Verified Answer :

  • The phrase "quotient" signifies division.
  • Assign the variable \(w\) to represent "a number".
  • Divide the number \(w\) by 6, resulting in \(\frac{w}{6}\).
  • The correct algebraic expression is \(\boxed{\frac{w}{6}}\).

Explanation

  1. Analyzing the Verbal Phrase

The objective is to translate the verbal phrase "the quotient of a number and six" into an algebraic expression. In mathematics, a "quotient" refers to the result of a division operation. When we speak of the "quotient of a and b", it means that we are dividing a by b. In this problem, "a number" is represented by the variable \(w\), and "six" is the divisor.

  1. Formulating the Expression

To translate the phrase "the quotient of a number and six" into an algebraic expression, we identify the key components:

  • "A number" is represented by the variable \(w\).
  • "Quotient" indicates the operation of division.
  • "And six" indicates that \(w\) is being divided by 6.

Combining these, we write the division of \(w\) by 6 as \(\frac{w}{6}\).

  1. Selecting the Correct Option

Comparing our derived expression \(\frac{w}{6}\) with the given options:

  • \(6 + w\) (represents "six plus a number")
  • \(6w\) (represents "six times a number")
  • \(6 - w\) (represents "six minus a number")
  • \(\frac{w}{6}\) (represents "the quotient of a number and six")

The correct expression is \(\frac{w}{6}\).

Examples

Algebraic expressions are used in everyday life to model relationships between quantities. For instance, if you are planning to share a bag of \(w\) cookies equally among 6 friends, the number of cookies each friend receives is represented by the expression \(\frac{w}{6}\). By using algebra, we can easily calculate how many cookies each person gets regardless of the initial total in the bag!

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