Problem 105 - Introductory Algebra for College Students

Question

Translate from English to an algebraic expression or equation, whichever is appropriate. Let the variable \(x\) represent the number. A number decreased by \(\frac{1}{4}\) of itself

Step-by-Step Solution

Answer

The algebraic expression for the given statement is 'x - \(\frac{1}{4}x'.

Step 1: Understand the Statement

Read the statement carefully. 'A number decreased by \(\frac{1}{4}\) of itself' can be interpreted as 'taking a number and subtracting \(\frac{1}{4}\) of that number.' 'Decreased by' implies subtraction.

Step 2: Identify the Variables

In this case, it is mentioned that 'x' is the variable representing the number. So 'a number' can be represented by 'x'.

Step 3: Formulate the Expression

The entire phrase can be translated into an algebraic expression as follows: 'A number' is 'x'. 'Decreased by' translates to subtraction '-'. And '\(\frac{1}{4}\) of itself' translates to '\(\frac{1}{4}\) of x' or '\(\frac{1}{4}x'. Therefore, combining all the parts, the algebraic expression is 'x - \(\frac{1}{4}x'.