RULES OF DIVISION OF INTEGERS
1) The quotient of two integers need not be an integer.
If (+ x) , (+ y) are integers, but (+ x) ÷ (+ y) is not an integers.
2) As we all know for every non-zero integer x, we have x ÷ x = 1
- 7 + 10
Example.2) ---------- = 1 or ------------ = 1
- 7 + 10
3) For every non-zero integers x, we have 0 ÷ x = 0
0 ÷ (+ 15) = 0 , 0 ÷ (- 30) = 0
4) For unequal non-zero integers x and y, there are x ÷ y = y ÷ x ( Not Equal )
5) If unequal non-zero integers x, y and z, we have ( x ÷ y ) ÷ z = x ÷ ( y ÷ z )
DIVISION OF INTEGERS –
The quotient of two integers with the same sign is the positive of the Integer obtained by dividing the numerical value of the dividend with the numerical value of the divisor.
+ 45
Example.1) ---------- = + 5
+ 9
+ 108
Example.2) ---------- = + 9
+ 12
- 100
Example.3) ---------- = + 5
- 20
- 96
Example.4) --------- = + 12
- 8
The quotient of two integers with different signs is the negative of the integer obtained by dividing the numerical value of the dividend with the numerical value of the divisor.
- 50
Example.1) --------- = - 10
+ 5
+ 56
Example.2) --------- = - 8
- 7