When doing a calculation involving zoning laws, Tim comes across the following expression:
fraction a- open vertical bar a close vertical bar over denominator a end fraction,
where a is either a positive or a negative number.
(A) What is the value of the expression when a equals 5?
(B) What is the value of the expression when a equals negative 5?
Plug in the numerical value for a into the expression. Remember that the absolute value of a number is always non-negative. Follow the order of operations to find the value of the expression.
If the fraction is
(a-|a|)/a
then its value is
0 if a is positive
2 if a is negative
since
|a| = a if a is positive
|a| = -a if a is negative
To find the value of the expression, let's plug in the numerical values for both parts of the expression and apply the order of operations.
(A) When a equals 5:
The expression becomes:
|5| / 5
The absolute value of 5 is 5, so the expression simplifies to:
5 / 5 = 1
Therefore, when a equals 5, the value of the expression is 1.
(B) When a equals -5:
The expression becomes:
|-5| / -5
The absolute value of -5 is 5, so the expression simplifies to:
5 / -5 = -1
Therefore, when a equals -5, the value of the expression is -1.
Remember that to find the value of the expression, you need to substitute the value of "a" into the expression, find the absolute value (or modulus) of the resulting number, and then divide it by the value of "a". Following the order of operations, simplify the expression step by step to find the final value.