### Properties of Division on Integers:

**Property 1:**

If a and b are integers then (a/b) is **not necessarily** an integer.

**Verification:** We have,

1) 14 and 3 are both integers, but (14/3) is not an integer.

2) 17 and 6 are both integers, but (17/6) is not an integer.

**Property 2:**

If a is an integer and **a is not equal to 0** then (a/a) = 1.

**Verification:** We have,

1) (4/4) = 1.

2) ((-5)/(-5)) = 1.

**Property 3:**

If a is an integer, then (a/1) = a.

**Verification:** We have,

1) (6/1) = 6.

2) ((-17)/1) = -17.

**Property 4:**

If a is a non zero integer, then (0/a) = 0, but **(a/0) is not meaningful**. Division by Zero is undefined.

**Verification:** We have,

1) (0/2) = 0.

2) (0/(-9)) = 0.

3) (6/0) is not meaningful.

(a/0) is not meaningful

**Property 5:**

If a, b, c are any three integers then **(a/b)/c is not equal to a/(b/c)**, unless c= 1.

**Verification:**

Let a = 8, b = 4 and c = 2. Then,

(a/b)/c = (8/4)/2 = (2/2) = 1.

a/(b/c) = 8/(4/2) =(8/2) = 4.

Therefore, (a/b)/c is not equal to a/(b/c).

If c = 1 then,

(a/b)/c = (8/4)/1 = (2/1) = 2.

a/(b/c) = 8/(4/1) =(8/4) = 2.

Therefore, In this case (a/b)/c is equal to a/(b/c).

**Property 6:**

If a, b, c are integers and a > b then

1) (a/b) > (b/c), if c is positive

2) (a/c) < (b/c), if c is negative

**Verification:**

1) 27 > 18, and 9 is positive, that implies 27/9 > 18/9

2) 27 > 18, and (-9) is negative, that implies 27/(-9) < 18/(-9)