Which algebraic expression represents this word description?
The quotient of nine and the sum of a number and one
A. $\frac{9}{x}+1$
B. $\frac{x+1}{9}$
C. $\frac{x}{9}+1$
D. $\frac{9}{x+1}$
Answer (1)
Define the variable: Let "x" represent the number.
Express the sum: The sum of the number and one is x + 1 .
Express the quotient: The quotient of nine and the sum is x + 1 9 .
Identify the correct option: The algebraic expression is x + 1 9 .
Explanation
Understanding the Problem Let's break down the word description step by step to construct the correct algebraic expression.
Defining the Variable The word description is 'The quotient of nine and the sum of a number and one'. Let's use 'x' to represent the number.
Finding the Sum First, we need to find the sum of a number and one, which can be written as x + 1 .
Finding the Quotient Next, we need to find the quotient of nine and the sum we just found. This means we divide nine by ( x + 1 ) , which gives us x + 1 9 .
Matching the Expression Now, let's compare our expression x + 1 9 with the given options:
A. x 9 + 1 B. 9 x + 1 C. 9 x + 1 D. x + 1 9
Our expression matches option D.
Final Answer Therefore, the algebraic expression that represents the word description 'The quotient of nine and the sum of a number and one' is x + 1 9 .
Examples
Understanding how to translate word descriptions into algebraic expressions is a fundamental skill in algebra. For example, if you're trying to determine how many apples each person gets when dividing 9 apples among a group of people, where the size of the group is one more than the number of children in your family, you would use the expression x + 1 9 , where x represents the number of children. This skill is also useful in more complex scenarios, such as calculating rates, proportions, and percentages in everyday life.
