*Photo by Martin Thomas via flickr. In this Homeschooling Math with Profound Understanding (PUFM) Series, we are studying Elementary Mathematics for Teachers and applying its lessons to home education.*

When adding, we combine two addends to get a sum. For subtraction we are given the sum and one addend and must find the “missing addend”.

— Thomas H. Parker & Scott J. Baldridge

Elementary Mathematics for Teachers

Notice that subtraction is not defined independently of addition. It must be taught along with addition, as an inverse (or mirror-image) operation. The basic question of subtraction is, “What would I have to add to this number, to get that number?”

Inverse operations are a very fundamental idea in mathematics. The inverse of any math operation is whatever will get you back to where you started. In order to fully understand a math operation, you must understand its inverse.