# Fractions & Decimals

### Topics

## Introduction to :

Adding and subtracting fractions can be time-consuming because it often involves a few extra steps. This is a really important and commonly-used skill, though. So let's get to it.

Here is .

There is a total of 4 blue fourths, which combine to make 1 whole, so .

Here is .

Now there is a total of 7 blue fifths, which combine to make 1 whole and 2 fifths, so .

The most important thing to remember when adding or subtracting fractions is that we ** must** have a common denominator.

**When the denominators are the same, all you have to do is add or subtract the numerators** and keep the denominator the same.

## Examples with common denominators

Example 1 | |

Add the numerators | |

Change into an improper fraction | |

Simplify | |

Change to a mixed number | |

Example 2 | |

Subtract the numerators | |

Reduce the fraction | |

## Adding or Subtracting Fractions with Different Denominators

Try adding using pictures.

This can be a little tricky at first, but once you get the hang of it, it’s a breeze.

To add two fractions with different denominators, we need to **convert one or both fractions so they have matching - or common - denominators**.

- Use the Least Common Multiple of the denominators and use it as your
*common denominator*.- Or, if you can't easily find the LCM, just multiply the denominators together. This will usually create a little more work, as you'll have to reduce the fraction later. The LCM is your best bet, but both will lead you to a correct answer.

- Once the original fractions are converted to two fractions with common denominators, just add the numerators and keep the denominator.

**Look Out**: when adding fractions, don't fall into the trap of mistakenly adding the denominators together. Here's a quick way to remember: we all know that two halves make one whole. If we made the mistake of adding denominators, we would get ½ + ½ = 2/4 = ½, which is obviously wrong.

#### Example 1

The LCM of 4 and 5 is 20, so we need to convert the fractions so they each have a denominator of 20. and |

#### Example 2

The LCM of 8 and 3 is 24, so we need to convert each fraction to one with a denominator of 24 and |

#### Example 3

The LCM of 7 and 6 is 42, so we need to convert each fraction to one with a denominator of 42. and |

#### Example 4

The LCM of 9 and 3 is 9. Since the first fraction already has a denominator of 9, we only need to convert the second one. |