Add: `(7)/(24)and((-5))/(16)`

Answer

To solve the problem of adding \( \frac{7}{24} \) and \( -\frac{5}{16} \), we will follow these steps:

### Step 1: Write the expression
We start with the expression:
\[ \frac{7}{24} + \left(-\frac{5}{16}\right) \]

### Step 2: Find the LCM of the denominators
The denominators are 24 and 16. We need to find the Least Common Multiple (LCM) of these two numbers.

- The prime factorization of 24 is \( 2^3 \times 3^1 \).
- The prime factorization of 16 is \( 2^4 \).

To find the LCM, we take the highest power of each prime factor:
- For 2, the highest power is \( 2^4 \).
- For 3, the highest power is \( 3^1 \).

Thus, the LCM is:
\[ LCM = 2^4 \times 3^1 = 16 \times 3 = 48 \]

### Step 3: Convert each fraction to have the LCM as the denominator
Now we convert each fraction to have the denominator of 48.

For \( \frac{7}{24} \):
\[ \frac{7}{24} = \frac{7 \times 2}{24 \times 2} = \frac{14}{48} \]

For \( -\frac{5}{16} \):
\[ -\frac{5}{16} = -\frac{5 \times 3}{16 \times 3} = -\frac{15}{48} \]

### Step 4: Add the fractions
Now we can add the two fractions:
\[ \frac{14}{48} + \left(-\frac{15}{48}\right) = \frac{14 - 15}{48} = \frac{-1}{48} \]

### Step 5: Write the final answer
Thus, the final answer is:
\[ \frac{7}{24} + \left(-\frac{5}{16}\right) = -\frac{1}{48} \]

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