Inverse operations | Year 3

01 / LEARN

Understand the idea.

Undo a calculation

Addition joins parts to make a whole. Subtraction starts with the whole and removes one part. They are inverse operations because subtracting a part that was added takes you back to the other part.

For $36 + 24 = 60$ , the parts are $36$ and $24$ , and the whole is $60$ . Swap the parts for another addition, or subtract either part from the whole to find the other.

Use the inverse as a check

Check a subtraction by rebuilding the whole with addition. If $154 - 67 = 87$ , add $87 + 67$ . The result must be $154$ because the remaining and removed parts together make the starting amount.

Two different parts usually give four related facts: two additions and two subtractions. If the parts are equal, swapping them repeats the same addition. The number of different facts changes, but the part–whole connection stays the same.

Keep the roles clear

Keep track of each number's role. In the related subtractions for $23 + 41 = 64$ , start with the whole, $64$ . Removing $23$ leaves $41$ ; removing $41$ leaves $23$ . Swapping the subtraction numbers does not preserve those facts.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Build a fact family

Use 28 + 35 = 63 to write the other related facts.

Worked solution

1
Swap the two added parts.
$35 + 28 = 63$
Changing the order of addition does not change the total.
2
Remove the first part from the whole.
$63 - 28 = 35$
The other part remains when twenty-eight is removed.
3
Remove the second part from the whole.
$63 - 35 = 28$
The same whole contains both original parts.

Answer

35 + 28 = 63; 63 − 28 = 35; 63 − 35 = 28.

EXAMPLE 02

Check subtraction

Levi says 304 − 168 = 136. Check using addition.

Worked solution

1
Identify the parts that must rebuild the whole.
$136 + 168$
The proposed difference and the removed amount should total three hundred and four.
2
Add the hundreds, tens and ones.
$\begin{aligned} 100 + 100 & = 200 \\ 30 + 60 & = 90 \\ 6 + 8 & = 14 \end{aligned}$
Splitting by place value accounts for both numbers completely.
3
Combine and compare with the starting number.
$200 + 90 + 14 = 304$
The addition recovers the starting whole, so Levi’s subtraction is correct.

Answer

The answer is correct: 136 + 168 = 304.

03 / YOUR TURN

Try it yourself.

Check your understanding

Complete the related fact: if 47 + 18 = 65, then 65 − 18 = __.

Show answer & reasoning

In $47 + 18 = 65$ , the two parts are $47$ and $18$ . Removing the $18$ from the whole $65$ leaves $47$ .

Keep practising

6 worksheet questions

Open worksheet Worked solutions

Read the questions online

Use $32 + 19 = 51$ to complete $51 - 32 =__$ .
Write two subtraction facts for $45 + 27 = 72$ .
Check $82 - 36 = 46$ with addition.
Check $250 - 114 = 146$ with addition. Is it correct?
A jar had some marbles. After 26 more are added, it contains 73. Which subtraction finds the starting amount? Find it.
Write the fact family using the parts 18 and 18 and whole 36. List each different fact once.

Read the worked solutions

Use $32 + 19 = 51$ to complete $51 - 32 =__$ .
The missing value is the other part.
19
Write two subtraction facts for $45 + 27 = 72$ .
Start with the whole, 72, each time.
$72 - 45 = 27$ and $72 - 27 = 45$ .
Check $82 - 36 = 46$ with addition.
$40 + 30 = 70$ and $6 + 6 = 12$ ; $70 + 12 = 82$ .
$46 + 36 = 82$ , so it is correct.
Check $250 - 114 = 146$ with addition. Is it correct?
$146 + 114 = 260$ , not 250; $136 + 114 = 250$ .
No. The correct difference is 136.
A jar had some marbles. After 26 more are added, it contains 73. Which subtraction finds the starting amount? Find it.
Undo adding 26 by subtracting 26 from 73.
$73 - 26 = 47$ marbles.
Write the fact family using the parts 18 and 18 and whole 36. List each different fact once.
Equal parts make the two addition facts identical and the two subtraction facts identical.
$18 + 18 = 36$ and $36 - 18 = 18$ .

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Mental strategies; two-/three-digit calculations; regrouping; inverse operations; missing values.

Official curriculum source ↗

In this lesson

Understand the idea.

Undo a calculation

Use the inverse as a check

Keep the roles clear

See the method in action.

Build a fact family

Swap the two added parts.

Remove the first part from the whole.

Remove the second part from the whole.

Check subtraction

Identify the parts that must rebuild the whole.

Add the hundreds, tens and ones.

Combine and compare with the starting number.

Try it yourself.

Check your understanding

Keep practising