Solve the Fraction Expression: 3/5 - 1/5 + 3/15 Step by Step

To solve this problem, we will follow these steps:

• Step 1: Find the least common denominator (LCD) for the fractions.
• Step 2: Convert each fraction to an equivalent fraction with the common denominator.
• Step 3: Perform the operations in the given order, subtraction first, then addition.

Now, let's work through each step:

Step 1: The denominators of the given fractions are 5 and 15. The least common multiple (LCM) of these numbers is 15, so 15 will be our common denominator.

Step 2: Convert each fraction to have the denominator of 15:
- $\frac{3}{5}$ is converted by multiplying both the numerator and denominator by 3, resulting in $\frac{9}{15}$.
- $\frac{1}{5}$ is converted by multiplying both the numerator and denominator by 3, yielding $\frac{3}{15}$.
- $\frac{3}{15}$ is already in terms of the common denominator.

Step 3: Perform the subtraction and addition:
- Start by subtracting $\frac{3}{15}$ from $\frac{9}{15}$:

$\frac{9}{15} - \frac{3}{15} = \frac{6}{15}$

Now, add $\frac{6}{15}$ and $\frac{3}{15}$:

$\frac{6}{15} + \frac{3}{15} = \frac{9}{15}$

Finally, simplify $\frac{9}{15}$ by dividing the numerator and denominator by their greatest common divisor, which is 3:

$\frac{9}{15} = \frac{3}{5}$

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