3.5 Doing calculations with fractions
3.5.1 Adding and subtracting fractions
Suppose we want to add the two fractions shown below:
We cannot just add the 3 and the 2. The 3 represents 3 quarters and the 2 represents 2 fifths, so adding the 3 to the 2 would be like trying to add 3 apples and 2 penguins – you just can’t do it!
In order to add or subtract two fractions, it is necessary for them both to have the same denominator (bottom line).
Fractions with the same denominator are said to have a ‘common denominator’. One way to find a common denominator when adding or subtracting two fractions is to multiply the top and bottom of the first fraction by the denominator of the second fraction, and the top and bottom of the second fraction by the denominator of the first fraction. A return to our example may make this clearer:
Note that the and are equivalent fractions (Section 3.1) as are and , and that and can be added without difficulty because they have a common denominator of 20.
Question 3.6
Work out the following, leaving each answer as the simplest possible fraction:
- a.
- b.
