How many times in school did you hear the term long division? This always confused me when I was learning how to do division. If there is a long division, shouldn’t there be a short division?

Maybe I was absent the day the idea of short division was covered, or maybe it was just never covered. Many years later I was looking through a arithmetic book from the 1800’s, and within that book the concept of short division was demonstrated.

I couldn’t have been more excited! At the time I was teaching 6th grade, forever remembered in my household as the year my hair started going grey. I was 27.

Anyway, I was excited that my 6th-grade students would learn this valuable skill that was left out of my personal education. To be successful at short division, a student needs to have a solid grasp of their multiplication tables.

Short Division is best used when the divisor (the number you are dividing by) is a single-digit number. It is easiest, best to use a divisor symbol when doing short division.

Problem:
Divide 6258 by 8:

Step 1: Divide 62 by 8. Much of short division is done with mental math (i.e., in your head). Think: 62 divided by 8 equals 7 (or 7 * 8 = 56). Write 7 for the first step of the solution in the hundreds spot.

Since we have a remainder of 6 (62 – 56 = 6), we need to note that somewhere in the equation rather than trying to keep everything in our head. In short division, we note the remainder as superscript (i.e. a small number at the top) beside the next digit which is 5.

So we now need to divide 65 by 8, which equals 8.

As 65 minus 64 equals 1, we add a 1 as a superscript by the final 8 of our equation

The final step is to divide 18 by 8 which equals 2 with a remainder of 2.

And there you have it, you have now completed a division problem using short division.
While it won’t work for every division problem, it is handy for doing single digit division quickly. With a little practice, you might even be able to do the entire division problem in your head.
While most teachers are going to want you to show your work on your division problems, this method is very handy when you have to do standardized tests.