Add 6 1/3 + 7 1/2 what is the sum

To add the mixed numbers \( 6 \frac{1}{3} \) and \( 7 \frac{1}{2} \), we can follow these steps:

1. Convert mixed numbers to improper fractions:

   • For \( 6 \frac{1}{3} \): \[ 6 \frac{1}{3} = 6 \times 3 + 1 = 18 + 1 = 19 \quad \Rightarrow \quad \frac{19}{3} \]
   • For \( 7 \frac{1}{2} \): \[ 7 \frac{1}{2} = 7 \times 2 + 1 = 14 + 1 = 15 \quad \Rightarrow \quad \frac{15}{2} \]

2. Find a common denominator:

   • The least common denominator (LCD) of 3 and 2 is 6.

3. Convert fractions to have a common denominator:

   • Convert \( \frac{19}{3} \) to sixths: \[ \frac{19}{3} = \frac{19 \times 2}{3 \times 2} = \frac{38}{6} \]
   • Convert \( \frac{15}{2} \) to sixths: \[ \frac{15}{2} = \frac{15 \times 3}{2 \times 3} = \frac{45}{6} \]

4. Add the fractions: \[ \frac{38}{6} + \frac{45}{6} = \frac{38 + 45}{6} = \frac{83}{6} \]

5. Convert back to a mixed number:

   • Divide 83 by 6: \[ 83 \div 6 = 13 \quad \text{with a remainder of } 5 \]
   • So, \( \frac{83}{6} = 13 \frac{5}{6} \).

Thus, the sum of \( 6 \frac{1}{3} + 7 \frac{1}{2} \) is \( 13 \frac{5}{6} \).