INTEGERS

Ordering of Integers :

Let us once again observe the integers which are represented on the number line.

• We know that 7 > 4 and from the number line shown above, we observe that 7 is to the right of 4 
• Similarly, 4 > 0 and 4 is to the right of 0. Now, since 0 is to the right of –3 so, 0 > – 3.
• Again, – 3 is to the right of – 8 so, – 3 > – 8.

Thus, we see that on a number line the number increases as we move to the right and decreases as we move to the left.

Therefore, – 3 < – 2, – 2 < – 1, – 1 < 0, 0 < 1, 1 < 2, 2 < 3 so on.

Where we should use positive sign and where we should use negative sign ?

Represent the following numbers as integers with appropriate signs.

Example 1 :

An aeroplane is flying at a height two thousand meter above the ground.

Solution :

If we consider 0 is ground level,

2000 meter above the ground level  =  +2000

Example 2 :

A submarine is moving at a depth, eight hundred meter below the sea level.

Solution :

We consider the sea level as 0.

Eight hundred meter below the sea level  =  -800

Example 3 :

A deposit of two hundred dollars.

Solution :

Deposit of two hundred dollars  =  +200

Example 4 :

Withdrawal of seven hundred dollars.

Solution :

Withdrawal of seven hundred dollars  =  -700

Example 5 :

Following is the list of temperatures of five places in India on a particular day of the year.

Place Temperature

(i)  Siachin 10°C below 0°C .................

(ii)  Shimla 2°C below 0°C .................

(iii)  Ahmedabad 30°C above 0°C .................

(iv)  Delhi 20°C above 0°C .................

(v)  Srinagar 5°C below 0°C .................

Solution :

(i)  Temperature in Siachin is -10°C.

(ii)  Temperature in Shimla -2°C.

(iii)  Temperature in Ahmedabad +30°C.

(iv)  Temperature in Delhi is +20°C.

(v)  Temperature in Srinagar is -5°C.

Example 6 :

In each of the following pairs, which number is to the right of the other on the number line?

(a) 2, 9 (b) – 3, – 8 

Solution :

(i)  9 is in right of 2.

(ii)  -2 is in right of -8.

Example 7 :

Write all the integers between the given pairs (write them in the increasing order.)

(a) 0 and – 7 (b) – 4 and 4

Solution :

(a)  Between 0 and -7 are,

 -6, -5, -4, -3, -2, -1

(b) Between –4 and 4 are,

-3, -2, -1, 0, 1, 2, 3

Example 8 :

Write four negative integers greater than – 20.

Solution :

In the number line, by keep on moving right side we will get greater values.

Greater than -20 are 

-19, -18, -17, -16, .............

Example 9 :

For the following statements, write True (T) or False (F). If the statement is false, correct the statement.

(a) – 8 is to the right of – 10 on a number line.

(b) – 100 is to the right of – 50 on a number line.

(c) Smallest negative integer is – 1.

Solution :

(a)  True

(b)  False

(c)  True

Example 10 :

Using the number line write the integer which is :

(a) 3 more than 5

(b) 5 more than -5.

Solution :

(a) To find more, we will move rightward. From 5, we should move 3 units to the right.

So we will be at 8.

(b)  From -5, we should move 5 units right.

So, we will be at 0.

Example 11 :

a)  The temperature was -7^oC and it has fallen a further 18^oC. What is the temperature now?

b) A submarine is 23 m below sea level and dives a further 36 m. How deep is it now?

c) A bird flying 9 m above a lake suddenly drops 10:5 m to catch a fish. How far under the surface was the fish?

Solution :

a) Now the temperature = -7^oC

Temperature fallen to = 18^oC

Now the temperature = -7 - 18

= -25^oC

b) The location of submarine below the sea level = -23 m

Dives a further of 36 m 

Now the location is = -23-36

= -59 m

So, the new location is 59 m below the sea level.

c) The height of a bird = 9 m (above the lake)

So, +9 m

It drops 10.5 m. So, -10.5

= 9 - 10.5

= - 1.5 m

So, the fish is 1.5 m under the surface.

Example 12 :

If we add or subtract two integers, is the answer always an integer

Solution :

By adding or subtracting two integers, the answer will always be an integer.

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