Question

Add −3 1/6+5 3/4
. Write your answer as a reduced mixed number

Answer 1

To add the mixed numbers \(-3 \frac{1}{6}\) and \(5 \frac{3}{4}\), we can follow these steps:

1. Convert the mixed numbers into improper fractions.
2. Find a common denominator.
3. Add the fractions.
4. Convert back to a mixed number, if necessary.

### Step 1: Convert to improper fractions

\(-3 \frac{1}{6}\):
\[
-3 \frac{1}{6} = -\left(3 \times 6 + 1\right)/6 = -\frac{19}{6}
\]

\(5 \frac{3}{4}\):
\[
5 \frac{3}{4} = 5 \times 4 + 3/4 = \frac{20 + 3}{4} = \frac{23}{4}
\]

### Step 2: Find a common denominator

The denominators are \(6\) and \(4\). The least common multiple (LCM) of \(6\) and \(4\) is \(12\).

### Step 3: Rewrite each fraction with the common denominator

Convert \(-\frac{19}{6}\) to have a denominator of \(12\):
\[
-\frac{19}{6} = -\frac{19 \times 2}{6 \times 2} = -\frac{38}{12}
\]

Convert \(\frac{23}{4}\) to have a denominator of \(12\):
\[
\frac{23}{4} = \frac{23 \times 3}{4 \times 3} = \frac{69}{12}
\]

### Step 4: Add the two fractions

Now we can add:
\[
-\frac{38}{12} + \frac{69}{12} = \frac{69 - 38}{12} = \frac{31}{12}
\]

### Step 5: Convert to a mixed number

Since \(\frac{31}{12}\) is an improper fraction, we convert it to a mixed number:
\[
31 \div 12 = 2 \quad \text{(remainder 7)}
\]
So, \(\frac{31}{12} = 2 \frac{7}{12}\).

### Final Answer

Thus, the final answer is:
\[
2 \frac{7}{12}
\]