MSC #13 – Short Division

Almost sixty years ago, I learned the “long” division method from my teachers at the San Roque (now Manuel Roxas) Elementary School in Cavite City. I often wondered why this is called as such when we were not taught the “short” division procedure.

However, during times when I have no calculator or pen and paper, I was forced to divide by merely looking at the figures. So when I was writing lessons for MATH-Inic, I described my “one-line” division method.

It was only about three years ago, when I was viewing one the video lessons from The Great Courses’ “The Secrets of Mental Math” by Prof. Arthur T. Benjamin that I learned than my “one-line” method really is the “short” division method.

This “short” division works well with small (20 or less) divisors.

It follows the same procedure as the long division except that most of the solution is not written. Thus with a little practice, one can just look at the figures and announce the answer without need of pencil and paper.

In our example, 9657 ÷ 7, 7 goes into 9, 1 time with a remainder of 2. We put 1 as the first digit of the answer and place 2 in front of the 6 in the dividend line. The next dividend then is 26.

Next we know that 7 goes into 26 3 times with a remainder of  5. Again we place the 3 in the answer line and the 5 before the 5 in the dividend line. 55 will then be the next dividend.

The cycle is repeated until we reach the last digit of the dividend. At this point, we will leave the remainder as a whole number as shown in the figure. Of course, we can decimalize the remainder, but we will discuss converting fractions in a later “special”.