Subtracting integers | Year 7

01 / LEARN

The idea, step by step

Subtraction and the opposite

A difference compares a final value with a starting value. The change from −3 to 4 is $4 - (- 3)$ : final minus initial. Subtraction of an integer can be rewritten as addition of its opposite.

In $a - b$ , change the operation to addition and replace only the number being subtracted by its opposite. Keep the first number unchanged.

a - b = a + (- b)

Two roles for the minus sign

A sign attached to a number tells its value. A subtraction sign describes an operation. Brackets separate these roles: $- 2 - 5$ starts at −2 and subtracts positive 5.

Subtracting a negative reverses a leftward change, so it adds the corresponding positive amount. It does not make every minus sign in an expression disappear.

A common trap

Any two minus signs turn into a plus.

Instead: Only subtraction of a negative amount becomes adding its positive opposite. Keep other signs in their correct roles.

02 / WORKED EXAMPLES

See the thinking

Example 1

Subtract a negative

Calculate $4 - (- 3)$ .

The opposite of −3 is +3.
Rewrite as $4 + 3$ .
The result is 7.

Example 2

Subtract from a negative start

Calculate $- 2 - 5$ .

Subtracting 5 moves left five units.
Start at −2 and finish at −7.
Equivalently, calculate $- 2 + (- 5)$ .

−7

Check your understanding

Calculate $- 6 - (- 10)$ .

Show answer

Rewrite as $- 6 + 10 = 4$ .

03 / WORKSHEET

Your turn

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

Worksheet PDF Worked solutions

Read the questions online

Calculate $8 - 13$ .
2 marks
Calculate $- 6 - (- 2)$ .
2 marks
Calculate $- 4 - 7$ .
2 marks
Calculate $0 - (- 9)$ .
2 marks
The temperature changes from −3°C to 4°C. Use subtraction to find the signed change.
3 marks
Calculate $- 5 - (- 8)$ .
2 marks

Read the worked solutions

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

Calculate $8 - 13$ .
2 marks
Rewrite as $8 + (- 13)$ .
Five negative units remain after cancellation.
−5
Calculate $- 6 - (- 2)$ .
2 marks
Subtracting −2 is adding 2.
$- 6 + 2 = - 4$ .
−4
Calculate $- 4 - 7$ .
2 marks
Rewrite as $- 4 + (- 7)$ .
Combine the negative amounts.
−11
Calculate $0 - (- 9)$ .
2 marks
The opposite of −9 is 9.
$0 + 9 = 9$ .
9
The temperature changes from −3°C to 4°C. Use subtraction to find the signed change.
3 marks
Change is final minus initial.
$4 - (- 3) = 4 + 3 = 7$ .
+7°C
Calculate $- 5 - (- 8)$ .
2 marks
Subtracting −8 adds 8.
$- 5 + 8 = 3$ .
3

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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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