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Chapter 1: Problem 105

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

Short Answer

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

Step by step solution

01

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.
02

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'.
03

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'.

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