This section introduces the idea of equivalent fractions.
These are fractions which appear differently but have the same value
Look at this diagram.
We can see that the fraction shaded in the left-hand shape is ,
and the fraction shaded in the right-hand shape is .
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You might have noticed something else about the equivalent fractions. Look at the diagram on the left. Both the numerator (the top number) and the denominator (the bottom number) have been multiplied by the same value. |
If we multiply or divide the top and bottom numbers in a fraction by the same value, we will get an equivalent fraction. |
(a) Are these two fractions equivalent?
and
(b) What number should go in place of the question mark?
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Question 1
The three diagrams below represent the same fraction; they are equivalent fractions.
Write down the three different (but equivalent) fractions represented by the diagrams below.
Question 2
Work out the missing number on each of these questions. You may find the diagram on the right useful.
Question 3
Work out the missing number on each of these questions. You can use the diagram on the right to help you, but try
using the method of multiplying the numerator (top) and denominator (bottom) by the same value.
Question 4
In this question you have to divide both parts of the fraction by the same number to get the equivalent fraction.
If we keep dividing both parts of the fraction by the same number until there are no more numbers which we can divide by, the number is said to be in its simplest form.
Question 5
Write each of the fractions below in its simplest form.
Question 6
By thinking about equivalent fractions, indicate whether each of the statements below is true of false.