Solve the Fraction Problem: 5/6 - 1/4 - 3/12 Step by Step

To solve this problem, we'll follow these steps:

• Step 1: Identify the least common denominator (LCD).
• Step 2: Convert each fraction to have the common denominator.
• Step 3: Subtract the numerators and simplify the final result.

Now, let's work through each step:
Step 1: The denominators are $6$, $4$, and $12$. The smallest number that is a multiple of all these denominators is $12$, so our LCD is $12$.
Step 2: Convert each fraction to have a denominator of $12$:

• $\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}$
• $\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$
• $\frac{3}{12}$ already has the denominator $12$.

Step 3: Subtract the fractions, now rewritten as having the same denominator:

$\frac{10}{12} - \frac{3}{12} - \frac{3}{12}$.

Subtract the numerators:

$10 - 3 - 3 = 4.$

The resulting fraction is $\frac{4}{12}$.

We simplify $\frac{4}{12}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $4$:

$\frac{4 \div 4}{12 \div 4} = \frac{1}{3}$.

Therefore, the simplified result of the operation is $\frac{1}{3}$.