In this worksheet, we will learn how to simplify fractions.
This process is often carried out at the end of a fraction calculation to make the fraction more simple.
If we divide the top (the numerator) and the bottom (the denominator) of a fraction by the same number we get an equivalent fraction.
This is called simplifying a fraction.
When we simplify a fraction as much as possible, it is called reducing it to its lowest terms.
We do this by dividing the numerator and the denominator by their highest common factor.
Example 1
Simplify this fraction to its lowest terms
36 |
45 |
Answer
We look for the highest number that goes into 36 and 45.
This will be 9, because 4 × 9 = 36 and 5 × 9 = 36.
So we divide the numerator and the denominator by the magic number 9, to get 4 and 5.
36 | = | 4 |
45 | 5 |
We cannot simplify this any further, so the answer is:
4 |
5 |
Example 2
Simplify this fraction to its lowest terms.
64 |
96 |
Answer
Sometimes it is hard to find the highest common factor.
We look for any number that goes into 64 and 96.
This could be 8, because 8 × 8 = 64 and 12 × 8 = 96.
So we divide the numerator and the denominator by the magic number 8, to get 8 and 12.
64 | = | 8 |
96 | 12 |
Now we can simplify again by looking for the highest number that goes into 8 and 12.
This is 4 because 2 × 4 = 8 and 3 × 4 = 12.
So we divide the numerator and the denominator by the magic number 4, to get 2 and 3.
So the answer is:
2 |
3 |
Let's have a go at the questions now.