Page 277 - Ganit Kaushal

(ii) left of the first integer, if the second integer (Movement) is negative.

(Like in Example 2 above: 9 + (−6) = 3)
Step 3: The integer representing the point reached (Target Number), in the above-mentioned steps, represents
the sum of the given integers.

Subtraction of Integers

From the above two examples, it is clear that subtracting an integer ‘b’ from ‘a’, i.e., (a − b), is equal to an
integer which, when added to ‘b’ gives ‘a’. As above, 3 – 9 = – 6, since −6 added to 9 gives 3, and also 9 – 5 = 4,
since 4 added to 5 gives 9.
Another way to understand subtraction is by using the concept of ‘Addition of Inverse’.

To subtract an integer, it is enough to add the additive inverse of the integer that is being subtracted, i.e.,
subtract an integer by adding its inverse. (This addition can be performed by the steps mentioned above for
the addition of integers)
For example: 3 – 9 = 3 + (additive inverse of 9) = 3 + (−9) = −6 (Same as obtained above)

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

Start with the starting number 3 and then move 9 units to the left of 3. You will reach (– 6).

Remark
 The number that is being subtracted can be replaced by its inverse and then added instead.
For example: 5 − 2 = 5 + (additive inverse of 2) = 5 + (−2) = 3
 The number that is being added can be replaced by its inverse and then subtracted instead.
For example: 5 + 2 = 5 − (additive inverse of 2) = 5 − (−2) = 7

Addition and Subtraction of More than Two Integers

Addition and subtraction of three or more integers can be carried out similarly. First, operate on any two
integers, and then the result is operated on by the third one and so on. We can also group positive and negative
numbers separately and then solve them accordingly.

Examples:
(a) 5 − 2 − 8 = 3 − 8 [ 5 − 2 = 3]

= −5
(b) (−7) – 8 – (−25) = −15 – (−25) [ −7 − 8 = −15]

= −15 + (additive inverse of −25)
= −15 + 25 = 10
(c) (−13) + 32 – 8 −1 = 19 – 8 − 1 [ (−13) + 32 = 19]
= 11−1 [ 19 − 8 = 11]

= 10

The Other Side of Zero 275