Topics
3. Multiplication strategies
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Australia
Year 4

3.07 x5, x10

Lesson
Practice
Lesson

Are you ready?

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:

TensUnits
7

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.

TensUnits
70

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.

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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:

This image shows 10 rows of 4 squares.
Apply the idea

The above shape has 40 squares in total.

\displaystyle 10\times4\displaystyle =\displaystyle 40
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:

TensUnits
4

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:

TensUnits
40

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.

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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.

The image shows eight rows of five squares.
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.

\displaystyle 8\times 10\displaystyle =\displaystyle 80Add a 0 to the end
\displaystyle 8\times 5\displaystyle =\displaystyle 40Halve 80
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

AC9M4N05

solve problems involving multiplying or dividing natural numbers by multiples and powers of 10 without a calculator, using the multiplicative relationship between the place value of digits

AC9M4A02

recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator

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