# 3.07 x5, x10

Lesson

## Ideas

There is a relationship between the 10 times tables and the 5 times tables.

### Examples

#### Example 1

Find the value of 10\times7.

Worked Solution
Create a strategy

Use the fact that when multiplying whole numbers by 10, we move the digit up in place value and place a 0 at the end of the number.

Apply the idea

The number 7 has a 7 digit in the units column:

But when we multiply 7 by 10, the 7 moves up in place value to the tens and we put a place holder of 0 in the units column.

So we get: 10\times 7=70

Idea summary

When adding 10 each time in the pattern, we will notice that the units value does not change.

## Multiply numbers by 10

Let's look at how to multiply numbers by 10.

### Examples

#### Example 2

Find the value of 10\times 4.

Worked Solution
Create a strategy

We can think of 10\times 4 as 10 groups of 4 just like in the image below that has 10 groups of 4 squares:

Apply the idea

The above shape has 40 squares in total.

Reflect and check

We can also use a place value table and increase the place value of the 4.

The number 4 has a 4 digit in the ones column:

But when we multiply 4 by 10,, the 4 moves up in place value to the tens and we use 0 as a place holder:

So we get: 10\times 4=40

Idea summary

A quick way to multiply any whole number by 10 is to add a 0 at the end.

## Multiply numbers by 5

Similar to how we can use a  doubling strategy  for our 2, 4, and 8 times tables, we can use a halving strategy for our 5 times tables because half of 10 groups is 5 groups. Watch this video to see how.

### Examples

#### Example 3

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

Reflect and check

We can also do this by finding 8\times 10 and then halving the answer.

Idea summary

To multiply a number by 5 we can multiply the number by 10 then halve the answer.

You can also reverse this strategy and double the answers to 5 times tables to work out the answers to the 10 times tables.

### Outcomes

#### MA2-6NA

uses mental and informal written strategies for multiplication and division