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

4 1/3

−4 1/6

4 1/6

Answer 1

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

1. Convert the mixed numbers into 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. Now, we need to find a common denominator to add these two fractions. The denominators are 2 and 3.

   • The least common denominator (LCD) is 6.

3. Convert both fractions to have a denominator of 6:

   • For \( -\frac{5}{2} \): \[ -\frac{5}{2} = -\frac{5 \times 3}{2 \times 3} = -\frac{15}{6} \]
   • For \( \frac{20}{3} \): \[ \frac{20}{3} = \frac{20 \times 2}{3 \times 2} = \frac{40}{6} \]

4. Now, we can add the two fractions: \[ -\frac{15}{6} + \frac{40}{6} = \frac{-15 + 40}{6} = \frac{25}{6} \]

5. Convert the improper fraction back to a mixed number: \[ \frac{25}{6} = 4 \frac{1}{6} \]

Therefore, the answer is \( 4 \frac{1}{6} \).

Hence, the correct response is: 4 1/6.