Solve: (5/6 × 1/2) - (1/2 × 2/6) Mixed Fraction Operations

To solve the problem, we need to evaluate the expression

$\frac{5}{6} \cdot \frac{1}{2} - \frac{1}{2} \cdot \frac{2}{6}$.

Let's go through this step-by-step:

• Step 1:
  Calculate the first multiplication:
  $\frac{5}{6} \cdot \frac{1}{2} = \frac{5 \cdot 1}{6 \cdot 2} = \frac{5}{12}$
• Step 2:
  Calculate the second multiplication:
  $\frac{1}{2} \cdot \frac{2}{6} = \frac{1 \cdot 2}{2 \cdot 6} = \frac{2}{12}$ Simplify $\frac{2}{12}$ by dividing the numerator and the denominator by their greatest common divisor, 2:
  $\frac{2}{12} = \frac{1}{6}$
• Step 3:
  Subtract the second result from the first:
  Since we have $\frac{5}{12} - \frac{1}{6}$, find a common denominator for the fractions, which is 12. Convert $\frac{1}{6}$ to a denominator of 12:
  $\frac{1}{6} = \frac{2}{12}$ Now, perform the subtraction:
  $\frac{5}{12} - \frac{2}{12} = \frac{3}{12}$ Simplify $\frac{3}{12}$ by dividing the numerator and denominator by their greatest common divisor, 3:
  $\frac{3}{12} = \frac{1}{4}$

Therefore, the solution to the problem is $\frac{1}{4}$.