Skip to content
Skip to main content

About this free course

Download this course

Share this free course

Numbers, units and arithmetic
Numbers, units and arithmetic

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

1.7 Simplest form of a fraction

The fraction one divided by three, 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); two divided by six or four divided by 12, on the other hand, can be simplified to one divided by three 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 equation sequence part 1 six divided by 15 equals part 2 two multiplication three divided by five multiplication three equals part 3 two divided by five. This is the simplest form of six divided by 15.

Example 6

  • (a) Find some equivalent fractions for one divided by four.

  • (b) What is the simplest form of 15 divided by 20?


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

  • (a) Some examples are equation sequence part 1 two multiplication one divided by two multiplication four equals part 2 two divided by eight times three multiplication one divided by three multiplication four equals part 3 three divided by 12 times 25 multiplication one divided by 25 multiplication four equals part 4 25 divided by 100

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

    equation sequence part 1 15 divided by 20 equals part 2 15 division five divided by 20 division five equals part 3 three divided by four

    3 and 4 have no common factors so three divided by four is the simplest form.

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

Note one and one divided by two may also be written as 1.5 or as three divided by two.