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6.09 Multiplication by 10


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Remembering how to count by 10's can help us when we need to multiply by 10.


Example 1

Complete the pattern by adding 10 each time.

20,⬚,40, ⬚, ⬚

Worked Solution
Create a strategy

Use the place value table to add 10 to each number.

Apply the idea

Put 20 in the place value table and add 10.


The amount in the tens place goes up by one and we get a result of\,30. The units value does not change. We add ten again to complete the pattern by adding 1 to the tens place each time.

The complete pattern is 20,\,30,\,40,\,50,\,60.

Idea summary

When adding 10 each time in the pattern, the units digit does not change and the tens digit increases by 1.

Multiply numbers by 10

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

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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 units column:


But when we multiply 4 by 10, the 4 moves up in place value to the tens.


To have the correct value we put a place holder of 0 in the units column.


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.

That moves all our numbers up one place in the place value table, with the 0 as a place holder in the units column.

However, this rule is ONLY true for whole numbers, so you have to be careful once fractions or decimals are involved.



uses mental and informal written strategies for multiplication and division

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