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Chapter 1: Problem 107

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.

Short Answer

Expert verified
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 by step solution

01

Identify the Unknown

In this problem, the unknown is the number, which we will represent as the variable \(x\).
02

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 '\(\frac{x}{2}\).'
03

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.

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Most popular questions from this chapter

Perform the indicated subtraction. $$1.3-(-1.3)$$

Simplify each series of additions and subtractions. $$-1.9-3-(-0.26)$$

Perform the indicated subtraction. $$-\frac{4}{5}-\frac{1}{5}$$

Perform the indicated subtraction. $$23-23$$

Write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. The quotient of \(-2\) and a number, subtracted from the quotient of \(-5\) and the number.
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