Solve: 3/5 + 1/5 - 3/15 Fraction Operation Challenge

To solve this problem, we'll perform the following steps:

• Step 1: Determine a common denominator for the fractions.
• Step 2: Convert each fraction to have this common denominator.
• Step 3: Perform the addition and subtraction operations on these fractions.
• Step 4: Simplify the resulting fraction, if possible.

Now, let's work through each step:

Step 1: To combine $\frac{3}{5}$, $\frac{1}{5}$, and $\frac{3}{15}$, identify the least common denominator (LCD). The denominators here are 5, 5, and 15. The least common multiple of 5 and 15 is 15. Therefore, our common denominator is 15.

Step 2: Convert each fraction to an equivalent fraction with a denominator of 15:
$\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}$,
$\frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}$,
$\frac{3}{15}$ is already with the common denominator.

Step 3: Add and subtract the fractions:
$\frac{9}{15} + \frac{3}{15} = \frac{12}{15}$
$\frac{12}{15} - \frac{3}{15} = \frac{9}{15}$.

Step 4: Simplify the resulting fraction:
$\frac{9}{15} = \frac{3}{5}$ (dividing the numerator and denominator by their greatest common divisor, which is 3).

Therefore, the solution to the problem is $\frac{3}{5}$.