We're going to look at how addition and subtraction are related, and number lines can help us with that. Do you recall how to use a number line to work out subtraction problems ?

Examples

Example 1

Use the number line to help you find the value of 35-24.

Worked Solution

Create a strategy

Find the bigger number on the number line and count the number of jumps back to the lower number given.

Apply the idea

Here are 35 and 24 on the number line:

There are 11 jumps between 35 and 24. So:35-24=11

Idea summary

To subtract one number from another, count the number of jumps between the numbers on the number line.

Addition and subtraction

We can see how addition and subtraction are related by looking at their fact families, just like in this video.

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Examples

Example 2

Use the fact family of 5, 7 and 12.

An image showing 7 green blocks plus 5 blue blocks equals 12 yellow blocks.

What is 5+7?

Worked Solution

Create a strategy

Count up all the blocks above 7 and 5.

Apply the idea

There are 12 blocks altogether, so:5+7=12

Reflect and check

You could also use the fact family below:

Blocks showing the fact family 5 plus 7 equals 12. Ask your teacher for more information.

The 5 blocks and 7 blocks in the bottom row make up the 12 blocks in the top row. So:5+7=12

What is 12-7?

Worked Solution

Create a strategy

Cross out 7 blocks from the yellow blocks and count the remaining blocks.

Apply the idea

If we cross out 7 of the yellow blocks, we will be left with 5 blocks. So:12-7=5

Reflect and check

You could also use the fact family below:

Both rows have 12 blocks. If we take away the 7 blocks in the second row we are left with 5 blocks. So:12-7=5

What is 12-5?

Worked Solution

Create a strategy

Cross out 5 blocks from the yellow blocks and count the remaining blocks.

Apply the idea

If we cross out 5 of the yellow blocks, we will be left with 7 blocks. So:12-5=7

Reflect and check

You could also use the fact family below:

Both rows have 12 blocks. If we take away the 5 blocks in the second row we are left with 7 blocks. So:12-7=5

Idea summary

There are four different number sentences we can make for each fact family, two addition and two subtraction. If we start with the numbers, 12, 13 and 25, we can make the following fact family:

\begin{array}{c} 12+13=25 \\ 13+12=25\\ 25-13=12\\ 25-12=13 \end{array}

Outcomes

AC9M3A01

recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences

5.01 Relate addition and subtraction

Ideas

Are you ready?

Examples

Example 1

Addition and subtraction

Examples

Example 2

Outcomes

AC9M3A01

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