Question

translate a verbal expression into an algebraic expression.
which of the following expressions represents: the quotient of five times a number and eight squared?

\\(\frac{5x}{16}\\)
\\(\frac{5x}{8^2}\\)
\\(5x - 8^2\\)
\\(\frac{5x}{\sqrt{8}}\\)
\\(\frac{8^2}{5x}\\)
\\(5x + 8^2\\)

Explanation:

Define the variable and terms

Let the unknown number be represented by the variable \(x\).
The phrase "five times a number" translates to the algebraic term \(5x\).
The phrase "eight squared" translates to the exponential term \(8^2\).

Translate the operation

The word "quotient" indicates division between two quantities.
The quotient of \(A\) and \(B\) is written as the fraction \(\frac{A}{B}\).
Using Algebraic Properties, we set \(A = 5x\) and \(B = 8^2\).

Form the final expression

Combining the terms, the quotient is written as:

$$\frac{5x}{8^2}$$

This matches the second option.

Answer:

• (A) \(\frac{5x}{16}\)
• (B) \(\frac{5x}{8^2}\) (Correct answer)
• (C) \(5x - 8^2\)
• (D) \(\frac{5x}{\sqrt{8}}\)
• (E) \(\frac{8^2}{5x}\)
• (F) \(5x + 8^2\)