When doing a calculation involving zoning laws, Tim comes across the following expression:
fraction numerator a minus 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
To evaluate the given expression, "fraction numerator a minus open vertical bar a close vertical bar over denominator a end fraction," for a specific value of a, follow these steps:
1. Replace every instance of 'a' in the expression with the given value.
2. Find the absolute value of the resulting number.
3. Divide the obtained number by the original value of 'a'.
Now, let's evaluate the expression for the given values of 'a':
(A) When a equals 5:
Substitute 'a' with 5 in the expression:
"fraction numerator 5 minus open vertical bar 5 close vertical bar over denominator 5 end fraction"
Find the absolute value of 5, which is 5:
"fraction numerator 5 minus open vertical bar 5 close vertical bar over denominator 5 end fraction = fraction numerator 5 minus 5 over 5 end fraction"
Subtract 5 from 5, which gives 0:
"fraction numerator 5 minus 5 over 5 end fraction = fraction numerator 0 over 5 end fraction"
Divide 0 by 5, which results in 0:
"fraction numerator 0 over 5 end fraction = 0"
Therefore, when a equals 5, the value of the expression is 0.
(B) When a equals -3:
Substitute 'a' with -3 in the expression:
"fraction numerator -3 minus open vertical bar -3 close vertical bar over denominator -3 end fraction"
Find the absolute value of -3, which is 3:
"fraction numerator -3 minus open vertical bar -3 close vertical bar over denominator -3 end fraction = fraction numerator -3 minus 3 over -3 end fraction"
Subtract 3 from -3, which gives -6:
"fraction numerator -3 minus 3 over -3 end fraction = fraction numerator -6 over -3 end fraction"
Divide -6 by -3, which results in 2:
"fraction numerator -6 over -3 end fraction = 2"
Therefore, when a equals -3, the value of the expression is 2.