Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Jan 24, 2024

Find the algebraic expression for "Eight divided by the difference of $x$ and $m$ ". Options: A) $\frac{8}{m}-x$ , B) $8-\frac{x}{m}$ , C) $\frac{x-m}{8}$ , D) $\frac{8}{x-m}$

STEP 1

Assumptions
1. We are looking for an algebraic expression.
2. The verbal expression is "eight divided by the difference of $x$ and $m$ ".
3. We need to translate the verbal expression into a mathematical one.

STEP 2

Identify the mathematical operation that corresponds to the word "divided by" in the verbal expression.
"Divided by" corresponds to the division operation, which is represented by the symbol $/$ .

STEP 3

Identify the mathematical representation of the phrase "the difference of $x$ and $m$ ".
The word "difference" indicates a subtraction operation, so the difference of $x$ and $m$ is represented by $x - m$ .

STEP 4

Combine the operations identified in steps 2 and 3 to form the algebraic expression.
The expression "eight divided by the difference of $x$ and $m$ " is represented as $\frac{8}{x - m}$ .

STEP 5

Match the resulting algebraic expression with the given options.
The correct algebraic expression is $\frac{8}{x - m}$ , which corresponds to option (D).
The algebraic expression for the given verbal expression is $\frac{8}{x - m}$ .

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