Add -3 1/6 + 5 3/4. Write your answer as a reduced mixed number. (1 point)

1 answer

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

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

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

Now we add the two improper fractions: \[ -\frac{19}{6} + \frac{23}{4} \]

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

Convert both fractions to have a denominator of 12: \[ -\frac{19}{6} = -\frac{19 \times 2}{6 \times 2} = -\frac{38}{12} \] \[ \frac{23}{4} = \frac{23 \times 3}{4 \times 3} = \frac{69}{12} \]

Now 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: \[ 31 \div 12 = 2 \quad \text{(whole number part)} \] with a remainder of \(31 - 2 \times 12 = 31 - 24 = 7\).

Thus, we can express \(\frac{31}{12}\) as: \[ 2 \frac{7}{12} \]

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