---
tags:
  - Mathematics
  - Prealgebra
  - fractions
  - division
---

# Adding and subtracting fractions

## Adding/ subracting fractions with common denominators

For two fractions $\frac{a}{c}$ and  $\frac{b}{c}$ with a common denominator, their sum is defined as:

$$
    \frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}
$$

For example:

$$
    \frac{2}{8} + \frac{3}{8} = \frac{5}{8}
$$

The same applies to subtraction:

$$
    \frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}
$$


## Adding/ subracting fractions without common denominators

* Find the lowest common denominator for the two fractions
* Use this to create two equivalent fractions
* Add/subtract
* Reduce 

Demonstration: $\frac{4}{9} + \frac{1}{6}$ :

The lowest common denominator is **the smallest number divisible by both of the denominators of the fractions without remainder**.