Learn to divide using dots and lines
If you’ve ever seen the Japanese trick for multiplying using lines, you know that doing math by hand doesn’t have to mean doing it the old-fashioned way. If long division always confused you or you simply want to try something new, this trick might be for you.
Start by choosing a number to divide by another: We’re going to try 145,824 divided by 112. The first step is to draw dots on a piece of paper in columns where each column has a number of dots that represents a digit in the number you are dividing. So here, we have a column with one dot, a column with four dots, a column with five dots and so on.
Next, we are going to trace lines between the dots. Since we are dividing by 112, we’re going to connect one dot from a column to one dot from the next column to two dots from a third column. You always start as far left as you can (where there are empty dots).
The last step involves counting the number of groups of lines that start in each column. In our example, one group starts in the first column (red), three groups start in the next column (blue), then none and then two (green). That gives us our answer: 1302. You have to remember to put a zero for any column that doesn’t start new lines, but you can ignore the columns at the end — unless the answer ends in zeros. I recommend multiplying it back through to check whether or not you need them.
In some cases, this technique can get a little tricky when there aren’t enough dots in a particular column. In that case, you’ll have to transform one of the dots from a column into ten dots in the following column. Here’s one more example to see how that works: 3328/104. In this case, one of the dots from the second column is converted to 10 dots in the third column (shown in gray).
Watch the video below to see how this technique can be used for long division of polynomials as well!