Page 23 - Maths Skill - 6

The Other Side of Zero 21

Solved Example for Track Movement
Example 1: Start from the Cinema and press + 3 in the lift. Where will you reach? ________

Solution: We can describe this by using an expression:
Starting Floor + Movement = Target Floor.
The starting floor is + 1 (Cinema) and the number of button presses is + 3. Therefore, you reach
the target floor (+ 1) + (+ 3) = + 4 (Sports).

Example 2: Start from the ice cream parlour and press - 5 in the lift. Where will you reach ? _________
Solution: The starting floor is + 2 (Ice cream parlour) and the number of button presses is - 5.
Therefore, you reach the target floor (+ 2) + (- 5) = - 3 (Toys).

REPRESENTATION OF INTEGERS ON A NUMBER LINE
Let’s draw a line and mark any point ‘O’ on it. Consider this point ‘O’ as zero. Now mark points at equal distances
on the right as well as on the left of ‘O’. Label the points on the right side of 0 as 1, 2, 3, 4, 5, ..., etc. and on left
side of 0 as –1, –2, –3, –4, –5, ..., etc.

Negative Numbers O Positive Numbers

–5 – 4 – 3 – 2 – 1 0 1 2 3 4 5
Clearly, 1 and –1 are equidistant from 0 but in opposite directions. Similarly, 2 and –2 are equidistant from 0 but
in opposite directions and so on.
Let’s show some more integers like –7, –2, 4 and 9 on the number line.

ORDERING OF INTEGERS

It is convenient to arrange positive integers in an order, e.g., we know that 9 > 7, 3 > 0, etc. But in case of negative
integers, we need to be a little careful. Let’s assume that you along with your parents are planning to go on a short
trip to any one of the three places, i.e., Amritsar, Shimla or Chandigarh in the month of January. The weather
forecast is indicating that the temperature in these places would be – 2°C, – 4°C and 0°C respectively during that
period. Which place will be the coldest and which place will be relatively warmer?

Let’s mark these temperatures on a number line given below:
Shimla Amritsar Chandigarh

– 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5
Clearly, the temperature in Chandigarh is maximum as 0°C is occurring in the extreme right on the number line,
i.e., – 4°C < – 2°C < 0°C. On the other hand, temperature in Shimla would be the least and one would feel the
coldest there. We may conclude that:
(i) Every positive integer is greater than a negative integer.
(ii) Zero is smaller than every positive integer. Absorbing Facts

(iii) Zero is greater than every negative integer. While comparing negative integers
(iv) Zero is neither a negative integer nor a positive integer. the number with smaller numerical
(v) Farther a number is to the right of zero, larger is its value. value is greater i.e.,
(vi) Farther a number is to the left of zero, smaller is its value. - 14 < - 7