Division of integers:

Division is the inverse operation of multiplication.

Since 3 × 5 = 15
So 15 ÷ 5 = 3 and 15 ÷ 3 = 5
Similarly, 4 × 3 = 12 gives 12 ÷ 4 = 3 and 12 ÷ 3 = 4
We can say for each multiplication statement of whole numbers there are two division statements.

1) Dividing any negative integer by a positive integer:

Observe the following example:
(– 12) ÷ 2 = (– 6)
(– 20) ÷ 5 = (– 4)
(– 32) ÷ 4 = (– 8)
(– 45) ÷ 5 = (– 9)

We observe that when we divide a negative integer by a positive integer, we divide them as whole numbers and then put a minus sign (–) before the quotient.

In general, for any two positive integers a, and b, - a ÷ (b) = (- a) ÷ b where b ≠ 0.

2) Dividing any positive integer by a negative integer:

We also observe that:
72 ÷ (– 8) = –9
50 ÷ (– 10) = – 5
72 ÷ (– 9) = – 8
50 ÷ (– 5) = – 10

So we can say that when we divide a positive integer by a negative integer, we first divide them as whole numbers and then put a minus sign (–) before the quotient.

In general, for any two positive integers a, and b, (- a) ÷ (- b) = (- a) ÷ (- b) where b ≠ 0.

3) Dividing any negative integer by a negative integer:

Lastly, we observe that
(–12) ÷ (– 6) = 2;
(–20) ÷ (– 4) = 5;
(–32) ÷ (– 8) = 4;
(– 45) ÷ (–9) = 5
So, we can say that when we divide a negative integer by a negative integer, we first divide them as whole numbers and then put a positive sign (+).

In general, for any two positive integers a, and b, (– a) ÷ (– b) = a ÷ b where b ≠ 0.

Rules of the division of integers:

• We cannot divide any number by zero.
• The quotient of two positive integers is a positive number.
• The quotient of two negative integers is a positive number.
• The quotient of a positive integer and a negative integer is always a negative number.