My younger son is working his way through Art of Problem Solving’s Introduction to Number Theory this summer. He’s currently learning about different bases and how to convert from base 10 into those other bases.

A few days ago he wondered about how multiplication would work. Yesterday we worked through one example and was a great reminder about what a kid learning math can look like:

Today we looked at multiplication in different bases more carefully. First I picked a simple example to show him that the same process you use in base 10 works in other bases (so, you don’t have to convert to base 10 first):

Next I asked him to pick two numbers to multiply. Somewhat unluckily he picked two 4 digit numbers in base 2 so the calculation is a little tedious. Still, though, it all worked!

This was a really fun project – I can’t wait to work with him a little more on arithmetic in different bases.