Solve: 1/2 - 1/6 - 3/12 Fraction Subtraction Problem

Solve the following exercise:

$\frac{1}{2}-\frac{1}{6}-\frac{3}{12}=\text{?}$

To solve this problem, we need to subtract three fractions: $\frac{1}{2} - \frac{1}{6} - \frac{3}{12}$.

First, let's find the least common denominator (LCD) for the fractions. The denominators are 2, 6, and 12. The smallest number that all these denominators divide evenly into is 12, so the LCD is 12.

Next, convert each fraction to have 12 as the denominator:

• $\frac{1}{2} = \frac{1 \times 6}{2 \times 6} = \frac{6}{12}$
• $\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}$
• $\frac{3}{12}$ is already with denominator 12

Now, perform the subtraction using these equivalent fractions:

$\frac{6}{12} - \frac{2}{12} - \frac{3}{12}$

Subtract the fractions in sequence while keeping the common denominator:

$\frac{6}{12} - \frac{2}{12} = \frac{4}{12}$

Then, $\frac{4}{12} - \frac{3}{12} = \frac{1}{12}$

The fraction $\frac{1}{12}$ is already in its simplest form.

Therefore, the solution to the problem is $\frac{1}{12}$.