Add `(-13)/(20) and (14)/(15)`.

Answer

To solve the problem of adding \(-\frac{13}{20}\) and \(\frac{14}{15}\), we will follow these steps:

### Step 1: Identify the fractions to be added
We have:
\[ -\frac{13}{20} + \frac{14}{15} \]

### Step 2: Find the Least Common Multiple (LCM) of the denominators
The denominators are 20 and 15. We need to find the LCM of these two numbers.

- The prime factorization of 20 is \(2^2 \times 5\).
- The prime factorization of 15 is \(3 \times 5\).

To find the LCM, we take the highest power of each prime factor:
- For 2: \(2^2\)
- For 3: \(3^1\)
- For 5: \(5^1\)

Thus, the LCM is:
\[ LCM = 2^2 \times 3^1 \times 5^1 = 4 \times 3 \times 5 = 60 \]

### Step 3: Convert each fraction to have the same denominator
Now we will convert both fractions to have the denominator of 60.

For \(-\frac{13}{20}\):
\[ -\frac{13}{20} = -\frac{13 \times 3}{20 \times 3} = -\frac{39}{60} \]

For \(\frac{14}{15}\):
\[ \frac{14}{15} = \frac{14 \times 4}{15 \times 4} = \frac{56}{60} \]

### Step 4: Add the fractions
Now we can add the two fractions:
\[ -\frac{39}{60} + \frac{56}{60} = \frac{-39 + 56}{60} = \frac{17}{60} \]

### Step 5: Write the final answer
Thus, the result of adding \(-\frac{13}{20}\) and \(\frac{14}{15}\) is:
\[ \frac{17}{60} \]