# 3.09 x9

Lesson

## Ideas

Multiplication looks at equally sized groups. Can you solve this problem?

### Examples

#### Example 1

Find the value of 8 \times 5.

Worked Solution
Create a strategy

This can be thought of as 8 groups of 5 squares, as represented in the image below.

Apply the idea

There are 40 squares in the above image.8 \times 5 = 40

Idea summary

Thinking of multiplication as equally sized groups of objects can make multiplication easier.

## 9 times table

9 groups is 1 less than 10 groups. Let's look at how we can use this to help us learn the 9 times tables.

### Examples

#### Example 2

Find the value of 5\times9.

Worked Solution
Create a strategy

We can think of this as 10 groups of 5 minus 1 group of 5.

Apply the idea

First find 10 groups of 5:

1 group of 5 is just 5. So now we subtract 5 from 50:

So we have:

Idea summary

When mutiplying by 9:

• 9 groups can be thought of as 10\text{ groups }- 1\text{ group.}
• When we look at the answers up until 9\times10, the units have a descending pattern and the tens have an increasing pattern: 9, \, 18, \, 27, \,36, \, \ldots
• If we add the digits in the answers of the nine times tables until we get a single digit, that digit is always 9.

### Outcomes

#### MA2-6NA

uses mental and informal written strategies for multiplication and division