Bases Part I

Today we are going to start learning about using different bases for couting, addition, subtraction, multiplication, division, etc. We use base ten everyday without thinking about it, so it's easy to take for granted how hard it is to learn these functions.

So, what's a base?
An example of a base we are all familiar with is base ten- it uses the numbers 0,1,2, 3,4,5,5,7, 8, and 9. Once we need a bigger number than 9, we exchange/borrow for the next larger manipulative piece, since we want to use the least amount of pieces as possible. A useful way to illustrate this is by using manipulatives. Below is a video that demonstrates using manipulatives for addition in base ten.





Here is another example: 19
+ 7
____

This means that we have one long and nine units, and we are adding seven units. First we add the units together. 9+7 = 16. Since 16 is larger than 9, we have to exchange some of the units for a long. A long uses 10 units, so we take away ten units out of the 16 we have. This leaves us with 6 units (on the ones side), and another long to put on the tens side. Now we have:
1
19
+ 7
___
6
Next, we have to add the longs together. There are only 2, so no exchanges need to be made. This means we have 2 longs and 6 units which means we have 26.
19
+ 7
____
26