Which algebraic expression represents the phrase "the quotient of negative eight and the sum of a number and three"?
$\frac{-8}{g+3}$
$\frac{8}{g+3}$
$\frac{-8+9}{3}$
$\frac{-8}{g}+3$
Answer (2)
The phrase "the quotient of negative eight and the sum of a number and three" translates to a division.
Negative eight is represented as -8.
The sum of a number and three is represented as g + 3.
Combining these, the algebraic expression is g + 3 − 8 .
Explanation
Understanding the Phrase We need to translate the given phrase "the quotient of negative eight and the sum of a number and three" into an algebraic expression. Let's break down the phrase:
"the quotient of" indicates a division.
"negative eight" means -8.
"the sum of a number and three" means we add 3 to a number. Let's represent the number with the variable 'g', so this part becomes g + 3.
Therefore, the expression will be a fraction where the numerator is -8 and the denominator is g + 3.
Forming the Expression Combining the parts, we get the algebraic expression: g + 3 − 8
This expression represents the quotient of -8 and the sum of a number (g) and 3.
Matching the Expression Comparing our expression with the given options:
g + 3 − 8 - This matches our derived expression.
g + 3 8 - This has 8 in the numerator instead of -8.
3 − 8 + 9 - This is a numerical expression and doesn't involve the variable 'g'.
g − 8 + 3 - This represents -8 divided by 'g', plus 3, which is different from the original phrase.
Final Answer Therefore, the correct algebraic expression is g + 3 − 8 .
Examples
Algebraic expressions are used in many real-world scenarios. For example, if you want to calculate the average test score of a class, you might use an expression like N S , where S is the sum of all scores and N is the number of students. Similarly, if you're calculating the total cost of items with a discount, you might use an expression like P − ( D × P ) , where P is the original price and D is the discount rate. Understanding how to translate phrases into algebraic expressions is a fundamental skill for solving these types of problems.
The expression representing "the quotient of negative eight and the sum of a number and three" is g + 3 − 8 . This is derived from identifying the components of the phrase and forming the appropriate mathematical expression. Therefore, the correct option from the choices provided is g + 3 − 8 .
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