Page 296 - Math_Genius_V1.0_C6_Flipbook

E:\Working\Focus_Learning\Math_Genius-6\Open_Files\15_Chapter_10\Chapter_10
\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

Token/Counter Model of Integers

Suppose we have two colour counters/tokens: blue counters for (–1) and red counters for (+1). Or, a
single counter with two colour faces: red (representing +1) on its front side and blue (representing
–1) on its back. The counter can be inverted whenever necessary. In another way, if the blue counter
(–) is inverted to get red (+) its sign gets changed.

A negative and a positive counters cancel each other.

= –1
= 0
= +1

Addition of Integers using Counters/Tokens

Let’s understand it with examples.

Adding two Positive Integers

Let us add: (+3) + (+4)
For the first number take 3 counters and place them in a row in such a way that the top faces are
red. Now for the second number take 4 more counters and place them in the other row so that
their top faces are red.

Total number of red face counters = 7 which represents (+7). Hence, (+3) + (+4) = +7

Adding two Negative Integers

Let us add: (–2) + (–5)
First take 2 counters and place them in a row in such a way that the top faces are blue. Now, take
5 more counters and place them in the other row so that their top faces are also blue.

Total number of blue face counters = 7 which represents (–7). Hence, (–2) + (–5) = (–7)
Adding one Positive Integer and one Negative Integer

Let us add: +5 + (–3)
First take 5 counters and put them in a row in such a way that their top faces are red. Now take 3
more counters and place them in the second row so that their top faces are blue.

Mathematics-6 294