Find the value of :
`(-7)/(12) + ((-2)/(13))`

Answer

To find the value of \((-7)/(12) + (-2)/(13)\), we will follow these steps:

### Step 1: Identify the fractions
We have two fractions:
1. \(-\frac{7}{12}\)
2. \(-\frac{2}{13}\)

### Step 2: Find the Least Common Multiple (LCM) of the denominators
The denominators are 12 and 13. Since 12 and 13 have no common factors (13 is a prime number), the LCM is:
\[ \text{LCM}(12, 13) = 12 \times 13 = 156 \]

### Step 3: Rewrite each fraction with the common denominator
Now we will convert each fraction to have the common denominator of 156.

For \(-\frac{7}{12}\):
\[ -\frac{7}{12} = -\frac{7 \times 13}{12 \times 13} = -\frac{91}{156} \]

For \(-\frac{2}{13}\):
\[ -\frac{2}{13} = -\frac{2 \times 12}{13 \times 12} = -\frac{24}{156} \]

### Step 4: Add the fractions
Now we can add the two fractions:
\[ -\frac{91}{156} + (-\frac{24}{156}) = -\frac{91 + 24}{156} = -\frac{115}{156} \]

### Step 5: Final answer
Thus, the value of \(-\frac{7}{12} + (-\frac{2}{13})\) is:
\[ -\frac{115}{156} \]

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