factors of 18 are 1, 2, 3, 6, 9 and 18, and 6 is the largest that also divides 24, so 18/24 = 3/4. For large numbers, the calculator finds the GCD with Euclid's algorithm: keep replacing the larger number with the remainder of dividing it by the smaller one until the remainder is zero. The [GCF and LCM calculator](https://calculatorswithsteps.com/gcf-lcm-calculator) shows that process in full.

## Fractions, decimals and percentages

Every fraction is a division. Dividing the numerator by the denominator gives a decimal that either stops or repeats forever:

- 3/8 = 0.375 = 37.5% (stops, because 8 = 2 × 2 × 2)
- 1/8 = 0.125 = 12.5%
- 1/3 = 0.(3) = 0.333…
- 2/7 = 0.(285714), a six-digit repeating block

A fraction in lowest terms gives a terminating decimal only when its denominator has no prime factors other than 2 and 5. That is why fifths, eighths and twentieths stop, while thirds, sixths and sevenths repeat. Going the other way, 0.75 = 75/100 = 3/4. For percentage problems such as discounts and marks, the [percentage calculator](https://calculatorswithsteps.com/percentage-calculator) is a better fit.

## Common mistakes with fractions

- **Adding the denominators.** 1/2 + 1/3 is not 2/5. The pieces are different sizes, so convert to sixths first: 3/6 + 2/6 = 5/6.
- **Forgetting to convert mixed numbers.** Multiplying 2 1/3 × 1 1/2 as (2 × 1) and (1/3 × 1/2) gives 2 1/6, which is wrong. Convert to 7/3 and 3/2 first to get 3 1/2.
- **Flipping the wrong fraction.** When dividing, flip only the second fraction (the divisor), never the first.
- **Misreading negative mixed numbers.** −1 1/2 means −(1 + 1/2) = −3/2, not −1 + 1/2.
- **Rounding too early.** Working in decimals, 1/3 + 1/6 might become 0.33 + 0.17 = 0.50 by luck, but other sums drift. Exact fractions avoid that, and so does this calculator. For ratios such as 3:4, the [ratio calculator](https://calculatorswithsteps.com/ratio-calculator) uses the same simplifying rules.

## Frequently asked questions

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

Rewrite both fractions over their least common denominator, then add the numerators. For 1/2 + 1/3 the LCD is 6, so 1/2 = 3/6 and 1/3 = 2/6, and 3/6 + 2/6 = 5/6.

### How do you convert a fraction to a decimal?

Divide the numerator by the denominator. 3/8 = 3 ÷ 8 = 0.375. Some fractions repeat forever: 1/3 = 0.333… and 2/7 = 0.285714285714…, where the block 285714 repeats.

### How do I simplify a fraction like 18/24?

Find the greatest common divisor of the top and bottom numbers and divide both by it. The GCD of 18 and 24 is 6, so 18/24 = 3/4. Choose Simplify a in the calculator to do this for any fraction or decimal.

### How do you divide fractions?

Flip the second fraction and multiply. 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8, which is 1 7/8 as a mixed number or 1.875 as a decimal.

### How do I type a mixed number?

Put a space between the whole number and the fraction, such as 2 1/3. For a negative mixed number, put the minus sign in front: −1 1/2 means −(1 + 1/2) = −3/2.

### How do you multiply a fraction by a whole number?

Treat the whole number as a fraction over 1 and multiply across. 4 × 2/3 = 4/1 × 2/3 = 8/3, which is 2 2/3.

### How do I turn a fraction into a percentage?

Convert it to a decimal and multiply by 100. 3/8 = 0.375, so 3/8 is 37.5%. The calculator shows the percentage for every answer.

### Can the fraction calculator handle negative fractions?

Yes. Type a minus sign before the fraction. For example, −3/4 + 1/2 = −3/4 + 2/4 = −1/4.

## Sources

- [Wikipedia – Fraction (arithmetic with fractions)](https://en.wikipedia.org/wiki/Fraction)
- [Wikipedia – Lowest common denominator](https://en.wikipedia.org/wiki/Lowest_common_denominator)
- [Wikipedia – Greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor)