Evaluate :
(iii) `(1)/(-15)+(5)/(-12)`

Options

A. `-29/60`
B. `-19/60`
C. `-29/80`
D. `-28/50`

Answer

To evaluate the expression \( \frac{1}{-15} + \frac{5}{-12} \), we can follow these steps:

### Step 1: Rewrite the fractions
The given expression can be rewritten to make the negative signs clearer:
\[ \frac{1}{-15} + \frac{5}{-12} = -\frac{1}{15} - \frac{5}{12} \]

### Step 2: Find the LCM of the denominators
Next, we need to find the Least Common Multiple (LCM) of the denominators 15 and 12.

- The prime factorization of 15 is \( 3 \times 5 \).
- The prime factorization of 12 is \( 3 \times 4 \) (or \( 3 \times 2^2 \)).

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

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

### Step 3: Rewrite each fraction with the LCM as the denominator
Now we can rewrite both fractions with the common denominator of 60:
\[ -\frac{1}{15} = -\frac{1 \times 4}{15 \times 4} = -\frac{4}{60} \]
\[ -\frac{5}{12} = -\frac{5 \times 5}{12 \times 5} = -\frac{25}{60} \]

### Step 4: Add the fractions
Now we can add the two fractions:
\[ -\frac{4}{60} - \frac{25}{60} = -\frac{4 + 25}{60} = -\frac{29}{60} \]

### Final Result
Thus, the evaluated result of the expression \( \frac{1}{-15} + \frac{5}{-12} \) is:
\[ -\frac{29}{60} \]

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