Use the rules of adding rational numbers to solve. Calculators are not allowed.

Question

−2 1/2+6 2/3
(1 point)
Responses

9 1/6
9 and 1 sixth
4 1/6
4 and 1 sixth

−4 1/6
negative 4 and 1 sixth

4 1/3

Answer 1

To solve \(-2 \frac{1}{2} + 6 \frac{2}{3}\), we will follow these steps:

1. Convert mixed numbers to improper fractions.

   For \(-2 \frac{1}{2}\): \[ -2 \frac{1}{2} = -\left(2 \times 2 + 1\right)/2 = -\frac{5}{2} \]

   For \(6 \frac{2}{3}\): \[ 6 \frac{2}{3} = 6 \times 3 + 2/3 = \frac{20}{3} \]

2. Find a common denominator.

   The denominators are 2 and 3. The least common denominator (LCD) is 6.

3. Convert fractions to have the same denominator.

   Convert \(-\frac{5}{2}\) to sixths: \[ -\frac{5}{2} \times \frac{3}{3} = -\frac{15}{6} \]

   Convert \(\frac{20}{3}\) to sixths: \[ \frac{20}{3} \times \frac{2}{2} = \frac{40}{6} \]

4. Add the fractions.

   Now, add \(-\frac{15}{6}\) and \(\frac{40}{6}\): \[ -\frac{15}{6} + \frac{40}{6} = \frac{-15 + 40}{6} = \frac{25}{6} \]

5. Convert back to a mixed number.

   Divide 25 by 6: \[ 25 \div 6 = 4 \quad \text{(remainder 1)} \] So, \(\frac{25}{6} = 4 \frac{1}{6}\).

Thus, the answer is:

4 and 1 sixth (or written as \(4 \frac{1}{6}\)).