Problem 107 - 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 \(\frac{1}{4}\) is half of that number.

Step-by-Step Solution

Answer

The algebraic equation representing 'A number decreased by \(\frac{1}{4}\) is half of that number' is \(x - \frac{1}{4} = \frac{x}{2}\).

Step 1: Identify the Unknown

In this problem, the unknown is the number, which we will represent as the variable \(x\).

Step 2: Decode the Sentence Into Mathematical Terms

The sentence states: 'A number decreased by \(\frac{1}{4}\)' which translates to '\(x - \frac{1}{4}\)'. The phrase 'is half of that number' translates to '\(\frac{x}{2}\).'

Step 3: Construct the Equation

Now we can combine Step 2 to create the equation: \(x - \frac{1}{4} = \frac{x}{2}\). This is the equation that represents the number decreased by \(\frac{1}{4}\), which equals half of the number itself.