How to Multiply Using the Lattice Method

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.

Blank lattice to multiply numbers

Step 2 Add the num­bers to be multiplied:

Add Numbers to the Lattice

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.

Lattice Method Add the Diagonals

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.

Multiply Out the Lattice

 

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

Lattice Method Add the Diagonals

Step 6 Read off the final answer

Lattice Method of Multiplication 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.

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