Numbers
2. Fractions
2.2. Simplifying fractions
In this simple example, with a cake cut into four equal slices, it is easy to spot that two quarter slices are equal to exactly half of the cake.
Half of anything is written as 1 over 2, to represent one of two equal parts of the whole.
So rather than saying 2/4 (two quarters) of our cake, we can simply say 1/2 (half, or one half).
Cancelling down
Mathematically, fractions are simplified using a process known as cancelling down, in which both the numerator and the denominator are divided by the largest number above 1, by which both can equally (i.e. with no remainder) be divided.
Division is the process of breaking a number into equal parts. The division symbol (÷) is used in this operation. For example, when you divide 12 by 4, you break 12 into 4 equal groups of 3 (12 ÷ 4 = 3).
Taking our example of 2/4 equal slices of cake, both the numerator and the denominator can be divided equally by 2.
2 ÷ 2 = 1
4 ÷ 2 = 2
which gives us our simplified fraction of 1/2 (half).
Let’s look at another example.
What fraction of this rectangular shape is shaded blue?
We can see that the shape has been divided into 9 equal rectangles, and 6 of these have been shaded. So we can say 6/9 (6 out of nine, 6 ninths) have been shaded.
Can this fraction be simplified?
Remember, we cancel a fraction down by dividing both the numerator and the denominator by the largest number, above 1, by which both can equally be divided.
Well, 6 is the largest number that the numerator (6) can be divided by. Can we divide the denominator (9) by 6? No.
What about 5? No.
4? No.
3? Yes!
Both the numerator and the denominator can be divided equally by 3.
6 ÷ 3 = 2
9 ÷ 3 = 3
which gives us a simplified fraction of 2/3, or two thirds of the whole.
