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LATTICE ALGORITHM

FOR MULTIPLICATION

Created by Paula Cantera Elk Neck

Elementary

The lattice algorithm for multiplication has

been traced to India, where it was in use before

A.D. 1100.

Many students find that this is one of their

favorites. It helps them keep track of all the

partial products without having to write extra

zeros - and it helps them practice their

multiplication facts!

With this algorithm, numbers are placed around

and within a lattice - a special kind of grid in

which the dotted-line rails within the cells

help form diagonals.

Write one factor along the top outside of the

grid, one digit per cell.

35

X 26

3

5

Write the other factor along the outer right side

of the grid, one digit per cell.

35

X 26

3

5

2

6

Begin with the first digit from the side factor,

and multiply it by each digit in the

top factor.

35

X 26

3

5

2

6

Record the product in the

upper right-hand cell.

Multiply 2 x 5.

3

5

1

2

0

6

Multiply 2 x 3.

Record the product in the

upper left-hand cell.

3

5

0

1

2

0

6

6

Since 6 is a product less than 10 you must

enter a zero in the top half of the cell!

Record the product in the

lower right-hand cell.

Multiply 6 x 5.

3

5

0

1

2

0

6

3

6

0

Multiply 6 x 3.

Record the product in the

lower left-hand cell.

3

5

0

1

2

0

6

3

1

6

8

0

Now, add along the diagonal. Begin with the

bottom right diagonal and work toward the upper

left diagonal.

3

5

0

1

2

0

6

3

1

6

8

0

Regroup each tens digit to the top of the next

diagonal as needed.

3

5

0

1

2

0

6

3

1

6

8

0

0

Notice we needed to regroup this time!

3

5

1

0

1

2

0

6

3

1

8 3 0 11

6

8

0

1

0

3

5

1

0

1

2

0

6

1 6 1 1 9

3

1

8 3 0 11

6

8

0

9

1

0

3

5

1

0

1

2

0

6

1 6 1 1 9

0

3

1

8 3 0 11

6

8

0

9

1

0

The product of 35 x 26 is 910 !

3

5

1

0

1

2

0

6

1 6 1 1 9

0

3

1

8 3 0 11

6

8

0

9

1

0

Of course you can use the Lattice Algorithm for

any number of digits.

Simply adjust your lattice grid to fit the

factors that you are multiplying!

Three digit by a two-digit 251 x 36

2

5

1

3

6

Shall we try to solve this one?

2

5

1

0

3

3

6

2

5

1

1

0

3

3

5

6

So far so good! Keep going!

2

5

1

0

1

0

3

3

5

6

6

Excellent work so far! You have the hang of it!

2

5

1

0

1

0

3

3

5

6

0

6

6

2

5

1

0

1

0

3

3

5

6

0

3

6

6

0

Youre almost there! Keep going!

2

5

1

0

1

0

3

3

5

6

1

0

3

6

6

0

2

Wasnt that easy? Do you remember what to do

next?

Of course! You add the diagonals!

2

5

1

1

0

0

1

3

3

5

6

0

3

1

0

6

6

0

2

9

6

0

3

The product of 251 x 36 is 9,036 !

2

5

1

1

0

0

1

3

3

5

6

0

3

1

0

6

9

6

0

2

6

0

3

Lattice Multiplication is lots of fun! Give it a

try!