Adding integers | Year 7 | Ascent Library

01 / LEARN

The idea, step by step

Addition applies a change

Adding a positive integer moves right. Adding a negative integer moves left. The starting value may have either sign. For example, adding 9 to −6 moves six units to zero and then three further units right.

Opposite integers cancel because their changes balance: $- 6 + 6 = 0$ . Think of cancelling positive and negative units, then describe the units left over.

Compare the directions

When both amounts are negative, both point left, so the combined size grows in that negative direction. Thus $- 4 + (- 7) = - 11$ . Brackets keep the added negative amount clear.

When signs differ, cancellation leaves some amount in the direction of the larger size. Explain what remains rather than guessing a sign from the size alone.

A common trap

Adding always makes a value greater.

Instead: Adding a negative amount makes it smaller; adding zero leaves it unchanged.

02 / WORKED EXAMPLES

See the thinking

Example 1

Add different signs

Calculate $- 6 + 9$ .

Six positive units cancel the negative six.
Three positive units remain.

Example 2

Add two negative amounts

Calculate $- 4 + (- 7)$ .

Start at −4.
Adding −7 moves seven more units left.
The finish is −11.

−11

Check your understanding

Calculate $- 9 + 14$ .

Show answer

Nine positive units cancel the negative nine, leaving five positive units.

03 / WORKSHEET

Your turn

6 questions · 13 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Calculate $- 8 + 3$ .
2 marks
Calculate $6 + (- 10)$ .
2 marks
Calculate $- 5 + (- 9)$ .
2 marks
Calculate $- 12 + 12$ .
2 marks
A balance of −7 dollars receives a deposit of 20 dollars. Find the new balance.
2 marks
Calculate $2 + (- 6) + (- 3)$ .
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Calculate $- 8 + 3$ .
2 marks
Cancel three opposite units.
Five negative units remain.
−5
Calculate $6 + (- 10)$ .
2 marks
Move ten units left from 6.
Six units reach zero and four more reach −4.
−4
Calculate $- 5 + (- 9)$ .
2 marks
Both amounts are negative.
Combine sizes 5 and 9 in the negative direction.
−14
Calculate $- 12 + 12$ .
2 marks
The amounts are opposites and cancel exactly.
0
A balance of −7 dollars receives a deposit of 20 dollars. Find the new balance.
2 marks
The deposit is positive.
$- 7 + 20 = 13$ .
13 dollars
Calculate $2 + (- 6) + (- 3)$ .
3 marks
First $2 + (- 6) = - 4$ .
Then $- 4 + (- 3) = - 7$ .
−7

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum

Positive and negative numbers in context; comparing and ordering integers; number lines and directed change; adding integers; subtracting integers; mixed addition/subtraction problems. Multiplication/division of negative integers is a labelled preview, not the Year 7 core endpoint.

Official curriculum source ↗

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