Improper fractions, mixed numbers and like fractions · Usually met around P4
Equivalent fractions: expanding and simplifying
Times or divide top and bottom by the same number.
How to do it
Method
Times or divide top and bottom by the same number
23 = (2 × 4)/(3 × 4) = 812
Another way
Simplify step by step
1218 = 69 = 23
In full
Multiply the top and bottom by the same number, or divide both by the same number, and the fraction's size doesn't change: 23 = 812 (both times 4), 812 = 23 (both ÷ 4). Simplify until the top and bottom share no factor but 1: that is the simplest form. Divide by the highest common factor in one go, or step by step until you can't any more. Or look at a picture: a rectangle cut in 3 with 2 shaded and one cut in 12 with 8 shaded have the same amount shaded. Careful: adding the same number to the top and bottom does change the fraction.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
810 = □/5
Show the answer and working
Answer: 4
The bottom 10 ÷ 2 is 5, so the top is ÷ 2 too: 8 ÷ 2 = 4.
Example 2
27 = 621
True or false?
Show the answer and working
Answer: True
Equal fractions come from multiplying (or dividing) the top and bottom by the same number; adding a number changes the size.
Example 3
18 = □/16 = 6/□
Fill in each box
Show the answer and working
Answer: 2，48
8 × 2 = 16, so the top is 1 × 2 = 2; 1 × 6 = 6, so the bottom is 8 × 6 = 48.
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