YEAR 7 · INTEGERS · 12 MIN

Subtracting integers

Subtract an integer by adding its opposite and interpret a difference.

In this lesson

Subtracting 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.

Subtraction and the opposite

Subtracting an integer is equivalent to adding its opposite. Keep the first number unchanged; replace the subtraction by addition and reverse the sign of only the number being subtracted. This works for positive, negative and zero starting values.

A difference can also describe change: final value minus starting value. Moving from $- 3$ to 4 gives $4 - (- 3)$ . The positive result tells us the finish is higher than the start.

a - b = a + (- b)

Two roles for the minus sign

A minus sign may identify a negative number or indicate subtraction. Brackets distinguish these roles in $4 - (- 3)$ . Subtracting $- 3$ reverses a negative change and has the same effect as adding $+ 3$ .

Do not change every minus sign you see. In $- 2 - 5$ , the first minus belongs to the starting number, while the second subtracts a positive 5. The start remains $- 2$ , and the change takes it further left.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Subtract a negative

Calculate $4 - (- 3)$ .

Worked solution

1
Find the opposite of the subtracted number.
$- (- 3) = 3$
The opposite of negative three is positive three.
2
Rewrite subtraction as addition.
$4 - (- 3) = 4 + 3$
Subtracting a number adds its opposite, without changing the initial 4.
3
Add the positive amounts.
$4 + 3 = 7$
A rightward change of three from 4 finishes at 7.

Answer

EXAMPLE 02

Subtract from a negative start

Calculate $- 2 - 5$ .

Worked solution

1
Rewrite the subtraction.
$- 2 - 5 = - 2 + (- 5)$
The opposite of the subtracted positive 5 is −5; the first number stays −2.
2
Combine the negative amounts.
$- 2 + (- 5) = - 7$
Both amounts point left, so their distances from zero combine.
3
Check with the inverse operation.
$- 7 + 5 = - 2$
Adding back the five that was subtracted recovers the starting value.

Answer

−7

03 / YOUR TURN

Try it yourself.

Check your understanding

Calculate $- 6 - (- 10)$ .

Show answer & reasoning

The opposite of $- 10$ is $+ 10$ , so $- 6 - (- 10) = - 6 + 10 = 4$ . Ten rightward units from −6 finish at 4.

Keep practising

6 worksheet questions · 13 marks

Open worksheet 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 ↗

In this lesson

Understand the idea.

Subtraction and the opposite

Two roles for the minus sign

See the method in action.

Subtract a negative

Find the opposite of the subtracted number.

Rewrite subtraction as addition.

Add the positive amounts.

Subtract from a negative start

Rewrite the subtraction.

Combine the negative amounts.

Check with the inverse operation.

Try it yourself.

Check your understanding

Keep practising