Page 281 - Ganit Kaushal

Ex 2. Let us subtract: + 4 – (–6).

Sol. Start with 4 plus tokens.
We have to take away 6 minus tokens from these. But there are no minus tokens at all.
We can overcome this problem by adding some zero pairs, as this does not change the value of the set
of tokens.
But how many zero pairs should we add?
Correct! We have to take away 6 minus tokens, so we
add 6 zero pairs.
Now, we can take away 6 minus tokens.
See what is left? 10 plus tokens are left.
\ We conclude + 4 – (– 6) = +10

 In a similar manner, we can perform the addition
and subtraction of three or more integers with the help of plus and minus tokens. First, perform the
operation on any two integers, and then the result is operated on by the third one and so on.
Ex 3. Calculate [4 + (−6) − 2] using tokens.

Sol. Start with 4 plus tokens and 6 minus tokens.
First, we calculate 4 + (−6). This will cancel four pairs, and we will be
left with 2 minus tokens
\ 4 + (−6) = −2
Now, to calculate 4 + (−6) − 2, we will take away two plus tokens. But
there are no plus tokens. To overcome this issue, we will add two zero-
pairs and then take away two plus tokens.
How many are you left with?
We finally have 4 minus tokens with us.
\ We conclude 4 + (−6) −2 = – 4.

Exercise 10.3

1. Using the token model, evaluate the following:
(a) 5 − 7 (b) (−5) – (−3) (c) (−2) − 5 (d) −6 – (−2) + (−1)
(e) 7 – 2 – (−3) (f) 2 + 8 – 7

Miscellaneous Solved Examples

There are four options in the following questions, out of which only one is correct. Choose the correct
option.
Ex 1. Every integer less than 0 has the sign
(a) + (b) – (c) × (d) ÷
Sol. (b)
Ex 2. Which integer is 5 units to the right of 0 on the number line?

(a) +5 (b) –5 (c) +4 (d) –4
Sol. (a) [ Integers to the right of 0 are +ve]

The Other Side of Zero 279