Problem 106 - 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 \(\frac{1}{3}\) of itself

Step-by-Step Solution

Answer

The algebraic expression for 'A number decreased by \(\frac{1}{3}\) of itself' is given by \(x - \frac{1}{3}x\).

Step 1: Identify the variable

The problem states that \(x\) represents the number. So, first start with the variable \(x\).

Step 2: Translate the operation

A number 'decreased by' suggests a subtraction operation. The phrase '\(\frac{1}{3}\) of itself' can be translated into an operation of multiplication with the fraction \(\frac{1}{3}\). So, '\(\frac{1}{3}\) of itself' would translate to \(\frac{1}{3}x\).

Step 3: Construct the algebraic expression

Putting both components together, the complete expression will be 'the number \(x\) minus \(\frac{1}{3}\) times the number \(x\)'. In algebraic terms, this can be written as \(x - \frac{1}{3}x\).