Topics
7. Multiplication and division
topic badge
AustraliaNSW
Stage 2

7.07 Balance number sentences with mixed operations

Lesson
Practice
Lesson

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.

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.

Loading video...

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

MA2-8NA

generalises properties of odd and even numbers, generates number patterns, and completes simple number sentences by calculating missing values

What is Mathspace

About Mathspace