The absolute value of a number is its distance from 0 on a number line. For example, the number "9" is 9 units away from zero. So its absolute value is 9.
Negative numbers are more interesting compared to positive numbers, because the number -4 is still 4 units away from 0. The absolute value of the number -4 is therefore positive 4.
The sign | | represents absolute value.
Now let us see some examples to know how to compare absolute values with integers.
Example 1 :
Evaluate the following :
|56 - 15| ⋅ 8 + |14|/2
Solution :
= |56 - 15| ⋅ 8 + |14|/2
= |41| ⋅ 8 + 14/2
= 41 ⋅ 8 + 7
= 328 + 7
= 335
Example 2 :
Evaluate the following :
Solution :
= |-7 ⋅ 4|/2 ⋅ |10|/|-5|
= |-28|/2 ⋅ 10/5
= 28/2 ⋅ 2
= 14 ⋅ 2
= 28
Example 3 :
Compare the following :
Solution :
To compare the above numerical expressions, first we have to simplify both L.H.S and R.H.S separately.
L.H.S :
= |30|/|10| + |-2 + 7|/5 ⋅ 8
= 30/10 + 5/5 ⋅ 8
= 3 + 1 ⋅ 8
= 3 + 8
= 11
R.H.S :
= |-32|/8 - |9 ⋅ 2| + |4|
= -32/8 - |18| + |4|
= -4 - 18 + 4
= -18
By comparing answers on both sides L.H.S is greater than right hand side.
Hence,
|30|/|10| + |-2 + 7|/5 x 8 > |-32|/8 - |9 x 2| + |4|
Example 4 :
Compare the following :
Solution :
To compare the above numerical expressions, first we have to simplify both L.H.S and R.H.S separately.
L.H.S :
= |9 + 2| - |45|/|3|
= |11| - 45/3
= 11 - 15
= -4
R.H.S :
= |22 + 1| + |1|/|3| ⋅ 6
= |23| + (1/3) ⋅ 6
= 23 + (1 ⋅ 2)
= 23 + 2
= 25
By comparing answers on both sides R.H.S is greater than L.H.S.
Hence,
|9 + 2| - |45|/|3| < |22 + 1| + |1|/|3| x 6
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