# Fraction Calculator — Add, Subtract, Multiply & Divide with Steps

> Add, subtract, multiply and divide fractions and mixed numbers with the LCM common-denominator steps shown, plus the simplified, mixed and decimal results and pie visuals.

- **Category:** Math
- **Interactive calculator:** https://youcalc.com/en/math/fraction-operations/
- **Price:** Free, no sign-up required

## Overview

This calculator adds, subtracts, multiplies or divides two fractions and shows every step along the way. Use it to double-check homework, understand how a common denominator is found, or convert a fraction to its decimal equivalent in one click.

## How to read your result

The main result card shows the simplified fraction — for example 17/12 — along with the equivalent mixed number (1 5/12) and the decimal value. Below the result, the step-by-step breakdown explains the common denominator used for addition or subtraction, or how the numerators and denominators were multiplied together for multiplication or division. Three pie charts visualise each fraction and the result.

## Method

For addition and subtraction the calculator finds the LCM of the two denominators, rewrites each fraction over that common denominator, and combines the numerators. For multiplication it multiplies numerator by numerator and denominator by denominator. For division it multiplies the first fraction by the reciprocal of the second. In every case the result is then reduced by dividing numerator and denominator by their GCD (computed via the Euclidean algorithm), and a mixed-number form is derived when the absolute numerator exceeds the denominator.

## Example

- **Setup:** Add 2/3 and 3/4.
- **Result:** The LCM of 3 and 4 is 12, so 2/3 becomes 8/12 and 3/4 becomes 9/12. Adding gives 17/12, which simplifies to the mixed number 1 5/12 and the decimal 1.417.

## Frequently asked questions

### Why do you need a common denominator for addition and subtraction?

Fractions can only be added or subtracted when they refer to equal-sized parts. Finding the lowest common multiple (LCM) of the two denominators gives the smallest denominator that both fractions can be rewritten with, so the numerators become directly comparable.

### Why does multiplication not need a common denominator?

When multiplying, you combine two fractions into a new fraction by multiplying numerator by numerator and denominator by denominator. No alignment of parts is required — the operation works directly on the two fractions as given.

### What does it mean to simplify a fraction?

A fraction is in its simplest (or lowest) terms when its numerator and denominator share no common factor other than 1. The calculator divides both by their greatest common divisor (GCD) automatically, so the result is always fully reduced.

## Related calculators

- [Percentage Calculator](https://youcalc.com/en/math/percentage/)
- [Prime Factorization Calculator](https://youcalc.com/en/math/prime-factorization/)
- [Scientific Notation & Significant Figures Calculator](https://youcalc.com/en/math/scientific-notation/)

## Sources

- https://mathworld.wolfram.com/Fraction.html
- https://www.khanacademy.org/math/arithmetic-home/arith-review-fractions

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Interactive version: https://youcalc.com/en/math/fraction-operations/ · From YouCalc — https://youcalc.com