Solve the Fraction Subtraction: 2/5 - 2/6 Step-by-Step

To solve this problem, we'll walk through these steps:

• Step 1: Determine the least common denominator (LCD) for the denominators 5 and 6.
• Step 2: Convert each fraction to an equivalent fraction with the LCD.
• Step 3: Subtract the numerators of the equivalent fractions.
• Step 4: Simplify the resulting fraction if possible.

Now, let's work through each step:

Step 1: Determine the least common denominator (LCD).
The denominators are 5 and 6. Since there is no common factor, the LCD is $5 \times 6 = 30$.

Step 2: Convert each fraction to an equivalent fraction with the LCD.
For $\frac{2}{5}$, multiply numerator and denominator by 6 to get $\frac{2 \times 6}{5 \times 6} = \frac{12}{30}$.
For $\frac{2}{6}$, multiply numerator and denominator by 5 to get $\frac{2 \times 5}{6 \times 5} = \frac{10}{30}$.

Step 3: Subtract the fractions with the same denominator.
$\frac{12}{30} - \frac{10}{30} = \frac{12 - 10}{30} = \frac{2}{30}$.

Step 4: Simplify the resulting fraction.
$\frac{2}{30}$ can be simplified by dividing numerator and denominator by their greatest common divisor, which is 2.
Thus, $\frac{2}{30} = \frac{1}{15}$.

Therefore, the solution to the problem is $\frac{1}{15}$.