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# MSC #13: “Short” Division

About 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 four years ago, when I was viewing one of 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 divisors.

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

Compare this traditional solution to our accompanying illustration:

The common procedure is to:

1. Divide 9, the first digit of the dividend, by 7 to get 1, the first figure of the quotient.
2. Multiply 1 by 7 to get 7 and this is written below the 9.
3. Subtract 7 from 9 to get 2
4. Bring down 6 so that the next dividend will be 26.
5. Repeat steps 1 to 4 until there is no digit in the dividend that  can be brought down. The difference in the last subtraction is the remainder in the division.

In our short division technique, we do not have to show the division-multiplication-subtraction cycle which we can easily compute mentally. We just have to use the remainder as a prefix to the next figure in the dividend.

If we try dividing our featured example mentally, 9, 657 by 7, we can immediately see the 7 goes into 9 once so we can start announcing the answer as One Thousand …

With the remainder 2, our next dividend is 26 and we know that 7 goes into 26 3 times with a remainder of 5. We continue to say, Three Hundred

Our next dividend is 55 and there are seven 7s and a remainder of 6 in 55 so we say Seventy ..

Our last dividend is 67. 7 goes into 67 nine times with a remainder of 4. We can then finish off with Nine remainder Four

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