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This content is taken from the National STEM Learning Centre's online course, Maths Subject Knowledge: Fractions, Decimals, and Percentages. Join the course to learn more.
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National STEM Learning Centre

Skip to 0 minutes and 8 seconds MICHAEL ANDERSON: So let’s have a look at multiplying with mixed numbers. If we have 3 and 1/4 multiplied by 3/5, then it’s not quite the same as the examples that we’ve been looking at. In order to make them the same as the examples that we’ve already done, we’re going to take this mixed number and turn it into a top-heavy fraction. So 3 and 1/4– well, there’s four quarters in each whole, so that’s going to be 12 quarters plus the extra one. That’s 13/4, and then I’m going to multiply that by 3/5. And again, just multiplying across– 13 multiplied by 3 gives us 39, and 4 multiplied by 5 gives us 20.

Skip to 0 minutes and 53 seconds We’ve got a number here now that is, again, in top-heavy form, so what we would normally do, although it can’t be simplified, we’re going to write it back as a mixed number. So that would give us, well, one 20 plus another 19/20, so that’s one whole and 19/20. So let’s have a look at another example of these types of questions.

Skip to 1 minute and 16 seconds So in the first example, we had a mixed number, 3 and 1/4. We’re now going to, with the second number, have another mixed number, 2 and 2/5. So what we’re going to have to do is convert both of these numbers into top-heavy fractions. So what we’ll have, again, 3 and 1/4 gave us 13/4, 13 quarters. And we’re going to multiply that by 2 and 2/5. Well, 5/5 make one, so this 2 is going to represent 10/5 plus another 2 gives us 12/5. Now, just like we’ve seen before, I can try and cancel down a little bit with this fraction by noticing that 4 and 12 are both multiples of 4.

Skip to 1 minute and 59 seconds So I’m going to divide this side by 4 to give me 1 and this bit by 4 to give me 3. And then I’m just going to multiply across. 13 multiplied by 3 gives us 39, and this 1 multiplied by 5 gives us 5. So I got 39/5. I’m not quite finished because, again, I’m going to have to change it from a top-heavy fraction to a mixed number. How many fives go into 39? Well, that’s going to give me 7 to get to 35 plus another 4 leftover, so that’s 7 and 4/5.

Multiplying fractions when in mixed number notation

In this section we consider how to find the product of two numbers expressed as mixed numbers. Before watching the video you may like to think about the following questions. How do you think they should be approached?

a. $$3\frac{1}{4} \times \frac{3}{5} = ?$$

b. $$3\frac{1}{4} \times 2\frac{2}{5} = ?$$

When teaching this it is important that students are fluent in expressing values both as mixed numbers and as top heavy fractions as covered in week one of the course.

Problem worksheet

Now complete question 6 from this week’s worksheet.