What is an absolute value? :
Absolute value is that value which does not depend on the " sign "( “plus “ or " minus ") of the number. The absolute value denoted by "| . |" symbol ( also called " modulus "). For example, the absolute value of 4 is 4 and -4. The figure below shows the absolute value is only the positive number
In general, we can write " | n | ", where n is a real number without regard of sign and read as " the absolute value of n ".Remember, Absolute value is always positive or else zero. The absolute value of "0 " is 0. Geometrically, Displacement represents the absolute value and therefore should always be positive.
In other words, the absolute value of a number is the number without sign ( plus or minus ) attached to it.
Defination of Absolute Value for Variables :
For variables we define the absolute value as,
Here for n > 0 the value is same as the number i.e. " n " and for n < 0 the value is " – n ". For example, when n = 4 the absolute value is |n| = 4 = n, and when n = -4 the values is | n | = -n = - ( - 4 ) = 4 . Since we got the positive number for the negative value of n. Hence absolute value does not depend on sign of the number. Here " minus " sign on the variable only indicates "the change in the sign of the value of variable ".
Note : The absolute value is denoted only by bars, and not by any other brackets or parentheses.
Some Examples on Absolute Value:
- Solve | -10 |.
Answer : | -10 | = 10.
2. Solve | 5 + 7 |.
Answer : | 5 + 7 | = | 12 |
= 12.
3. Solve | -4 × 4|.
Answer : | -4 × 4| = | -16 |
= 16.
4. Solve - | -8 |.
Answer : -| -8 | = -8.
5. Solve | 3x - 9 | = 0
Answer :We can write the above equation as,
3x - 9 = 0
3x = 9
x = 9/3.
x = 3.
6. |y|2 = y2 .
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What is Absolute Value , Explain Absolute Value , Problems on Absolute Value