Solve: Adding (-1/5) and (+3⅓) with Mixed Numbers

$(-\frac{1}{5})+(+3\frac{1}{3})=$

To solve this problem, we'll follow these steps:

• Step 1: Convert $3\frac{1}{3}$ to an improper fraction.
• Step 2: Find a common denominator for $-\frac{1}{5}$ and the improper fraction.
• Step 3: Add the fractions.
• Step 4: Simplify the result, converting it back to a mixed number if necessary.

Now, let's work through each step:

Step 1: Convert $3\frac{1}{3}$ to an improper fraction.
$3\frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{10}{3}$

Step 2: Find a common denominator for $-\frac{1}{5}$ and $\frac{10}{3}$.
The least common denominator of 5 and 3 is 15.

Step 3: Express each fraction with the common denominator:
$-\frac{1}{5} = -\frac{3}{15}$ (multiply the numerator and denominator by 3)
$\frac{10}{3} = \frac{50}{15}$ (multiply the numerator and denominator by 5)

Step 4: Add the fractions:
$-\frac{3}{15} + \frac{50}{15} = \frac{-3 + 50}{15} = \frac{47}{15}$

Step 5: Simplify $\frac{47}{15}$ back to a mixed number if needed:
Performing the division, 47 divided by 15 is 3 with a remainder of 2.
Therefore, $\frac{47}{15} = 3\frac{2}{15}$.

Therefore, the solution to the problem is $3\frac{2}{15}$.