1.2.1 Basic Arithmetic Operations Involving Integers


1.2.1 Basic Arithmetic Operations Involving Integers

1.2.1a Multiplication and Division of Integers
1. Multiplication and division of like signs gives (+)

( + ) × ( + ) = + ( + ) ÷ ( + ) = + ( − ) × ( − ) = + ( − ) ÷ ( − ) = +


2. Multiplication and division of unlike signs gives (–)

( + ) × ( − ) = − ( + ) ÷ ( − ) = − ( − ) × ( + ) = − ( − ) ÷ ( + ) = −

Example:
  (a) –25 ÷ 5 = –5
  (b)   8 × (–5) = –40
 

3. Multiplication of 3 integers.

 ( + ) × ( + ) × ( + ) = ( + ) ( + ) × ( + ) × ( − ) = ( − ) ( + ) × ( − ) × ( − ) = ( + )


4. Division of 3 integers.

( + ) ÷ ( + ) ÷ ( + ) = ( + ) ( + ) ÷ ( + ) ÷ ( − ) = ( − ) ( + ) ÷ ( − ) ÷ ( − ) = ( + )


5. The product of an integer and zero is always zero.
Example:
–5 × 0 = 0


6. When zero is divided by any integer except zero, the quotient is zero. Any integer divided by zero is undefined.
Example:
  (a) 0 ÷ 9 = 0
  (b)   –6 ÷ 0 is undefined


1.2.1b Combined Operations of Integers
 
1. BODMAS → (Brackets of Division, Multiplication, Addition and Subtraction) 

 1. Operations in the brackets should be carried out first.
 2. Followed by × or ÷ from left to right.
 3. Followed by + or – from left to right.

Example 1:
(a) –52 ÷ 13 – 15 × 4
(b)   63 ÷ (16 – 7) × (–2)
(c) –30 + 9 × 7 – 16

Solution:
(a)
–52 ÷ 13 – 15 × 4
= (–52 ÷ 13) – (15 × 4) ← (calculate from left to right; ÷ and × are done first)
= –4 – 60
= –64

(b)
63 ÷ (16 – 7) × (–2)
= 63 ÷ 9 × (–2) ← (bracket is done first, then work from left to right)
= 7 × (–2)
= –14

(c)
–30 + 9 × 7 – 16
= –30 + (9 × 7) – 16 ← ( multiply first)
= –30 + 63 – 16
= 17

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