Addition and Subtraction of Integers

Addition and Subtraction of Integers

Addition of Positive Integers

Consider the addition of 2 + 3.

The plus sign, +, tells us to face the positive direction.
So, to evaluate 2 + 3, start at 2, face the positive direction and move 3 units forwards.

This suggests that:

Positive integers can be added like natural numbers.

Addition of Negative Integers

Consider the addition of (–2) + (–3).

The plus sign, +, tells us to face the positive direction.
So, to evaluate (–2) + (–3), start at –2, face the positive direction and move 3 units backwards.

Note:

We can write (–2) + (–3) as –2 + –3

Subtracting a Positive Integer from a Negative Integer

Consider the value of (–2) – (3).

The minus sign, –, tells us to face the negative direction.
So, to evaluate (–2) – (3), start at –2, face the negative direction and move 3 units forwards.

We notice that:

That is:

This suggests that:

Adding a negative integer is the same as subtracting a positive integer.

From the above discussion, we can state that:

Negative integer are added like natural numbers; but place a minus sign, –, in front of the sum.

Example 7

Find the value of:

Solution:

Addition of a Positive Integer and a Negative Integer

Consider the addition of 3 + (–7).

The plus sign, +, tells us to face the positive direction.
So, to evaluate 3 + (–7), start at 3, face the positive direction and move 7 units backwards.

Note:

3 + (–7) is often written as 3 – 7.

To find the value of 3 – 7, first ignore the signs and subtract the smaller number, 3, from the larger number, 7, and put the sign, –, of the larger number, 7, in front of the difference. That is:

Example 8

Find the value of:

Solution:

Subtracting a Negative Integer from a Positive Integer

Consider the subtraction of 2 – (–3).

The minus sign, –, tells us to face the negative