Solve: 1/2 - 2/8 + 1/4 | Fraction Operation Challenge

To solve the expression $\frac{1}{2} - \frac{2}{8} + \frac{1}{4}$, we must first find a common denominator for the fractions involved.

Step 1: Identify a common denominator. The denominators are 2, 8, and 4. The smallest common multiple of these numbers is 8.

Step 2: Convert each fraction to have the common denominator of 8.

• The fraction $\frac{1}{2}$ can be written as $\frac{4}{8}$ because $1 \times 4 = 4$ and $2 \times 4 = 8$.
• The fraction $\frac{2}{8}$ is already expressed with 8 as the denominator.
• The fraction $\frac{1}{4}$ can be written as $\frac{2}{8}$ because $1 \times 2 = 2$ and $4 \times 2 = 8$.

Step 3: Substitute these equivalent fractions back into the original expression:

$\frac{4}{8} - \frac{2}{8} + \frac{2}{8}$

Step 4: Perform the subtraction and addition following the order of operations:

• Subtract: $\frac{4}{8} - \frac{2}{8} = \frac{2}{8}$
• Add: $\frac{2}{8} + \frac{2}{8} = \frac{4}{8}$

Step 5: Simplify the result:

$\frac{4}{8}$ simplifies to $\frac{1}{2}$ by dividing the numerator and denominator by 4.

Therefore, the value of the expression is $\frac{1}{2}$.