Page 276 - Ganit Kaushal

10.7 THE NUMBER LINE

The ‘Infinite Lift’ we imagined above [section-10.6] can be converted into a number line.
But how can we visualise this?
In fact, if we rotate it by 90° in a clockwise sense, it basically becomes a number line with 0 in the
middle of it. To the left of 0 lie the negative integers –1, –2, –3, and to the right of 0 lie the positive
integers 1, 2, 3, and so on (see the picture below). Usually, we drop the + signs on positive numbers
and simply write them as 1, 2, 3, …

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10

Negative numbers Positive numbers
Now, instead of travelling up and down along the number line as a lift, we can simply imagine walking on it.
To the right of 0 is the positive (forward) direction, and to the left of 0 is the negative (backward) direction.
Smaller numbers are now to the left of bigger numbers, and bigger numbers are to the right of smaller numbers.
So, 2 < 5; –3 < 2; and –5 < –3, … etc.

10.8 ADDITION AND SUBTRACTION USING A NUMBER LINE

Ex 1. If, from 5 you wish to go over to 9, how far must you travel along the number line?
You must travel 4 steps to the right (a forward movement or ‘+’ movement) of the starting number as
the target number is bigger than the starting number. That is why 5 + 4 = 9.

0 1 2 3 4 5 6 7 8 9 10
(Recall: Starting Number + Movement = Target Number)
The corresponding subtraction statement is 9 – 5 = 4.
(Recall: Target Number – Starting Number = Movement needed)

Ex 2. Now, from 9, if you wish to go to 3, how much must you travel along the number line?
This time, you must travel 6 steps to the left (a backward movement or ‘−’ movement) from the starting
number as the target number is smaller than the starting number, i.e., you must move −6. That is why
9 + (−6) = 3.

0 1 2 3 4 5 6 7 8 9 10
(Recall: Starting Number + Movement = Target Number)
The corresponding subtraction statement is 3 – 9 = – 6.
(Recall: Target Number – Starting Number = Movement needed)

From the above two examples, we can now summarise the addition and subtraction procedures of two integers.

Addition of Integers

The addition of two integers can be summarised in the following three steps:
Step 1: Start from the point representing the first integer (Starting number) on the number line.
Step 2: Move as many units as the second integer (Movement) to the

(i) right of the first integer, if the second integer (Movement) is positive.
(Like in Example 1 above: 5 + 4 = 9)

274 Mathematics-6