# 4.06 Balance number sentences with mixed operations

Lesson

## Ideas

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.

### Examples

#### 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.

### Examples

#### 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.

### Outcomes

#### MA2-5NA

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

#### MA2-6NA

uses mental and informal written strategies for multiplication and division