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Equivalent Fractions
Objectives
To be able to recognize and calculate equivalent fractions.
To make a connection between the numerator and the denominator of equivalent fractions.
Resources
Abacus 4 Textbook 2 | Squared paper
Today's Lesson
Times Tables
Remember to login to TT Rockstars to practise your times tables at least 5 times a week.
Main Activity
Make up a few equivalent fractions, for example, 1/4 = 2/8 = 3/12 = 4/16 
Draw attention to the numerator and the denominator of each fraction and ask your student to make a connection between the two that can be applied to all of the equivalents.
For example, for 2/8 the connection is 8 ÷ 2 = 4 or ¼ of 8 = 2. The same connection applies for each of the fractions in the example. We can therefore see that if you divide the denominator by the numerator and the answer is 4, the fraction is equivalent to 1/4.
Look at the examples provided on page 29 in Abacus 4 Textbook 2.
Ask your student to work out the connection between 1/2, 2/4 and 3/6
For each of these fractions, the numerator is equal to exactly half of the denominator, therefore, the fractions are all equivalent to one half, or ½
To make up other equivalents for a given fraction, you can multiply the numerator and denominator by the same number.
For example:
1/3
If we multiply both top and bottom by 4, we find:
1 x 4 = 4
3 x 4 = 12
So we can say that 1/3 =4/12
Ask your student to complete Q1-4.
Before completing the rest of the page, watch the 'Simplifying fractions' video.
If you want to simplify fractions, it is important to look at the fraction and to establish in which times table both numbers occur, or to find what number ‘goes into’ both the numerator and the denominator (a common factor of both numerator and denominator) without leaving a remainder.
Then, divide both the numerator and denominator by that number and the answer will be an equivalent fraction, in a simpler form. The aim is usually to divide the fraction to its simplest form, so that the numerator is 1, or as low as it can go.
For example if we want to simplify 5/30
We know that both 5 and 30 occur in the 5 times table, and that therefore both can be divided by 5 with no remainders.
5 ÷ 5 = 1
30 ÷ 5 = 6
Therefore, 5/30 = 1/6
Once your student has understood the concept, ask them to copy and complete the the rest of the work on page 29. You may need to sit with your student, initially, to give some support or to ask leading questions, in order to ensure your student understands the calculations necessary. Recognise the importance of being able to recognise and recall tables and associated division facts.