Solve the Fraction Subtraction: 2/4 - 2/6 Step-by-Step

Solve the following exercise:

$\frac{2}{4}-\frac{2}{6}=\text{?}$

To solve this subtraction problem, let's follow these steps:

• Step 1: Identify and find the least common denominator (LCD) of the denominators 4 and 6.
• Step 2: Convert each fraction to have the common denominator.
• Step 3: Subtract the numerators of the converted fractions.
• Step 4: Simplify the result, if possible.

Now, let's work through each step:

Step 1: The denominators are 4 and 6. The LCD of 4 and 6 is 12, since 12 is the smallest number divisible by both 4 and 6.

Step 2: Convert each fraction to this common denominator.
- Convert $\frac{2}{4}$ to have a denominator of 12. We multiply both the numerator and denominator by 3:
$\frac{2}{4} = \frac{2 \times 3}{4 \times 3} = \frac{6}{12}$.
- Convert $\frac{2}{6}$ to have a denominator of 12. We multiply both the numerator and denominator by 2:
$\frac{2}{6} = \frac{2 \times 2}{6 \times 2} = \frac{4}{12}$.

Step 3: Subtract the fractions:
$\frac{6}{12} - \frac{4}{12} = \frac{6 - 4}{12} = \frac{2}{12}$.

Step 4: Simplify the result:
The fraction $\frac{2}{12}$ simplifies to $\frac{1}{6}$ by dividing both numerator and denominator by their greatest common divisor, which is 2.

Therefore, the solution to the problem is $\frac{1}{6}$.