Problem 37 - Introductory Algebra for College Students

Question

Perform the indicated subtraction. $$\frac{1}{2}-\frac{1}{4}$$

Step-by-Step Solution

Answer

The result of \(\frac{1}{2}-\frac{1}{4}\) is \(\frac{1}{4}\).

Step 1: Find a common denominator

The denominators of the two fractions are 2 and 4. The least common denominator (LCD) of these numbers is the smallest number that both denominators can divide into. In this case, the LCD is 4.

Step 2: Rewrite the fractions

Now, rewrite the fractions with the common denominator. The first fraction becomes \(\frac{2}{4}\) because \(1 \times 2 = 2\) (numerator) and \(2 \times 2 = 4\) (denominator). The second fraction remains the same, \(\frac{1}{4}\), because it already has the denominator 4.

Step 3: Subtract the fractions

Now that the fractions have the same denominators, subtract the numerators: \(\frac{2}{4} - \frac{1}{4} = \frac{1}{4}\).