Decomposition is a strategy we can use to add numbers. In this method, we break each number into pieces, and then add the pieces. This works thanks to the associative and commutative properties of addition.

We may want to break numbers up by place value. As an example, we can think of 47 as 40 + 7 and 19 as 10 + 9. This allows us to then add 40 + 10 to get 50, and 7 + 9 to get 16. Adding the two pieces then gives 50 + 16 = 66.

We may also break numbers up to give us more friendly numbers. As an example, when addition 47 and 19, we may want to think of 47 as 40 + 7 and 19 as 20 - 1. Then allows us to add 40 + 20 to get 60 and subtract 7 - 1 to get 6. Adding the two pieces then gives 60 + 6 = 66.