Integers

Addition and Subtraction

It should be noted that:
a) + –  =  –
b) – +  =  –
c) – –  =  +
d) + +  =  +

As a student, please try: ( For this questions, please draw a number line as the one shown above from -14 to +14 )
i) 4 + 8
ii) -4 + 8
iii) 4-(-8)
iv) 4-8

(Check solution below)

i) 4 + 8
This can be represented as: ⁺4 + (⁺8).
Using a number line, start at position 0. Move 4 steps to the right and further 8 steps to the right. What do you get?
If your answer is +12, you are correct.

ii) -4 + 8 is the same as ^–4 + (⁺8)
On the number line, start at position 0, move 4 to the left and then move 8 steps to the right.
Your answer should be +4 or simply, 4

iii) 4 – (-8) is the same as ⁺4 – (^–8).
Remember, – – = +, hence the above problem is the same as 4 + 8
On the number line, start at position 0. Move 4 steps to the right and a further 8 steps to the right.
Your answer should be +12 or simply, 12

iii) 4 – 8 is the same as ⁺4 – (⁺8).
Remember, – + = -, hence the above problem is the same as 4 – 8
On the number line, start at position 0. Move 4 steps to the right and a then 8 steps to the left.
Your answer should be -4

Multiplication and Division

Rules of Multiplication and Division:
Positive x positive = positive
Positive x negative = negative
negative x negative = positive
negative x positive = negative
Positive ÷ positive = positive
Positive ÷ negative = negative
negative ÷ negative = positive

Order of Operations

Remember BODMAS? This rule is followed in the order of operations.
BODMAS stands for Bracket, Of, Division, Multiplication, Addition, Subtraction

Example: Solve 4 x 2(10-4) + 9 ÷ 3 – 10

Using BODMAS
= 4 x 2(10 – 4) + 9 ÷ 3 – 10
= 4 x 2(6) + 9 ÷ 3 – 10
= 4 x 12 + 9 ÷ 3 – 10
= 4 x 12 + 3 – 10
= 48 + 3 – 10
= 51- 10
= 41