# 1.7 Simplest form of a fraction

The fraction , is the *simplest form* of all its equivalent fractions, because it cannot be ‘simplified’ further (by dividing top and bottom by the same whole number called a **common factor**); or , on the other hand, can be simplified to by dividing top and bottom by 2 and 4 respectively.

A fraction is in its **simplest form** if the numerator and the denominator have no **common factors**.

6 can be written as 2 × 3. 2 and 3 are called **factors** of 6.

15 can be written as 5 × 3. 5 and 3 are **factors** of 15.

3 is a **common factor** of 6 and 15. Hence . This is the **simplest form** of .

## Example 6

(a) Find some equivalent fractions for .

(b) What is the simplest form of ?

### Answer

Multiply or divide top and bottom by the *same* whole number to give an equivalent fraction.

(a) Some examples are

(b) Top and bottom are divisible by 5. So

3 and 4 have no common factors so is the simplest form.

You can indicate fractions along the number line by marking points between the whole numbers. The numbers and are shown below.

Note may also be written as 1.5 or as .