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 first convert them to improper fractions.

1. Convert \(-3 \frac{1}{6}\) to an improper fraction:
\[
-3 \frac{1}{6} = -\left(3 \times 6 + 1\right)/6 = -\left(18 + 1\right)/6 = -\frac{19}{6}
\]

2. Convert \(5 \frac{3}{4}\) to an improper fraction:
\[
5 \frac{3}{4} = 5 \times 4 + 3 / 4 = \frac{20 + 3}{4} = \frac{23}{4}
\]

Now we need to add \(-\frac{19}{6}\) and \(\frac{23}{4}\). To do this, 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 two fractions:
\[
-\frac{38}{12} + \frac{69}{12} = \frac{69 - 38}{12} = \frac{31}{12}
\]

Now, we convert \(\frac{31}{12}\) back to a mixed number:
\[
31 ÷ 12 = 2 \quad \text{(whole part)}
\]
\[
31 - (12 \times 2) = 31 - 24 = 7 \quad \text{(remainder)}
\]

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

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