In the previous sections we completed the discussion on direct and inverse proportions. In this chapter, we discuss a more basic topic of integers. Consider the following situation:
A chef is making fruit salad for a party. He wants 16 apples. But in the kitchen there are only 12. He needs 4 more. He goes to a nearby home and borrow 4 apples. Now he has all the required 16 apples. But he is in debt. He has to return the 4 apples to the nearby home. So he makes a note of it. In his diary he writes: 'Number of apples = 4'.
But writing simply like this may cause problems. After some time, looking at the diary, he may wonder what the number 4 really indicate?. Does he want 4 apples for himself, or does he have to give 4 apples to some one else?
So he must write it more clearly:
• No. of apples to be given away = 4. The mathematical way of writing this is:
• No. of apples = - 4.
In the second method, '-' (minus) sign is put before the number 4. This '-' sign has much significance. When the new stock of apples comes to the kitchen, the chef has to take 4 from it and give it to the nearby home. If this new stock has say, 25 apples, the chef will be left with 21 apples (since 25 – 4 = 21) only.
Another example:
The fig.4.1 below shows the diagram of a large water tank in a town. During the day time, people use water for various activities like bathing, cooking, washing etc., So the water level decreases. But during the night, there are no such activities, and so there is no decrease in water level during the night. And also, during the night, the used up water is replenished by water from a nearby treatment plant. So the water level rises to the previous level.
Thus the water level in the tank always maintains a constant level each morning. We can see from the fig. 4.1 that, this level is indicated as 'zero' in the scale.
But during summer, there will be scarcity of water. All the water that is used during day cannot be replenished during the night. So the water level will not rise back to zero each morning. It will always be below zero. At mid summer, when the intensity of heat is high, the level will go further and further below zero. The care taker of the water tank has to keep a close watch. He must tell others about the level of water in the tank every morning during summer. How would he say it?
He checks and finds by how many units the level is below zero. If it is 3, he would say: “The level is 3 units below zero”. An easier way is to say mathematically : “ The level is -3”. But for this, a simple modification has to be made to the scale in the tank. That is., a '-' sign should be placed in front of all the units below zero. This is shown in the fig.4.2 below.
If the level is 5 units below zero, he can say: “Level is -5”. The '-' sign instantly gives a clear picture of the seriousness of the situation.
Numbers with '-' sign in front are called negative numbers. All the readings below zero are negative readings.
We must note one peculiarity about these negative readings: As the level decreases, the negative value increases. For example, if the level falls even below -5 and reach -7, it means that we have still lesser water to use. But the value after the '-' sign has increased from 5 to a larger value of 7.
There are many situations where negative numbers are used in day to day life. In the next section we will see some more examples.
A chef is making fruit salad for a party. He wants 16 apples. But in the kitchen there are only 12. He needs 4 more. He goes to a nearby home and borrow 4 apples. Now he has all the required 16 apples. But he is in debt. He has to return the 4 apples to the nearby home. So he makes a note of it. In his diary he writes: 'Number of apples = 4'.
But writing simply like this may cause problems. After some time, looking at the diary, he may wonder what the number 4 really indicate?. Does he want 4 apples for himself, or does he have to give 4 apples to some one else?
So he must write it more clearly:
• No. of apples to be given away = 4. The mathematical way of writing this is:
• No. of apples = - 4.
In the second method, '-' (minus) sign is put before the number 4. This '-' sign has much significance. When the new stock of apples comes to the kitchen, the chef has to take 4 from it and give it to the nearby home. If this new stock has say, 25 apples, the chef will be left with 21 apples (since 25 – 4 = 21) only.
Another example:
The fig.4.1 below shows the diagram of a large water tank in a town. During the day time, people use water for various activities like bathing, cooking, washing etc., So the water level decreases. But during the night, there are no such activities, and so there is no decrease in water level during the night. And also, during the night, the used up water is replenished by water from a nearby treatment plant. So the water level rises to the previous level.
 |
| Fig.4.1 |
But during summer, there will be scarcity of water. All the water that is used during day cannot be replenished during the night. So the water level will not rise back to zero each morning. It will always be below zero. At mid summer, when the intensity of heat is high, the level will go further and further below zero. The care taker of the water tank has to keep a close watch. He must tell others about the level of water in the tank every morning during summer. How would he say it?
He checks and finds by how many units the level is below zero. If it is 3, he would say: “The level is 3 units below zero”. An easier way is to say mathematically : “ The level is -3”. But for this, a simple modification has to be made to the scale in the tank. That is., a '-' sign should be placed in front of all the units below zero. This is shown in the fig.4.2 below.
 |
| Fig.4.2 |
If the level is 5 units below zero, he can say: “Level is -5”. The '-' sign instantly gives a clear picture of the seriousness of the situation.
Numbers with '-' sign in front are called negative numbers. All the readings below zero are negative readings.
We must note one peculiarity about these negative readings: As the level decreases, the negative value increases. For example, if the level falls even below -5 and reach -7, it means that we have still lesser water to use. But the value after the '-' sign has increased from 5 to a larger value of 7.
There are many situations where negative numbers are used in day to day life. In the next section we will see some more examples.
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