Add the ones column first: 9 + 6 = 15. Bring down the 5 and carry the 1 to the tens column. \begin{array}{c} & &\text{}^1 1 &9 \\ &+ &1 &6 \\ \hline & & &5 \\ \hline \end{array}

Add the tens column: 1 + 1 + 1 = 3. \begin{array}{c} & &\text{}^1 1 &9 \\ &+ &1 &6 \\ \hline & &3 &5 \\ \hline \end{array}

The simplified number sentence would be: 48 - ⬚ = 35

Locate 48 in the number line.

Jump back from 48 and count the number of units until we reach 35.

We have jumped back 13 units from 48. So the complete number sentence would be: 48 - 13 = 19 + 16

Idea summary

For number sentences to be equivalent, or balanced, both sides must equal the same amount.

Find unknown quantities in single step problems

This video looks at how to find unknowns values in number sentences that involve one step.

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Examples

Example 2

Complete the statement with the missing number: 9\times⬚=135

Worked Solution

Create a strategy

Use the number line below to count how many jumps of 9 there are between 0 and 135.

Apply the idea

Locate where 0 and 135 is.

We can see that there are 15 jumps of 9 from 0 to 135. So, the complete statement is 9 \times 15 = 135

Idea summary

We can use a number line to find an unknown quantity.

Find unknown quantities in multi-step problems

Now we look at problems that will need more than one step to find the answer.

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Examples

Example 3

Complete the number sentence: 40 = 8 + 8 \times ⬚

Worked Solution

Create a strategy

Simplify the number sentence and solve it to help with the more complicated number sentence.

Apply the idea

We can simplify the number sentence to be: 40 = 8 + ⬚

To find the unknown, we locate where 8 is then jump to the right to get 40.

We have jumped 32 spaces to the right of 8.40 = 8 + 32

To complete the original number sentence, we need to find the unknown for the following number sentence: 8 \times ⬚ = 32

We can count up by multiples of 8 to get: 8,\,16,\,24,\,32, so we get 32 after 4 counts. This means that: 8\times 4 = 32

The complete number sentence is: 40 = 8 + 8 \times 4

Idea summary

To find the missing number in a multi-step number sentence, we can make the number sentence simpler and solve that one first.

Simplify problems

Sometimes you can make the problem easier if you simplify the question first, this video will show you how.

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Examples

Example 4

Let's work out what ⬚ must equal to make the following number sentence true.

⬚ + 16 = 3 \times 8

First, what does 3 \times 8 equal?

Worked Solution

Create a strategy

We can think of it as 3 groups of 8, like in the array below where there are 3 rows of 8 squares.

Apply the idea

Count the number of squares in the array to get: 3\times 8=24

So now we have ⬚ + 16 =24. What number plus 16 equals 24?

Worked Solution

Create a strategy

Use the number line below to count how many jumps are between the starting number and the target number.

Apply the idea

Plot 16 and 24 on the number line and count the number of jumps.

We have jumped 8 spaces to the right of 16. So: 8 + 16 = 24

This means that the unknown was 8: 8 + 16 = 3 \times 8

Idea summary

To balance a number sentence, work out the value of one side first, and use the answer as the target value to work out the other side.

Outcomes

MA3-6NA

selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operation

3.10 Find unknown quantities

Ideas

Are you ready?

Examples

Example 1

Find unknown quantities in single step problems

Examples

Example 2

Find unknown quantities in multi-step problems

Examples

Example 3

Simplify problems

Examples

Example 4

Outcomes

MA3-6NA

What is Mathspace

About Mathspace