# 3.2 Dividing mixed numbers and fractions

The same principles apply to dividing mixed numbers as dividing proper fractions.

Let's try to calculate

First, just as with multiplication, you rewrite the mixed numbers as improper fractions:

Then, you find the reciprocal of the fraction after the ÷ sign, and change the division symbol to the multiplication symbol, so your new calculation is:

Then, you cancel and multiply:

Because your original numbers were mixed numbers, it is appropriate to rewrite your answer as a mixed number as well. In this case, your answer is equivalent to .

Here’s another example:

Convert into an improper fraction:

Now you need to work out the reciprocal of 7. Remember, any whole number can be expressed as an improper fraction by using 1 as the denominator, thus , and its reciprocal is . Now, multiply by .

Now you’ve had a chance to work through a few examples, try the next activity yourself to see how you get on.

## Activity 6 Dividing fractions

Work through the following examples, using what you have just learned. Remember to convert any mixed numbers to improper fractions.

a.

- i.
- ii.

Hint: how do you convert division by a fraction into a multiplication problem?

### Answer

- i.
ii.Change the first fraction into an improper fraction before dividing:

b.If it takes of an hour to clean one car, how many cars can be cleaned in hours?

Hint: you are trying to determine how many hours are in hours.

### Answer

Here, you need to find how many times ‘three-quarters’ goes into ‘seven and a half’. So you need to divide by .

Thus, 10 cars can be cleaned in the given time.

- c.Imagine that you are trying to put a fence along the side of a garden. The side of the garden measures metres. The fencing available is made of panels that measure of a metre each. How many panels will be needed?

### Answer

You need to find how many metre sections there are in metres. The calculation is:

So, 17 panels are needed.

The more practice you get with anything the easier it becomes. So, as well as having a go at the activities in the next section, see if you can spot fractions in your everyday life and use them to solve problems.