Which expression correctly represents "six more than the quotient of three and a number, decreased by eight"?
[tex]6+\frac{3}{n}-8[/tex]
[tex]6+\frac{\pi}{3}-8[/tex]
[tex]6+\frac{3}{n}+8[/tex]
[tex]6+\frac{\pi}{3}+8[/tex]
Answer (1)
Translate 'the quotient of three and a number' to n 3 .
Translate 'six more than the quotient of three and a number' to 6 + n 3 .
Translate 'decreased by eight' to subtracting 8: 6 + n 3 − 8 .
The correct expression is 6 + n 3 − 8 .
Explanation
Understanding the Expression Let's break down the verbal expression step by step to translate it into an algebraic expression.
Translating the Quotient
The quotient of three and a number: This means we divide 3 by a number, which we can represent as n 3 , where 'n' is the number.
Adding Six
Six more than the quotient of three and a number: This means we add 6 to the quotient we found in the previous step. So, we have 6 + n 3 .
Subtracting Eight
Decreased by eight: This means we subtract 8 from the expression we have so far. So, we get 6 + n 3 − 8 .
Matching the Expression Now, let's compare our expression 6 + n 3 − 8 with the given options. The first option, 6 + n 3 − 8 , matches our expression.
Examples
Understanding how to translate verbal expressions into algebraic expressions is a fundamental skill in algebra. For example, if you are trying to calculate the total cost of buying 'n' items that cost $3 each, plus a fixed shipping fee of $6, and then you get an $8 discount, the expression 6 + n 3 − 8 could represent a simplified version of that calculation. This skill is essential for solving real-world problems involving quantities and relationships.
