Succeed with maths – Part 1
Succeed with maths – Part 1

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Succeed with maths – Part 1

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:

equation left hand side equals right hand side 22 divided by nine division four divided by three

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: 22 divided by nine multiplication three divided by four

Then, you cancel and multiply: equation sequence equals 22 super 11 divided by nine sub three multiplication three super one divided by four sub two equals 11 multiplication one divided by three multiplication two equals 11 divided by six

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: seven

Convert into an improper fraction: equals seven divided by four

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 seven equals seven divided by one, and its reciprocal is one divided by seven. Now, multiply seven divided by four by one divided by seven.

equation sequence seven divided by four division seven divided by one equals 71 divided by four multiplication one divided by seven sub one equals one divided by four

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

Activity _unit5.3.1 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 and click on reveal comment if you need a quick hint.

  • a. 

    • i.four division two divided by three
    • divided by 15


How do you convert division by a fraction into a multiplication problem?


  • a. 

    • i.equation sequence four division two divided by three equals four multiplication three divided by two equals four squared divided by one multiplication three divided by two sub one equals two multiplication three divided by one equals six divided by one equals six
    • ii.Change the first fraction into an improper fraction before dividing:

      equation sequence seven divided by 15 equals eight divided by three sub one multiplication 15 super five divided by seven equals eight multiplication five divided by one multiplication seven equals 40 divided by seven equals

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


You are trying to determine how many three divided by four hours are in hours.


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

    equation sequence three divided by four equals 15 divided by two division three divided by four equals 15 super five divided by two sub one multiplication four squared divided by three sub one equals five multiplication two divided by one multiplication one equals 10 divided by one equals 10

    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 one divided by two of a metre each. How many panels will be needed?


  • c.You need to find how many one divided by two metre sections there are in metres. The calculation is:

    equation sequence one divided by two equals 17 divided by two multiplication two divided by one equals 17

    So, 17 panels are needed.

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

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