To determine the correct algebraic expression that corresponds to the given word description, "The quotient of four and the sum of a number and three," let's break down the phrase step-by-step.
1. The word "quotient" indicates division.
2. "Four" represents the number 4.
3. "The sum of a number and three" refers to adding an unknown number, usually denoted as [tex]\( x \)[/tex], to 3. Thus, we can write this sum as [tex]\( x + 3 \)[/tex].
Putting this all together, the phrase "The quotient of four and the sum of a number and three" means we are dividing 4 by the expression [tex]\( x + 3 \)[/tex].
Now, let's evaluate the given options:
- A. [tex]\(\frac{4}{x} + 3\)[/tex]
- This expression represents 4 divided by [tex]\( x \)[/tex] and then 3 is added to the result. This does not match our description.
- B. [tex]\(\frac{x}{4} + 3\)[/tex]
- This expression represents [tex]\( x \)[/tex] divided by 4, and then 3 is added to the result. This does not match our description.
- C. [tex]\(\frac{4}{x+3}\)[/tex]
- This expression represents 4 divided by the sum of [tex]\( x \)[/tex] and 3, which matches our description precisely.
- D. [tex]\(\frac{x+3}{4}\)[/tex]
- This expression represents the sum of [tex]\( x \)[/tex] and 3 divided by 4. This does not match our description.
Thus, the correct algebraic expression that matches the description "The quotient of four and the sum of a number and three" is:
C. [tex]\(\frac{4}{x+3}\)[/tex]
