Twice the number divided by the sum of a number and 5.
The Correct Answer and Explanation is:
Let’s break down the expression “twice the number divided by the sum of a number and 5” step by step.
- Define the number: Let the number be represented as xxx.
- Twice the number: This means multiplying the number by 2. So, twice the number is 2x2x2x.
- The sum of the number and 5: This part is the sum of xxx and 5, which can be written as x+5x + 5x+5.
- The division: The phrase “divided by” indicates that we need to divide twice the number by the sum of the number and 5. So, the expression becomes: 2xx+5\frac{2x}{x + 5}x+52x
Thus, the expression for “twice the number divided by the sum of a number and 5” is 2xx+5\frac{2x}{x + 5}x+52x.
Explanation:
This expression involves two main operations: multiplication and division. We start by recognizing that “twice the number” simply means multiplying the number by 2. Next, we have “the sum of the number and 5,” which translates to adding 5 to the number. Finally, the division part tells us that we need to take the result of twice the number and divide it by the sum of the number and 5.
The result is a rational expression where the numerator is 2x2x2x (twice the number) and the denominator is x+5x + 5x+5 (the sum of the number and 5). This expression could be used in algebraic problems or equations where xxx is a variable representing an unknown number.
To summarize, the algebraic representation of the given statement is:2xx+5\frac{2x}{x + 5}x+52x
