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4.06 Balance number sentences with mixed operations


Are you ready?

Remembering how to find the  missing number  in a number sentence can help us solve problems in this lesson. Let's give this problem a try.


Example 1

Complete the statement with the missing number: 8\times⬚=80

Worked Solution
Create a strategy

We can rewrite the statement into a division statement.

Apply the idea

We can rewrite the statement as 80\div8=⬚.

To find the answer, we can count up by 8's until we get to 80. We can see that we needed to count up 10 times: 8, \, 16, \, 24, \, 32, \, 40, \, 48, \, 56, \, 64, \, 72, \,80. So: 80\div 8=10 Which also means:8\times10=80

Idea summary

We can rewrite multiplication statements as division statements to find unknown values.

Balance number problem

This video shows how to balance number sentences where there are different operators on either side of the equality symbol.

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Example 2

Complete the number sentence: 48 - ⬚ = 19 +16

Worked Solution
Create a strategy

Add 19 and 16, and then subtract the sum from 48.

Apply the idea

Add the numbers on the right side:19+16 = 35

Subract the result from 48 to see how much bigger the left side is: 48-35 = 13

So 48 is 13 bigger than the right side of the sentence. So to make both sides equal we need to subtract 13 from 48. 48 - 13 = 19 + 16

Idea summary

Whenever there is an equal sign we need to make sure that the value of the expressions on each side are the same.



uses mental and written strategies for addition and subtraction involving two-, three-, four and five-digit numbers


uses mental and informal written strategies for multiplication and division

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