If x/8 = 5, what is the value of 8/x?
Understand the Problem
The question asks us to find the value of 8 raised to the power of the reciprocal of x, given that x divided by 8 equals 5. We will first find the value of x and then calculate the expression.
Answer
The value of \( \frac{8}{x} \) is \( \frac{1}{5} \).
Answer for screen readers
The value of ( \frac{8}{x} ) is ( \frac{1}{5} ).
Steps to Solve
- Finding the value of ( x )
From the equation ( \frac{x}{8} = 5 ), we can solve for ( x ) by multiplying both sides by 8:
$$ x = 5 \times 8 $$ $$ x = 40 $$
- Finding the value of ( \frac{8}{x} )
Now that we know ( x = 40 ), we can find ( \frac{8}{x} ):
$$ \frac{8}{x} = \frac{8}{40} $$
- Simplifying ( \frac{8}{40} )
We simplify ( \frac{8}{40} ) by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 8:
$$ \frac{8}{40} = \frac{1}{5} $$
The value of ( \frac{8}{x} ) is ( \frac{1}{5} ).
More Information
This problem involves solving a simple linear equation and simplifying a fraction. The final result ( \frac{1}{5} ) indicates that for every 8 units given, they are distributed over 40 units total.
Tips
- Incorrectly calculating the multiplication of ( 5 \times 8 ). Ensure multiplicative operations are performed accurately.
- Forgetting to simplify ( \frac{8}{40} ) to its lowest terms. Always simplify fractions when possible.
