The Lattice Method of Multiplication
The lattice method has a number of different names, including: Gelosia, Sieve, Shabakh, Venetian Squares, Hindu Lattice. I discovered it the other day when my son was struggling to multiply decimals using the grid method. My daughter saw him getting frustrated and me struggling to explain where he had gone wrong, and said “Why don’t you just use the lattice method, it’s really easy”. I was skeptical but after she showed me how quickly and confidently she could do long multiplication, with or without decimals, I’m convinced it’s a valid and easy to understand method.
Example of the Lattice Method of Multiplication
The method can only really be explained by using an example:
723 x 63
Step 1 Draw the Blank Lattice
This example involves the multiplication of a 3 digit number by a 2 digit number. So we need a lattice with 3 columns and 2 rows (you will see that you’ll also need space around the lattice). This looks like a grid but as we progress it’s transformed into a lattice.
Step 2 Add the numbers to be multiplied:
Step 3 Draw Diagonals to form the Lattice
Notice how the diagonals project beyond the initial columns and rows. This gives space to write the answer.
Step 4 Multiply the Lattice
Notice how the multiplication results are entered into the lattice. There are 6 multiplications:-
7 x 6 = 42
2 x 6 = 12
3 x 6 = 18
7 x 3 = 21
2 x 3 = 6
3 x 3 = 9
Where there is a 2 digit answer, the first digit is entered to the left of the diagonal and the second digit is entered to the right of the diagonal. Where there is a one digit answer, zero is entered to left of the diagonal and the single digit entered to the right of the diagonal.
Step 5 Add up the Diagonals
Working from the right-hand side we have:-
9 = 9
8 + 6 =14 NB when you have a 2 digit answer, write down the second digit and carry the first digit over to the next diagonal. In this case we write down “4” and carry over “1” (see the number one written in green)
1 (the one carried over, see above) + 1 + 2 + 1 =5
1 + 2 + 2 = 5
4 = 4
Step 6 Read off the final answer
Final Answer 723 x 63 = 45,549
Advantages of the Lattice Method of Multiplication
1. You only need to know the times tables from 1 x 1 through to 9 x 9 to be able to complete any multiplication question. Check out “How to Learn Your Times Tables Fast” to become more confident with your times tables.
2. The method is step by step and relatively easy to follow.
3. You multiply and then add in 2 distinct separate steps.
4. As long as you take care drawing the diagonals you should not muddle units, tens, hundreds, thousands etc.
5. You can use this method to multiply decimals (separate article to follow).
Disadvantages of the Lattice Method of Multiplication
1. If you’re careless or untidy in preparing the lattice you are likely to make mistakes.
2. It’s possible to learn this method by rote without understanding why it works.