Adding Mixed Numbers

To add two mixed numbers, add the wholes to the wholes and the fractions to the fractions. Take 3 and 2/3 plus 1 and 1/2. The wholes give $3+1$, which is 4. The fractions give $\frac{2}{3}+\frac{1}{2}$, which over a common denominator is $\frac{4}{6}+\frac{3}{6}$, or $\frac{7}{6}$. So the sum is $4+\frac{7}{6}$.

This is allowed because a sum can be regrouped in any order. 3 and 2/3 plus 1 and 1/2 is just four numbers added, $3+\frac{2}{3}+1+\frac{1}{2}$, so the wholes may meet first and the fractions after.

Notice that $\frac{7}{6}$ is more than one whole: it is $1\tfrac{1}{6}$. A mixed number keeps its fraction part below 1, so carry that whole over to the 4: $4+1+\frac{1}{6}$, and the sum is $5\tfrac{1}{6}$.