Page 273 - Ganit Kaushal

Back to Zero (Ground Floor)

On the ground floor, Shella was in a hurry and by mistake, she presses +2.
Can you tell what she should do to cancel it and come back to the ground floor?

Very good! She can cancel it by pressing –2. That is: (+2) + (–2) = 0, and she will be back on the
ground floor.
We call –2 the ‘Additive Inverse’ or simply the ‘Inverse’ of +2. Similarly, the inverse of –2 is +2. Here is
another way to think of the concept of inverse. If you are on floor +3 and you press its inverse –3, then you
are back to zero, the ground floor! If you are on floor –2 and press its inverse +2, then you go to: (–2) + (+2)
= 0, again the ground floor!
Ex. Connect the inverses by drawing lines. (NCERT)

+5 –7 –8 +9

–9 +8 –5 +7

Sol. The inverses are connected with their respective numbers by the straight +5 –7 –8 +9
lines in the adjoining figure.

–9 +8 –5 +7

10.4 SUBTRACTION AS MOVEMENT NEEDED

Suppose you are at the Sports Centre (+1) and you need to go to the food court (+4).

What should be your button press?
You need to go three floors up, so you should press +3. Isn’t it?

This can be explained with an expression using subtraction as follows:

Target Floor – Starting Floor = Movement needed

In the above example, the starting floor is +1 (Sports Centre) and the target floor is +4 (Food Court). The button
presses to get to +4 from +1 are +3.

Therefore, (+4) – (+1) = +3
So, +3 is the movement needed to reach +4 from +1.

Therefore, we can say that subtraction is the ‘movement needed’ to reach the target floor from the
starting floor.
Ex. (a) What is the value of (–1) – (–2)? (b) What is the value of (–1) – (+3)?

(c) What is the value of (+ 2) – (– 2)?
Sol. (a) Here, we are on the starting floor –2 and need to go to the target floor –1.
\ We need to go up by one floor. So, the movement needed is +1. (+ve sign shows upward
movement.)

Hence, we have (–1) – (–2) = (+1).

The Other Side of Zero 271