# 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:

, so .

, so .

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.

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 (×).

#### Transcript

**so you're still going to have the same denominator, but your**numerator as an improper fraction is going to be 4 times 1 plus 3.

## Activity 4 Multiplying mixed numbers and fractions

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

- a.

### Comment

You need to change the mixed number into an improper fraction first.

### Answer

a., so

- b.

### Answer

- b.

- c.

### Answer

- c.

The examples in Activity 4 helped you develop your understanding of multiplying fractions. Now apply these new skills in a more practical situation (Activity 5).

In the previous activity, you might have approached the problem differently. Perhaps you found what one-fifth of the group was first by using division, and then used this portion to find three of those sets. Once you had this value, which indeed is 126 people, you could have then found the number of people with overdraft protection and debit cards as shown above. Both approaches are valid and will give you the correct answers. Choose whichever method is easier for you. Now you’ve dealt with multiplication of fractions, you’ll move onto the last of the four basic operations of maths: division.