NCERT 6TH CLASS MATHEMATICS CHAPTER INTEGERS
We have learnt about natural and whole numbers in the previous chapters. But when we subtract a greater whole number from a smaller whole number, then the difference will not be a whole number. Hence, there is a need to extend the number system to include such numbers.
In our day-to-day life, we often come across many situation involving the use of opposites. Some of these are discussed below.
Temperature : During the winter season, the minimum temperature on a particular day, say in Chennai, may be 20ºC. This means that the temperature in Chennai is higher than the melting point of ice, which is 0ºC. On the same day, the minimum temperature in Shimla may be 5ºC below 0ºC. How do we represent this? This can be represented as –5ºC, read as minus five degree centigrade.
Height : If we say that the height of a mountain is 2,000 metres, it means that the mountain top is 2,000 metres above the mean sea level. Here, mean sea level is considered to be the zero level. Simiarly, the depth of an ocean, say 300 metres below the mean sea level, can be expressed as –300 metres high. If height is considered as positive, depth is considered as negative height and vice versa.
=Direction : If we consider the direction towards North as positive, then 5 metres north would mean 5 metres towards the north, while -5 metres north would mean 5 metres in the opposite direction of north, i.e., 5 metres towards the south. Similarly, the negative of south is the positive of north.
Profit and Loss : If a profit of Rs 10 is expressed as Rs (+ 10), then a loss of Rs 20 is expressed as Rs (– 20) profit. We can say that negative profit is positive loss and negative loss is positive Profit.
EXAMPLE. If profit is considered as positive, state the following as profit :
(a) profit of Rs 50
(b) Loss of Rs 25
Sol. (a) profit of Rs. 50 is a positive quantity. So, profit is Rs (+ 50)
(b) Loss of Rs 25 is negative profit. Hence, loss of Rs 25 = Profit of Rs (– 25)
ORDERING OF INTEGERS
(a) Negative numbers and zero lie to the left of positive numbers, so all positive integers are greater than negative integers and zero.
i.e., – 2 < 2, – 3 < 1, – 4 < 3, 0 < 2
(b) 0 (zero) lies to the right of negative integers, so 0 is always greater than the negative integers.
i.e., – 1 < 0, – 2 < 0, – 3 < 0, – 10 < 0
(c) In positive integers, a number with greater numerical value is greater as these are on the right side on the number line.
i.e., 22 > 20, 121 > 51
(d) In negative integers, a number with greater numerical value is smaller as these are farther on the left side on the number line.
i.e., – 22 < – 20, – 121 < – 51
EXAMPLE. Insert > or <.
(a) 8 – 8 (b) – 10 – 6
Sol. On the number line, –8 is on the left of zero and 8 is on the right of zero, So, 8 is greater than – 8.
(b) – 10 is on the left of – 6 on a number line.
Hence, – 10 is less than – 6.
So, – 10 – 6
EXAMPLE. Arrange the following integers in ascending order :
– 20, – 65, 25, 5, – 10
Sol. The smallest number is – 65
The next one is – 20.
The next one is – 10.