This is a Burroughs Class 3 adding machine from 1919. Where the Class 1 I featured here earlier has fancy beveled glass and a full carriage on the back to accept ledgers, this later Class 3 has a simple paper spool and was used for general accounting.
The Class 3 is a rather different design from the Class 1. Like tech companies today, Burroughs expanded by buying competitors. This machine was originally made by the Pike company in 1909 which Burroughs bought in 1911 and it became a core part of a larger product line.
To add, enter the first number in the keyboard and then pull the lever to add it to the register and print it on the tape. The enter the second number and pull the lever again. The lever provides the force necessary to print. Here's 31337 + 5.
This is an adding machine--it only adds. To subtract, you have to use the complements method. For instance, to subtract 42 from 31342, I convert 42 to its complement (99999958) and add it. The carries shift off the left of the register and the difference remains.
Division is possible by repeated subtraction. Like with the Comptometer you have to watch the register before it underflows. To print a subtotal pull the lever once, hold the subtotal key and pull it again--a 2 handed operation. Total works the same but also clears the register.
While it's hard to beat the aesthetic appeal of the Burroughs Class 1 and 3, they are big, heavy, and slow. If you don't need a paper record you'd be better served by its 1919 competitors the Comptometer Model F or Monroe Model G I featured here earlier.
You multiply by repeated addition in the ones column, then shift left and repeat for each digit in the multiplicand. Normally the keys reset when you pull the lever, but by pressing the repeat key they stay down until you press the Total key. Here is 12 x 12.