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 2/3 + 1/2, which over a common denominator is 4/6 + 3/6, or 7/6. So the sum is 4 + 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 + 2/3 + 1 + 1/2, so the wholes may meet first and the fractions after.

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