The Lattice Multiplication Algorithm
Aside from the standard multiplication algorithm we know, and the Line Multiplication which I already discussed, there is another method that we can use to multiply. This is called lattice multiplication. We can do this in multiplying 2-digit by 2-digit numbers but it can be extended to numbers with more digits. The steps of are as follows.
Step 1: Create 2 by 2 grid and place the numbers you want to multiply at the top and at the side as shown in the next figure. In this case, we want to multiply 83 by 42.
Step 2: Draw diagonals on each rectangle. This forms two triangles. These triangles will contain the digits of the product of the two given numbers. As shown below, the yellow square will contain the product of 3 and 2.
Step 3: Multiply the numbers and place the product in the corresponding squares such that the tens digit of the product is in the triangle on the left and the ones digit is in the triangle on the right.
Zero should be added to the product containing 1 digit in order to fill in both triangles. For example, 3 x 2 becomes 06 instead of just 6.
Step 4: Add the numbers diagonally as shown below (see numbers with the same color). The number at the bottom-right corner is the ones digit of the product and the number at the top-left corner is thousands digit. Of course, in case the sum of the digits is more than 10, the tens digit will be carried over to the next place value of the digits of the product. As shown, the product of 83 and 42 is 3486.
As mentioned above, lattice multiplication may be extended to numbers more digits. Try it yourself.