Last month, we have learned a multiplication method using squares and diagonals. In this post, we are going to learn how to multiply using intersecting lines. In this method, we draw lines using one factor, draw lines to represent another factor, and then count the number of intersections to get the product.

Let’s try the first example.

Example 1: 32 × 21

First, we draw 2 lines (green) and 2 lines (red) to represent 32.

Next, we draw 3 lines (purple) and 2 lines (yellow) to represent 32.

Next, we count the number of intersections. The leftmost group as shown in the first square is the hundreds digit. In this case, we have 6 intersections, so the hundreds digit is 6.

The second group which is shown is the tens digit. So, here, we have four intersections at the top and 3 intersections at the bottom. Therefore, the tens digit is 4 + 3 = 7. A m

Third, the group on the right is the ones digit. So, the ones digit is 2.

Therefore, the product of 32 × 21 = 672.

A more detailed explanation about multiplying lines can be found in the video below. This includes multiplying of 3 digit numbers as well as how to deal with numbers containing zero.