3.5

## National STEM Learning Centre

Skip to 0 minutes and 7 secondsPAULA KELLY: So what's meant by 4/5 of 3?

Skip to 0 minutes and 10 secondsMICHAEL ANDERSON: 4/5 of 3 is sometimes written as 4/5 multiplied by 3. We can also think of this as 3 lots of 4/5 or 3 multiplied by 4/5.

Skip to 0 minutes and 21 secondsPAULA KELLY: When we're finding 4/5 of 3, we have to find 4/5 of each one, which is 4/5. Add them together to give us 12/5. We can also write this as 2 and 2/5.

Skip to 0 minutes and 40 secondsMICHAEL ANDERSON: A simpler example is the question, what is a quarter of 12?

Skip to 0 minutes and 45 secondsPAULA KELLY: This can be written as 1/4 multiplied by 12 or 12 multiplied by 1/4.

Skip to 0 minutes and 52 secondsMICHAEL ANDERSON: We can think of this question in two ways.

Skip to 0 minutes and 55 secondsPAULA KELLY: So method 1 is to ask, what's the value of 12 split into 4 equal parts?

Skip to 1 minute and 1 secondMICJAEL ANDERSON: Method 2 is to ask, what is the value of 12 lots of a quarter?

# Multiplying a whole number and a fraction

It is important to allow students time to think about the mathematical structure of what they are doing in order to develop deep understanding before concentrating upon the process of ‘how’ to multiply a fraction and a whole number.

We met earlier, in step 3.2, that young students are familiar with the fact that six lots of three is the same as three lots of six and therefore appreciate that the calculations $3 \times 6$ and $6 \times 3$ are equal and produce the same answer. We say that multiplication is commutative.

The commutativity of multiplication is true for all numbers and therefore is useful to develop understanding when multiplying a whole number and a fraction.

Multiplying a whole number by a fraction such as $12 \times \frac{1}{3}$ can be thought of as splitting the whole number into three equal pieces or as twelve lots of one third.

In the video, we consider these two different ways of thinking about what we mean when we find the product of a whole number and a fraction.

## Problem worksheet

Now complete question 3 from this week’s worksheet.