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Year 8AC9M8N04

Four Operations with Integers

Use the 4 operations with integers and with rational numbers, choosing and using efficient strategies and digital tools where appropriate.

Negative numbers follow the same rules as positive ones, plus one extra: watch the signs. Getting the sign right is most of the work.

Method

Two like signs make a plus
−(−5)=+53−(−2)=3+2-(-5) = +5 \qquad 3 - (-2) = 3 + 2
Minus a minus is a plus.
Multiplying or dividing: count the minus signs
(−)(−)=+(−)(+)=−(-)(-) = + \qquad (-)(+) = -
An even number of minuses gives a positive.
Adding a negative moves you left
5+(−8)=−35 + (-8) = -3
Think of the number line.
The order of operations still applies
Brackets, then indices, then times and divide, then add and subtract.

Worked example

e.g. Work out −6+4×(−3)\text{Work out } -6 + 4 \times (-3)
  1. Follow the order of operations. Do the multiplication first.4×(−3)4 \times (-3)
  2. One minus sign means the answer is negative.=−12= -12
  3. Now the addition. Rewrite it.−6+(−12)-6 + (-12)
  4. Adding a negative means moving left.=−18= -18
  5. Check the sign is sensible. Both parts were negative.−18✓-18 \quad\checkmark

Practice

Do the operation first, then decide the sign.

1
−7+12-7 + 12
Answer55
2
−4−(−9)-4 - (-9)
Answer55
3
(−6)×(−7)(-6) \times (-7)
Answer4242
4
−364\dfrac{-36}{4}
Answer−9-9
5
−3+2×(−5)-3 + 2 \times (-5)
Answer−13-13
6
(−2)3(-2)^3
Answer−8 — three minus signs multiply to a negative-8 \text{ — three minus signs multiply to a negative}
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