Page 280 - Ganit Kaushal

10.10 TOKEN MODEL OF ADDITION AND SUBTRACTION

In this model, we consider two types of tokens, a ‘Plus token’ and a ‘Minus token’ .

Addition Using Tokens

While adding two integers, say (+5) + (−3), we start by taking five plus tokens and three minus tokens. While
adding, a plus token and a minus token cancel each other out because the value of this pair of tokens together is
zero (also called a ‘zero pair’). The remaining tokens after cancellation will give you the answer to the addition.
Ex 1. Evaluate (+5) + (−3) using the token model.
Sol. Start with 5 ‘Plus tokens’ and 3 ‘Minus tokens’. As can be seen from the
adjoining figure, two plus tokens are left after cancellation.
\ (+5) + (−3) = 2

Ex 2. Use tokens to find: 5 + (−8) = ?
Sol. From the adjoining figure, we see that we can cancel five zero
pairs, and we are then left with 3 ‘Minus tokens’.
\ (+ 5) + (– 8) = –3.

Subtraction Using Tokens

In earlier classes, subtraction was introduced as ‘taking away’.

For example: There are 10 books on the shelf. You take away 4 books.
How many are left on the shelf?
We can express the answer using subtraction as 10 – 4 = 6, or ‘Ten take away four is six’.
We will use the same meaning here, and we’ll do it like this.

Take 10 plus tokens and ‘take away’ 4 of them (i.e., cut off by black lines).
How many ‘Plus tokens’ are left?
6 ‘Plus tokens’ are left.
\ 10 – 4 = +6

Let’s have some more examples:
Ex 1. Let us subtract: (+5) – (+6).
Sol. Take 5 plus tokens. We have to take away 6.

But there are not enough tokens to take away 6.
How can we solve this issue? Can you answer?
No! Never mind, let’s explain this.
To solve this, we can add a zero pair (a plus and a minus token), which
does not change the value of the set of tokens.
Now, we can take away 6 plus tokens!

See what is left: only 1 minus token.
\ We conclude (+5) – (+6) = – 1.

278 Mathematics-6