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Here, we will start from 0 and move 5 steps to the right to reach 5. Then, we will move 5 steps to
the left as we have to add (–5), a negative number. We reach at 0.

+5

–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8

–5
Therefore, 5 + (–5) = 0

Thus, –5 is the additive inverse of 5 and vice versa.

Rules for Addition

We add two integers by following these rules:

Addition of two like integers: When integers have same signs (like integers), add their absolute
values and assign the same sign to the sum.
Example 6: Add the following:

(a) (+4) + (+6) (b) (−5) + (−12)
Solution: (a) Since, 4 and 6 both have same sign, so, their absolute values 4 and 6 will be added

and common sign will be affixed.
4 + 6 = 10 Note: For a positive number, we can omit the ‘+’ sign.

(b) The absolute values of −5 and −12 are 5 and 12 respectively. The common sign (−)
will be affixed with the sum of their absolute values.
(−5) + (−12) = − (|−5| + |−12|) = −(5 + 12) = −17

Addition of unlike integers: When integers have different signs (unlike integers), find the
difference of their absolute values and assign the sign of the integer with a greater value to the
result.

Example 7: Add the following:
(a) −7 and 19 (b) −25 and +5

Solution: (a) Absolute value of −7 = |−7| = 7

Absolute value of 19 = |+19| = 19
Difference of absolute values = 19 − 7 = 12

Since, the integer with greater absolute value is +19, and its sign is (+).
Thus, (−7) + (+19) = +12.

(b) Absolute value of −25 = |−25| = 25

Absolute value of +5 = |+5| = 5
Difference of absolute values = 25 − 5 = 20

Since, the integer with greater absolute value is −25, and its sign is (−).

Thus, (−25) + (+5) = −20.

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