Science, Maths & Technology

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Numbers, units and arithmetic

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# 1.8 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 ?