# COMPARING ABSOLUTE VALUES

Comparing absolute values :

Comparison of absolute values is a difficult task for some students.

Actually it is not. Once we understand the stuff, we can easily compare them.

For example, 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.

## Comparing absolute values - Examples

Question 1 :

Compare |-7| and |-9|

Solution :

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.

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 |-7|  =  7 ------> (1)

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 |-9|  =  9 ------> (2)

From (1) and (2),

it is clear that 9 is greater than 7.

Hence, |-9| is greater than |-7|.

Question 2 :

Compare |-4| and |-4|

Solution :

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.

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 |-4|  =  4 ------> (1)

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)

From (1) and (2),

it is clear that 4 is equal to 4.

Hence, |-4| is equal to |4|.

After having gone through the stuff given above, we hope that the students would have understood "Comparison of absolute values".

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