COMPARING ABSOLUTE VALUES

Let us compare the two negative integers -9 and -7.

Clearly, -7 is greater than -9. 

Because, when a number becomes greater and greater with negative sign, the original value of the number becomes smaller and smaller. 

So, -7 > -9

If we take above value for both "-7" and "-9", the result will be different.

That is |-7| < |-9|. 

More clearly,  |-7| is smaller than |-9|. 

Because, |-7|  =  7  and |-9|  =  9.

Let us understand this with number line in the following examples.

Example 1 :

Compare |-7| and |-9|

Solution : 

Step 1 :

The absolute value of a number is the number’s distance from 0 on a number line.

To understand this, let us mark -7 and -9 on a number line. 

Step 2 :

On the above number line, -7 is 7 units from 0.

Since -7 is 7 units from 0, we say that the absolute value of -7 is 7.  

The absolute value of -7 is written |-7|.

And, we have

|-7|  =  7 ------> (1)

Step 3 :

On the above number line, - 9 is 9 units from 0.

Since -9 is 9 units from 0, we say that the absolute value of -9 is 9.  

The absolute value of -9 is written |-9|.

And we have

|-9|  =  9 ------> (2)

Step 4 : 

From (1) and (2), it is clear that 9 is greater than 7. 

So, |-9| is greater than |-7|. 

Example 2 :

Compare |-4| and |-4|

Solution : 

Step 1 :

The absolute value of a number is the number’s distance from 0 on a number line.

To understand this, let us mark -4 and 4 on a number line. 

Step 2 :

On the above number line, -4 is 4 units from 0 to the left.

Since -4 is 4 units from 0, we say that the absolute value of -4 is 7.  

The absolute value of -4 is written |-4|.

And we have

|-4|  =  4 ------> (1)

Step 3 :

On the above number line, 4 is 4 units from 0 to the right.

Since 4 is 4 units from 0, we say that the absolute value of 4 is 4.  

The absolute value of 4 is written |4|.

And |4|  =  4 ------> (2)

Step 4 : 

From (1) and (2), it is clear that 4 is equal to 4. 

So, |-4| is equal to |4|. 

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