Evaluate `(3)/(5)+(7)/(3)+(-11)/(5)+ (-2)/(3)`.

Options

A. `(2)/(15) `
B. `(1)/(15) `
C. `(3)/(15) `
D. `(4)/(15) `

Answer

To evaluate the expression \(\frac{3}{5} + \frac{7}{3} + \left(-\frac{11}{5}\right) + \left(-\frac{2}{3}\right)\), we will follow these steps:

### Step 1: Group the fractions with the same denominators
We can group the fractions with the same denominators together:
\[ \left(\frac{3}{5} + \left(-\frac{11}{5}\right)\right) + \left(\frac{7}{3} + \left(-\frac{2}{3}\right)\right) \]

### Step 2: Simplify the first group
For the first group \(\frac{3}{5} + \left(-\frac{11}{5}\right)\):
\[ \frac{3 - 11}{5} = \frac{-8}{5} \]

### Step 3: Simplify the second group
For the second group \(\frac{7}{3} + \left(-\frac{2}{3}\right)\):
\[ \frac{7 - 2}{3} = \frac{5}{3} \]

### Step 4: Combine the results from both groups
Now we combine the results from both groups:
\[ \frac{-8}{5} + \frac{5}{3} \]

### Step 5: Find a common denominator
The common denominator for 5 and 3 is 15. We will convert both fractions:
\[ \frac{-8}{5} = \frac{-8 \times 3}{5 \times 3} = \frac{-24}{15} \]
\[ \frac{5}{3} = \frac{5 \times 5}{3 \times 5} = \frac{25}{15} \]

### Step 6: Combine the fractions
Now we can combine the two fractions:
\[ \frac{-24}{15} + \frac{25}{15} = \frac{-24 + 25}{15} = \frac{1}{15} \]

### Final Answer
Thus, the evaluated expression is:
\[ \frac{1}{15} \]

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