COMPARING ABSOLUTE VALUES

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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