Solve: 1/4 - 3/4 + 1/2 - 5/10 Fraction Operations

To solve this problem, we need to first find a common denominator for all the fractions involved: $\frac{1}{4} - \frac{3}{4} + \frac{1}{2} - \frac{5}{10}$.

• Step 1: Identify the least common denominator (LCD). Here, the denominators are $4$, $4$, $2$, and $10$. The smallest number all these can divide into is $20$.
• Step 2: Convert each fraction to have this common denominator.
• $\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}$
• $\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}$
• $\frac{1}{2} = \frac{1 \times 10}{2 \times 10} = \frac{10}{20}$
• $\frac{5}{10} = \frac{5 \times 2}{10 \times 2} = \frac{10}{20}$
• Step 3: Substitute these equivalent fractions back into the expression and simplify:
  $\frac{5}{20} - \frac{15}{20} + \frac{10}{20} - \frac{10}{20}.$
• Step 4: Perform the arithmetic operations:
• $\left(\frac{5}{20} - \frac{15}{20}\right) = -\frac{10}{20}.$
• $\left(-\frac{10}{20} + \frac{10}{20}\right) = 0.$
• $0 - \frac{10}{20} = -\frac{10}{20} = -\frac{1}{2}.$

Therefore, the solution to the problem is $-\frac{1}{2}$.