# 1.1 The process of adding and subtracting

You might like to watch this next video before attempting Activity 1, which will guide you through the process of adding and subtracting fractions.

#### Transcript

## Activity 1 Adding and subtracting fractions

Have a go at these questions, 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.

- a.

Hint: Are both fractions out of the same number of parts? Remember as always to show your answer in the simplest form.

### Answer

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.

- b.

Hint: both fractions are eighths, so again you can add them directly.

### Answer

The answer is:

If this is converted to a mixed number, the answer is:

- c.

Hint: 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?

### Answer

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 .

- d.

Hint: try adding the whole numbers first, and then add the fractional parts together.

### Answer

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.

### Answer

Both the fractions are sixteenths so you subtract straightaway:

- f.

Hint: first ensure both fractions have the same denominator.

### Answer

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.

Therefore:

- g.Two children were squabbling about chocolate. Josie had been given of a bar by her aunt and of a bar by her dad. Tim had been given a bar by his mum and by his friend. All the original bars were the same size. Was Josie or Tim given more chocolate, or were they given equal amounts?

Hint: add up what fraction of a bar each child had. To compare your two fractions, cancel each to its lowest terms.

### Answer

Josie had of a bar. To add these, we need to put them over a common denominator. The common denominator is 12. So becomes . cancels down to of a bar.

Tim has of a bar. The common denominator is 6. So becomes . cancels down to of a bar.

Therefore, Josie and Tim had the same amount of chocolate.

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.