Simplifying Fractions

Objectives

To understand how to reduce a fraction to its simplest form by dividing the numerator and the denominator by the same number.

Resources

Abacus 4 Textbook 2 | Squared paper | Modelling Equivalent and Non-equivalent Fractions (MyMaths)

Today's Lesson

Main Activity

Further to the explanation from the previous lesson, ask your student to look at both the numerator and denominator of a fraction and to tell you which times table both are in (this means they are multiples of the same number).

For example, 16/48

Which times table are 16 and 48 both part of?

Your student might answer 2, 4 or 8.

Give your student additional examples. E.g. 9/63 or 10/80

When we want to simplify a fraction, the idea is to divide the numerator and denominator of the fraction by the same number, in order to make them as small as possible.

Look at, for example, 12/24

You could start by saying that both the numerator and the denominator are in the 2 times table, so we could divide both by 2 to form 6/12 .

This has reduced the fraction, but it is not yet in its simplest form.

The simplest form is to get the top number as close to 1 as possible. (This happens when the numbers are no longer in the same times table.) In this case, we can divide both numbers now by 6, to form ½. We could, of course, have divided both numbers by 12 initially to find the same fraction. It really does not matter how many divisions are carried out, as long as they are continued until we are sure we have reached the fraction’s simplest form.

However, not every numerator can go as low as 1, for example if we look at the fraction 6/9

Both numerator and denominator here are divisible by 3, but the simplest form we can reach is 2/3. The fraction cannot be reduced further.

Watch the 'Simplifying fractions' video from yesterday for further examples.

Once your student has shown a fair understanding of the concept, work with them on page 30 in Abacus 4 Textbook 2. If your student needs support, sit with them to help establish the process. Ask your student to copy and complete the page

If your student finds the concept difficult at this stage, do not worry or put pressure on your student. There will be more opportunities to work on these concepts later. It is very common for students to grasp difficult concepts and understand them the second or third time round.

Using an image such as a ‘fraction wall’ (below) may also be beneficial in recognizing equivalent fractions.

(If required, use Modelling Equivalent and Non-equivalent Fractions (MyMaths) for further practice with equivalent fractions.)

Extra Activities

You might like to try the homework activity on the My Portal section of MyMaths to practise this skill further.

MyMaths Homework - Modelling equivalent and non equivalent fractions

Citations

[1] app.mymaths.co.uk [2] app.mymaths.co.uk