The U.S. standard addition algorithm is one of the more well known algorithms. It uses two fundamental properties of addition: the associative property and the commutative property.

Using these properties, I can add things based on their place value. You always start on the right for this algorithm. You add the ones place together, and then regroup, if necessary. You write down how many ones there are as a result of the addition, and then regroup the tens to the tens place value. Continue this to get the final sum.

This is easiest demonstrated with base 10 blocks. You start by combining the one blocks and, if possible, exchange 10 one blocks for a 10 block. This is the idea of “carrying the 1,” where you regroup the ones as a group of tens and a group of ones.