Solve the Fraction Equation: 1/2 - 1/8 - 1/4 Step-by-Step

Solve the following exercise:

$\frac{1}{2}-\frac{1}{8}-\frac{1}{4}=\text{?}$

To solve this problem, we will follow these steps:

• Step 1: Find the least common denominator of the fractions involved.
• Step 2: Rewrite each fraction using this common denominator.
• Step 3: Subtract the fractions sequentially.

Now, let's work through each step:

First, we determine the least common denominator (LCD) of the fractions $\frac{1}{2}$, $\frac{1}{8}$, and $\frac{1}{4}$. The denominators are 2, 8, and 4. The least common multiple of these numbers is 8. Thus, the LCD is 8.

Next, we rewrite each fraction with the common denominator of 8:

• $\frac{1}{2} = \frac{4}{8}$
• $\frac{1}{8} = \frac{1}{8}$
• $\frac{1}{4} = \frac{2}{8}$

Now, we perform the subtraction:

$\frac{1}{2} - \frac{1}{8} - \frac{1}{4} = \frac{4}{8} - \frac{1}{8} - \frac{2}{8}$

First, subtract $\frac{1}{8}$ from $\frac{4}{8}$:

$\frac{4}{8} - \frac{1}{8} = \frac{3}{8}$

Then, subtract $\frac{2}{8}$ from $\frac{3}{8}$:

$\frac{3}{8} - \frac{2}{8} = \frac{1}{8}$

Therefore, the solution to the problem is $\frac{1}{8}$.