`((2)/(3)+(-4)/(5)+(7)/(15)+(-11)/(20))=?`

Options

A. `(-1)/(5)`
B. `(-4)/(15)`
C. `(-13)/(60)`
D. `(-7)/(30)`

Answer

To solve the expression \(\frac{2}{3} + \left(-\frac{4}{5}\right) + \frac{7}{15} + \left(-\frac{11}{20}\right)\), we will follow these steps:

### Step 1: Identify the denominators
The denominators of the fractions are 3, 5, 15, and 20. We need to find the least common multiple (LCM) of these denominators to combine the fractions.

### Step 2: Find the LCM
The LCM of 3, 5, 15, and 20 is 60.

### Step 3: Convert each fraction to have the common denominator
Now we will convert each fraction to have a denominator of 60:

- For \(\frac{2}{3}\):
\[ \frac{2}{3} = \frac{2 \times 20}{3 \times 20} = \frac{40}{60} \]

- For \(-\frac{4}{5}\):
\[ -\frac{4}{5} = -\frac{4 \times 12}{5 \times 12} = -\frac{48}{60} \]

- For \(\frac{7}{15}\):
\[ \frac{7}{15} = \frac{7 \times 4}{15 \times 4} = \frac{28}{60} \]

- For \(-\frac{11}{20}\):
\[ -\frac{11}{20} = -\frac{11 \times 3}{20 \times 3} = -\frac{33}{60} \]

### Step 4: Combine the fractions
Now we can combine all the fractions:
\[ \frac{40}{60} - \frac{48}{60} + \frac{28}{60} - \frac{33}{60} \]

Combine the numerators:
\[ 40 - 48 + 28 - 33 = 40 - 48 = -8 \]
\[ -8 + 28 = 20 \]
\[ 20 - 33 = -13 \]

Thus, we have:
\[ \frac{-13}{60} \]

### Final Answer
The final answer is:
\[ \frac{-13}{60} \]

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