Translate the algebraic expression 9x into an equivalent English phrase. Which of the following options correctly represents the meaning of 9x? The difference of nine and a number, The product of nine and a number, The sum of nine and a number, The quotient.
The Correct Answer and Explanation is :
The algebraic expression ( 9x ) translates into English as “the product of nine and a number.”
Explanation:
To break this down, let’s analyze the components of the expression:
- Understanding Variables: In the expression ( 9x ), the variable ( x ) represents an unknown number. Variables are commonly used in algebra to denote numbers that can vary or change.
- Coefficient: The number ( 9 ) is known as the coefficient. It indicates how many times the variable ( x ) is being multiplied. In this case, it shows that ( x ) is being multiplied by nine.
- Terminology:
- Product: In mathematics, the term “product” specifically refers to the result of multiplying two or more numbers together. Therefore, when we say “the product of nine and a number,” we are precisely describing the operation being performed in the expression ( 9x ).
- Difference, Sum, Quotient: The other options provided in the question refer to different mathematical operations:
- Difference: This term is used in subtraction, indicating the result when one number is subtracted from another. For example, “the difference of nine and a number” would be written as ( 9 – x ).
- Sum: This term is used in addition. “The sum of nine and a number” translates to ( 9 + x ).
- Quotient: This term refers to division. The phrase “the quotient” indicates that one number is being divided by another, which is not represented in the expression ( 9x ).
Thus, since ( 9x ) clearly describes a multiplication operation involving nine and a variable, the correct English phrase that represents the meaning of ( 9x ) is “the product of nine and a number.”