### Subtraction of Integers:

If a and b are two integers, then a – b = a + (-b).

To *subtract* one integer from another, we take the additive inverse of the integer to be subtracted and add it to other integer.

When we subtract a negative integer we get a greater integer.

For example, We know that additive inverse of (–7) is 7.

Thus, it appears that adding the additive inverse of –7 to 1 is the same as subtracting (–7) from 1.

We write 1 – (–7) = 1 + 7 = 8.

To

subtractone integer from another, we take the additive inverse of the integer to be subtracted and add it to other integer.

Let us now find the value of –5 – (–4) using a number line. We can say that this is the same as –5 + (4), as the additive inverse of –4 is 4.

We move 4 steps to the right on the number line starting from –5.

We reach at –1.

i.e. –5 + 4 = –1. Thus, –5 – (–4) = –1.

**Example 1:**

Find the value of – 8 – (–10) using number line

**Solution:** – 8 – (– 10) is equal to – 8 + 10 as additive inverse of –10 is 10.

On the number line, from – 8 we will move 10 steps towards right.

We reach at 2. Thus, –8 – (–10) = 2

Hence, to subtract an integer from another integer it is enough to **add the additive inverse of the integer that is being subtracted, to the other integer.**

**Example 2:**

Subtract (– 4) from (– 10)

**Solution:** (– 10) – (– 4) = (– 10) + (additive inverse of – 4)

= –10 + 4 = – 6

### Properties of Subtraction:

**Property 1:** (Closure Property)

The subtraction of any two integers is an integer, i.e., for any two integers a and b, a – b is an integer.

**Property 2:**

Subtraction of integers is not commutative, i.e., for any two integers a and b, (a – b) is not equal to (b – a).

For example, (2 – 3) is not equal to (3 – 2)

**Property 3:**

For any integer a, we have

a – 0 = a i.e.,

0 is the right identity for subtraction.

(0 – a) is not equal to a, i.e., 0 is not the

left identity.

**Property 4:**

If a, b and c are integers and a > b, then (a – c) > (b – c).