Question

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

Answer 1

To add \( -3 \frac{1}{6} + 5 \frac{3}{4} \), we first need to convert the mixed numbers to improper fractions.

1. For \( -3 \frac{1}{6} \):
\[
-3 \frac{1}{6} = -\left(3 \times 6 + 1\right)/6 = -\left(18 + 1\right)/6 = -19/6
\]

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

Next, we add these two improper fractions:
\[
-\frac{19}{6} + \frac{23}{4}
\]

To add the fractions, we need a common denominator. The least common multiple of 6 and 4 is 12.

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

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

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

Finally, convert \(\frac{31}{12}\) back to a mixed number:
- Divide 31 by 12, which results in 2 with a remainder of 7.

Thus:
\[
\frac{31}{12} = 2 \frac{7}{12}
\]

The answer, written as a reduced mixed number, is:
\[
\boxed{2 \frac{7}{12}}
\]