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Succeed with maths: part 1
Succeed with maths: part 1

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2.1 Multiplying mixed numbers and fractions

Say you want to calculate . The way to handle this is first by changing the mixed numbers to improper fractions, as you learned in Week 3, then you can once again multiply the numerators together followed by the denominators:

two equals eight divided by four, so equation sequence eight plus three divided by four equals 11 divided by four.

one equals three divided by three, so one equation sequence one divided by three equals three plus one divided by three equals four divided by three.

Now you can perform the calculation just as before, looking for ways to cancel first, as you did when multiplying fractions in the previous section.

equation sequence 11 divided by four sub one multiplication four super one divided by three equals 11 divided by three equals

Note that you should write the answer as a mixed number, if appropriate. You usually do this if the original numbers were given as mixed numbers.

Now try multiplying with fractions in Activity 4. If you would like to watch somebody working through multiplying mixed numbers, have a look at this video. Note again that the presenter refers to ‘fourths’ instead of quarters, and uses a dot at some points to represent multiplication rather than the more usual cross symbol (×).

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Activity 4 Multiplying mixed numbers and fractions

Timing: Allow approximately 10 minutes

Remember to cancel before multiplying, and convert mixed numbers to improper fractions if necessary.

  • a.10 divided by 27

Hint: you need to change the mixed number into an improper fraction first.


  • equals five divided by five, so equation sequence five plus four divided by five equals nine divided by five

    equation sequence 10 divided by 27 equals nine super one divided by five sub one multiplication 10 squared divided by 27 sub three equals two divided by three

  • b.


  • b.
    equation sequence 52 super 26 divided by nine multiplication five divided by two sub one equals 130 divided by nine equals
  • c.


  • c.
    equation sequence 77 divided by 25 multiplication 13 divided by three equals 1001 divided by 75 equals