Become an OU student

Succeed with maths: part 1

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

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

Timing: Allow approximately 10 minutes

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?

• 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.

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?