Page 42 - ICSE Math 6

From the number line, we can see that the integers 1 and –1 are in the opposite directions of 0 and
equidistant from 0. Similarly, integers 2 and –2 are in the opposite directions of 0 and equidistant
from 0, and so on.

Ordering of integers
It is convenient to arrange positive integers in an order, for example, we know that 7 > 6 and 5 < 8.
Ordering negative integers is little different from that of the positive integers. Let’s look at the
following example to understand how to order negative integers. On a particular day, the temperatures
of Amritsar, Shimla and Chandigarh are recorded to be –2°C, –4°C and 0°C respectively. To know
which place among them is the coldest and which is relatively warmer, we arrange these temperatures
on the number line as shown.

Shimla Amritsar Chandigarh

–5 –4 –3 –2 –1 0 1 2 3 4 5
On a number line, numbers from left to right are arranged in increasing order. So we can arrange these
temperatures as –4°C < –2°C < 0°C, which shows that Amritsar is the coldest of the three places and
Chandigarh is relatively warmer.
We also conclude that; Try These

• Every positive integer is greater than a negative integer. 1. Is –65 greater than –30?
• Zero is smaller than every positive integer. 2. Select the option in which integers are
arranged in a correct order.
• Zero is greater than every negative integer. (a) 5 < 0 < 7 (b) –5 < 0 < –7
• Farther a number is to the right of zero, larger is its value. (c) –5 < 0 < 7 (d) 5 < 0 < –7
3. Arrange integers which lie to the left of
• Farther a number is to the left of zero, smaller is its value. 0 and are greater than –5 in decreasing
order.
Example 1: Write the opposites of the following.

(a) Increase in weight (b) 50 km west (c) 305 AD
(d) Profit of ` 300 (e) 120 m above sea level
Solution: (a) Decrease in weight (b) 50 km east (c) 305 BC

(d) Loss of ` 300 (e) 120 m below sea level
Example 2: Answer the following questions using integers with appropriate signs.

(a) An aeroplane is flying at a height of three thousand feet. At what height is it flying?
(b) A submarine is eight hundred feet below sea level. What is its elevation?
(c) What is the change in amount in a bank account, if two thousand rupees are deposited?

(d) What is the change in amount in a bank account, if two hundred rupees are taken out?
Solution: (a) +3,000 feet (b) –800 feet (c) + ` 2,000 (d) – ` 200

Example 3: Represent the following integers on the number line.
(a) +9 (b) –10 (c) +7 (d) 0

Solution: The integers in part (a), (b), (c) and (d) are represented by the letters A, B, C and D
respectively.

B D C A

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

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