Solve the Fraction Equation: 5/6 - 1/3 - 2/12 Step-by-Step

To solve the subtraction of three fractions, follow these steps:

• Step 1: Identify the denominators of the fractions: 6, 3, and 12.
• Step 2: Determine the least common denominator (LCD), which is the least common multiple of 6, 3, and 12. The LCD is 12.
• Step 3: Convert each fraction to an equivalent fraction with the LCD of 12.
• $\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}$
• $\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$
• $\frac{2}{12}$ remains $\frac{2}{12}$.
• Step 4: Perform the subtraction with these equivalent fractions:
  $\frac{10}{12} - \frac{4}{12} - \frac{2}{12}$.
• Step 5: Subtract the fractions:
  $\frac{10 - 4 - 2}{12} = \frac{4}{12}$.
• Step 6: Simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
  $\frac{4}{12} = \frac{4 \div 4}{12 \div 4} = \frac{1}{3}$.

Therefore, the solution to the problem is $\frac{1}{3}$.