Mme. de Saint Juery Method for Long Division

Fellow Buckley faculty member Jacqueline de Saint Juery has been known to baffle our best math whizzes with a very efficient method for doing long division. Here is an example using her method (or actually a slightly modified version that flips the positions of dividend and quotient). Can you figure out how the method works?

For example here is what 1078 / 12 would look like using the de Saint Juery method:

          8 9.8 3 3 ...
   ___________
1 2|  1 0 7 8
        1 1 8
          1 0 0
              4 0
                4 0
                  .. etc ..