YEAR 7 · INTEGERS · 12 MIN

Adding integers

Use opposites and number-line movement to add integers.

In this lesson

Adding integers
Explain the signs and check the answer in its context.

Before you start

Whole-number addition and subtraction
Reading a number line

01 / LEARN

Understand the idea.

Addition applies a change

Adding an integer applies a directed change. Adding a positive number moves right; adding a negative number moves left. The starting value can have either sign, so decide the movement from the number being added.

Opposite amounts cancel: each positive unit can pair with a negative unit to make zero. For $- 6 + 9$ , six of the positive units cancel the six negative units. What remains determines both the size and the sign.

Compare the directions

Two negative amounts both point left. Their distances combine in the negative direction: $- 4 + (- 7) = - 11$ . Brackets around a negative addend make clear that its minus sign belongs to the number being added.

With opposite signs, subtract the smaller distance from the larger and retain the direction of the larger distance. Explain this through cancellation first, so that the sign follows from the remaining units rather than a memorised guess.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Add different signs

Calculate $- 6 + 9$ .

Worked solution

1
Split 9 into a cancelling part and a remainder.
$- 6 + 9 = - 6 + (6 + 3)$
Six positive units will cancel the six negative units.
2
Cancel the opposite amounts.
$(- 6 + 6) + 3 = 0 + 3$
Opposite integers add to zero, and addition may be regrouped.
3
Read the remaining amount.
$0 + 3 = 3$
Three positive units remain after cancellation.

Answer

EXAMPLE 02

Add two negative amounts

Calculate $- 4 + (- 7)$ .

Worked solution

1
Identify the two leftward amounts.
$- 4 + (- 7)$
Both addends are negative, so neither cancels the other.
2
Combine their distances.
$4 + 7 = 11$
Four leftward units and seven more make eleven leftward units.
3
Attach the negative direction.
$- 4 + (- 7) = - 11$
The combined position is eleven units to the left of zero.

Answer

−11

03 / YOUR TURN

Try it yourself.

Check your understanding

Calculate $- 9 + 14$ .

Show answer & reasoning

Split 14 into $9 + 5$ . Then $- 9 + 14 = (- 9 + 9) + 5 = 5$ , since the nine positive and nine negative units cancel.

Keep practising

6 worksheet questions · 13 marks

Open worksheet 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 ↗

In this lesson

Understand the idea.

Addition applies a change

Compare the directions

See the method in action.

Add different signs

Split 9 into a cancelling part and a remainder.

Cancel the opposite amounts.

Read the remaining amount.

Add two negative amounts

Identify the two leftward amounts.

Combine their distances.

Attach the negative direction.

Try it yourself.

Check your understanding

Keep practising