# Adding and subtracting fractions

**Adding and subtracting fractions**

Adding and subtracting fractions have the same denominator is quite straight forward, for example:

- When the denominator is the same, simply add the numerators
- The same rule applies for subtracting
- Fractions are described to have a common denominator if they have the same denominator.

However, fractions should also be reduced to their lowest terms as per the following example:

Fractions should always be cancelled down to their lowest terms.

It should also be noted that top-heavy (improper fractions should be written as mixed number, as per the below example:

Note – 12/9 is larger than 9 which mean that the 9/9 portion is converted to a whole number of 1 and the remaining 3/9 is the remaining portion of the fraction.

**Fractions with different denominators**

It is more difficult to add and subtract fractions with different denominators.

For example,

- Find the lowest common denominator for 6 and 9, which is 18
- Multiply the numerator by the same factor
- Subtract the numerators
- Cancel down the fractions (if possible) to the lowest terms

**Using a calculator**

It is also possible to add and subtract fractions using the following key on a calculator.

The calculator displays this as:

Pressing the following key converts this to:

Although it is easy to use a calculator to add and subtract fractions, the ability to use the full method must be demonstrated without using a calculator.