Page 21 - Maths Skill - 6

The Other Side of Zero 19

INTRODUCTION
So far we have studied about the whole numbers. There is no whole number less than zero. In the study of whole
numbers we found that subtraction is possible only when a smaller number is subtracted from a larger number
and not vice versa. But what happens when a larger whole number is subtracted from a smaller whole number
like 5 – 6, 8 – 10, 10 – 13, etc.?
Think you want to buy a pen from the market. You have only ` 12 and the pen costs ` 15. The shopkeeper wants
` 3 as due amount from you. He writes ` 3 in his diary to remember. That’s your debit. But how would he
remember whether ` 3 has to be given or taken from you.
He can do this with negative sign with number.

Thus, you see we need to use a sign going for number less than zero. The sign that is used in the placement of a
minus sign authenticates to the number. This indicates that number with a negative sign are less than zero. These
are called negative numbers.

INTERNATIONAL WEATHER
NEED OF NEGATIVE NUMBERS Forecast for Wednesday
In our day-to-day life, we often come across many situations where Place Max. Min.
negative numbers are involved. Observe the Table given carefully. New York 11°C 07°C
Do you notice the minimum temperature in Geneva, it is –5°C which is London 11°C 03°C
below the melting point of ice, i.e., 0°C. With the help of weather table Los Angeles 22°C 09°C
one can easily compare the climate of different countries and cities. Kuala Lampur 30°C 23°C

Similarly. In geography, you may have learnt the height of mountains. Singapore 28°C 24°C
For example; if the height of the Mt. Everest is 8848 m, it means the top Hongkong 20°C 17°C
of mountain is 8848 m above the sea level. Sea level is taken as zero Tokyo 08°C 02°C
level so, the depth of a sea, say 523 metres is expressed as –523 metres. Bengkok 31°C 20°C
Another real life situation where negative numbers are used in profit and Shanghai 11°C 09°C
loss, where profit is considered as positive because you gain whereas loss Dubai 26°C 17°C
is expressed as negative number. Paris 06°C 04°C
Geneva 04°C – 05°C
INTEGERS
The whole numbers along with the numbers –1, –2, –3, ..., etc. form the system of integers. Generally, the set of
integers is denoted by I or Z.
I = {............. - 3, - 2, - 1, 0, 1, 2, 3, ......} Fact-o-meter
The numbers –1, –2, –3, – 4, –5, – 6, ... etc. are called negative � We use the sign ‘–’ with negative
integers, and the numbers 1, 2, 3, 4, 5, 6, ... etc. are called integers. It does not indicate
positive integers. The number 0 which is an integer is neither subtraction, rather this sign is a
positive nor negative. part of the number.
To make a distinction between the two groups, the numbers
less than 0 are given the negative sign. The collection of whole
numbers and the negative numbers together make the collection called Integers. Let us draw a few figures to
represent the collection of numbers (Fig. a).

Natural numbers Whole numbers Zero

Fig. (a)