Chapter 1.4, Problem 62CCR

To determine

To translate the given phrase into an algebraic expression.

Answer to Problem 62CCR

  $\frac{x}{4}-8$

Explanation of Solution

Given information:

Eight less than the quotient of the number of quarters and four.

Concept Used:

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to translate the given phrase into an algebraic expression, observe that the number is 8 less than the quotient of the number of quarters and 4.

Let the number of quarters bex. So, the given phrase can be converted into an algebraic expression as

  $\begin{array}{c}\left(\text{Quotient of the number of quarters and 4}\right)-\text{ 8}\\ =\left(\frac{\text{Number of quarters}}{4}\right)-8\\ =\left(\frac{x}{4}\right)-8\\ =\frac{x}{4}-8\end{array}$

Thus, the algebraic expression for the given phrase is $\frac{x}{4}-8$ .