1.1 The process of adding and subtracting
You might like to watch this video before attempting Activity 1, which will guide you through the process of adding and subtracting fractions. Note, that in the video where there is reference to ‘fourths’, this is more usually known in the UK as quarters. There is also a section towards the end of the video where negative numbers are introduced. You will cover this in Weeks 7 and 8 of the course, so there is no need to watch this at the moment, unless you are interested.
Activity 1 Adding and subtracting fractions
Now try these examples, showing your answers in the simplest form or mixed number where relevant. Remember to make sure before you add or subtract to make the denominators the same. If you need a hint to help, click on ‘Reveal comment’.
Are both fractions out of the same number of parts? Remember as always to show your answer in the simplest form.
- a.Both the given fractions are eighteenths, so they can be added together directly:
To simplify to , divide the numerator (top) and the denominator (bottom) by 6.
Both fractions are eighths, so again you can add them directly.
- b.The answer is:
If this is converted to a mixed number, the answer is:
Can you find equivalent fractions for each given fraction that all share the same denominator? What number can be divided by both 6 and 7?
c.This sum involves sixths and sevenths, which are different types of fraction. However, you can change both into forty-seconds, since both 6 and 7 evenly divide into 42. So, by multiplying by 7 and by multiplying by 6.
Thus, the sum is .
Try adding the whole numbers first, and then add the fractional parts together.
- d.In this calculation you can add the whole numbers first (2 + 3 = 5) and then add the fractions. First, you must convert each fraction into twenty-fourths, as both 3 and 8 divide exactly into 24. So, the sum is:
- e.Both the fractions are sixteenths so you subtract straightaway:
First ensure both fractions have the same denominator.
f.You need both fractions to be out of the same number of parts (the denominators).
Since , you can multiply the top and bottom of by 3 to make the equivalent fraction of and then carry out the subtraction.
Well done – you’ve completed your first activity involving carrying out calculations with fractions! In the next activity you will look at a more practical application of fractions.