Chapter 16
DIRECT LONG DIVISION
Here is a very easy method for doing long division in your head. It is very similar to our method of
short division. As many people have trouble doing long division, even with a pen and paper, if you
master this method people will think you are a genius.
Here’s how it works.
Let’s say you want to divide 195 by 32.
Here is how I set out the problem:
We round off 32 to 30 by subtracting 2. Then we divide both numbers by 10 by moving the decimal
point one place to the left, making the number we are dividing 19.5 and the divisor 3. Now we divide by
3, which is easy, and we adjust for the −2 as we go.
Three won’t divide into 1 so we divide the first two digits by 3. Three divides into 19 six times with 1
remainder (6 × 3 = 18). The 1 is carried to the next digit of the dividend (the number we are dividing),
which makes 15.
Before we divide into 15 we adjust for the 2 in 32. We multiply the last digit of the answer, 6, by the
units digit in the divisor, 32, which is 2.
6 × 2 = 12
We subtract 12 from the working number, 15, to get 3.
What we have done is multiplied 32 by 6 and subtracted the answer to get 3 remainder. How did we
do this?
We subtracted 6 times 32 by first subtracting 6 times 30, then 6 times 2. This is really a simple
method for doing standard long division in your head.
Let’s try another one. Let’s divide 430 by 32 to 2 decimal places. We set out the problem like this: