Lattice Method of Multiplication

What is the Lattice Method? 

The lattice method is an alternative method of multiplication. The lattice method derives its name from being used with a type of grid with a diagonal criss-cross pattern called a lattice.

You may have heard that the lattice method is a new way of multiplying, but the truth is that the lattice method has been around since the middle era, or even before (and this is the way before your parents were born too!).

The lattice method helps to organize the process of long multiplication into smaller steps. This can be complicated at first, but with practice you can find that multiplying by a large number can be fun.

Using Multiplication Table

Let us first find out the lattice method by multiplying it with a multiplication table. Start with the following problem: 35 x 12.

If you write 35 x 12 in extended form, we get (30 + 5) x (10 + 2).

You can use multiplication table to get your answer.

The multiplication table is useful when multiplying small numbers, but not with large numbers. The lattice method can help with this by dropping the extra zeros and dividing each box into a tens and ones place.

Each box is split diagonally.

Let's multiply 35 x 12 again using the lattice method. Now you will multiply each respective row with each column and write your answer in the box.

Draw rows and columns based on the number of digits in each factor. Draw diagonal lines through each box. Write the first factor along the top columns and the second factor below the rows.

Begin by multiplying each row digit by each column digit. Start by multiplying 5 x 1. That equals 5, so put a 5 in the ones section and a 0 in the tens section, since there is no tens value. Again, multiply 3 x 1 and put 3 in the ones section and 0 in the tens section. Proceed in the same way and multiply 2 by 5 and 3, respectively.

Example: Multiply 948 x 827 by using lattice method.

Solution: First of all draw a 3 x 3 square grid and draw its diagonals as shown in the figure. Now, start multiplying 8 x 8. The result is 64. Put 6 in tens section and 4 in ones section. Similarly, multiply 4 x 8, 9 x 8, etc. Now, add diagonally and write as given below:  

                  6,  6 + 5 + 8,   4 + 1 + 8 + 2 + 3,   6 + 2 + 0 + 8 + 6,   3 + 2 + 1,    7

                  6,   19,   18,   22,   6,   7

                   6,   9,      9,     3,   8,    7

So, the product is 783996.

Lattice Method of Addition

Example: Add 3,95,678 and 2,97,845.

Solution:

Step 1: Write the total of the two numbers in each place, starting from the ones place as shown.

Here, in the ones place, 8 + 5 = 13.

Write 1 in the row above, and 3 in the row below.

Step 2: Repeat totals in the other places as shown.

Step 3: Draw slanting lines (diagonals) as shown.

Step 4: Add the numbers within the slanting lines to get the final sum.

Hence, 3,95,678 + 2,97,845 = 6,93,523