1.2 Adding and subtracting mixed numbers
To add or subtract mixed numbers, there are multiple methods you can use. The way you’re going to learn here will involve using improper fractions which you learnt about in Week 3.
To add or subtract mixed numbers, first change them all to improper fractions and then find the common denominator. Once you have found a common denominator you can do the addition or subtraction, before changing the improper fraction back to a mixed number.
For example, when presented as an improper fraction is .
The common denominator for these is 6 (as that’s the smallest number that both 2 and 3 go into). So you need to convert both to have a denominator of 6, then do the calculation:
Here the answer is a top-heavy fraction. By changing it back to a mixed number it gives: .
Now take a look at this second example, which looks at subtracting mixed numbers.
when presented using improper fractions is .
The common denominator for these is 21 (as that’s the smallest number that both 3 and 7 go into). So you need to convert both to have a denominator of 21, then do the subtraction:
As the answer is already a “normal” (not top-heavy) fraction, there is no need to change anything here.