Four operations with integers | Year 8

01 / LEARN

The idea, step by step

Direction before rules

Integers are whole-number values including zero and negative values. On a number line, a move right increases the value and a move left decreases it. Adding a negative number moves left; subtracting a negative number reverses that move. For example, $3 - (- 4)$ means the value four more than 3, so it is 7.

Multiplication, division and zero

A product or quotient of two numbers with the same sign is positive; different signs give a negative result. Work out the unsigned size, then apply the sign. A zero product is zero, and zero divided by a nonzero number is zero. Division by zero is undefined: no number multiplied by zero can produce a nonzero dividend.

A common trap

Subtracting a negative always makes the answer more negative.

Instead: Subtraction reverses the change. For example, removing a debt increases the balance.

02 / WORKED EXAMPLES

See the thinking

Example 1

Add across zero

Calculate $- 7 + 12$ .

Start at -7.
Adding 12 moves twelve places right, crossing zero.
$12 - 7 = 5$ .

Example 2

Use two operation rules

Calculate $(- 6) (- 4) - 18 \div (- 3)$ .

Multiply first: two negative factors give $24$ .
Divide: $18 \div (- 3) = - 6$ .
Then $24 - (- 6) = 24 + 6 = 30$ .

Check your understanding

Calculate $- 4 - (- 9)$ .

Show answer

$- 4 - (- 9) = - 4 + 9 = 5$ .

03 / WORKSHEET

Your turn

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

Worksheet PDF Worked solutions

Read the questions online

Calculate $- 9 + 4$ .
2 marks
Calculate $3 - (- 8)$ .
2 marks
Calculate $(- 7) \times 6$ .
2 marks
Calculate $(- 48) \div (- 8)$ .
2 marks
Calculate $- 5 + 3 (- 4)$ .
2 marks
A submarine is at -18 m relative to sea level. It rises 7 m, then descends 12 m. Find its final position.
3 marks

Read the worked solutions

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

Calculate $- 9 + 4$ .
2 marks
Move four places right from -9.
The result is -5.
-5
Calculate $3 - (- 8)$ .
2 marks
$3 - (- 8) = 3 + 8 = 11$ .
11
Calculate $(- 7) \times 6$ .
2 marks
Different signs give a negative result.
$7 \times 6 = 42$ , so the product is $- 42$ .
-42
Calculate $(- 48) \div (- 8)$ .
2 marks
Same signs give a positive result.
$48 \div 8 = 6$ .
6
Calculate $- 5 + 3 (- 4)$ .
2 marks
$3 (- 4) = - 12$ .
$- 5 + (- 12) = - 17$ .
-17
A submarine is at -18 m relative to sea level. It rises 7 m, then descends 12 m. Find its final position.
3 marks
$- 18 + 7 - 12 = - 11 - 12 = - 23$ .
It finishes 23 m below sea level.
-23 m

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Four operations with integers; signed fraction/decimal calculations; order of operations; terminating and recurring decimals; rational and irrational numbers; estimating square roots and recognising pi; choosing efficient exact/decimal representations.

Official curriculum source ↗

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