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 crisscross
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.
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