Find the sum of `-4 (5)/(6) and -7 (3)/(4)`.

Answer

To find the sum of \(-4 \frac{5}{6}\) and \(-7 \frac{3}{4}\), we will follow these steps:

### Step 1: Convert mixed numbers to improper fractions
First, we convert the mixed numbers into improper fractions.

For \(-4 \frac{5}{6}\):
\[ -4 \frac{5}{6} = -\left(4 \times 6 + 5\right)/6 = -\left(24 + 5\right)/6 = -\frac{29}{6} \]

For \(-7 \frac{3}{4}\):
\[ -7 \frac{3}{4} = -\left(7 \times 4 + 3\right)/4 = -\left(28 + 3\right)/4 = -\frac{31}{4} \]

### Step 2: Write the sum of the two improper fractions
Now, we need to find the sum:
\[ -\frac{29}{6} + -\frac{31}{4} \]

### Step 3: Find the least common multiple (LCM) of the denominators
The denominators are 6 and 4. The LCM of 6 and 4 is 12.

### Step 4: Convert each fraction to have the same denominator
Now, we convert both fractions to have the denominator of 12.

For \(-\frac{29}{6}\):
\[ -\frac{29}{6} = -\frac{29 \times 2}{6 \times 2} = -\frac{58}{12} \]

For \(-\frac{31}{4}\):
\[ -\frac{31}{4} = -\frac{31 \times 3}{4 \times 3} = -\frac{93}{12} \]

### Step 5: Add the fractions
Now we can add the two fractions:
\[ -\frac{58}{12} + -\frac{93}{12} = -\frac{58 + 93}{12} = -\frac{151}{12} \]

### Final Answer
The sum of \(-4 \frac{5}{6}\) and \(-7 \frac{3}{4}\) is:
\[ -\frac{151}{12} \]

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