How to do: How to do: Lattice Lattice MultiplicationMultiplication

Created by Lilian Patrick 2009Created by Lilian Patrick 2009

What is lattice What is lattice multiplication and when multiplication and when would we use it?would we use it?

Lattice multiplication is a way to multiply Lattice multiplication is a way to multiply larger numbers (bigger than a 1-digit larger numbers (bigger than a 1-digit number times another 1-digit number)number times another 1-digit number)

You can use lattice multiplication with You can use lattice multiplication with any big multiplication problem as long as any big multiplication problem as long as you can draw a big enough grid!you can draw a big enough grid!

Sounds Sounds great!great!

How do we get started?How do we get started?

Let’s start with a 2-digit Let’s start with a 2-digit by 1-digit example…by 1-digit example…

If you want to multiply:If you want to multiply:

42 x 942 x 9

First, you have to make a 2 by 1 grid First, you have to make a 2 by 1 grid (because it’s a 2-digit by 1-digit problem)(because it’s a 2-digit by 1-digit problem)

Next, in each box, you need to draw a Next, in each box, you need to draw a diagonal line from the upper right hand diagonal line from the upper right hand corner through the lower left hand corner. corner through the lower left hand corner. The line should go past the lower left hand The line should go past the lower left hand corner to the outside of your grid. corner to the outside of your grid.

Put the 2-digit number across the top of Put the 2-digit number across the top of your grid and the 1-digit number on the your grid and the 1-digit number on the right side of your grid.right side of your grid.

4 2

9

Then, multiply the number on the Then, multiply the number on the top of each column with the top of each column with the number to the right of that row. number to the right of that row.

4 2

92 x 9 4 x 9

The digit in the tens place of the product The digit in the tens place of the product goes to the left of the diagonal. The digit goes to the left of the diagonal. The digit in the ones place of the product goes to in the ones place of the product goes to the right of the diagonal. *If there are no the right of the diagonal. *If there are no tens or no ones in the product, don’t tens or no ones in the product, don’t forget to put a 0!forget to put a 0!

4 2

918

36

Now, you’re finished with the Now, you’re finished with the numbers 42 and 9. Be careful not numbers 42 and 9. Be careful not to use these numbers in the next to use these numbers in the next step!step!

4 2

918

36

Finally, you need to ADD the numbers Finally, you need to ADD the numbers inside the grid along the diagonals. Start inside the grid along the diagonals. Start with the diagonal on the right. Write the with the diagonal on the right. Write the answer in the space outside the grid.answer in the space outside the grid.

4 2

918

36

8 + nothing =

8

6 + 1 =

7

3 + nothing =

3

Your answer is the number Your answer is the number outside of the grid.outside of the grid.

4 2

918

36

873

42 x 9 = 378

Now let’s try a 2-digit by Now let’s try a 2-digit by 2-digit multiplication 2-digit multiplication problem… problem… Let’s multiply:Let’s multiply:

54 x 9754 x 97

Start by making your grid (a 2 by 2 grid this Start by making your grid (a 2 by 2 grid this time):time):

Add the diagonals:Add the diagonals:

And the numbers:Since they’re both 2-digits, it doesn’t matter which one goes on the top and which one goes to the right of the grid.

5 4

9

7

Multiply the number at the top of the Multiply the number at the top of the column with the side of the row.column with the side of the row.

5 4

7

4 x 9

4 x 7

5 x 9

5 x 7

5 4

9

7

36

2 8

45

35

9

Finally, add the numbers along the Finally, add the numbers along the diagonals. If the sum is greater diagonals. If the sum is greater than 10, carry the 1 into the next than 10, carry the 1 into the next diagonal.diagonal.

5 4

9

7

36

2 8

45

35

83

1

The 1 is carried from the previous diagonal:

5 + 2 + 6 = 13 The 3 goes at the bottom of that diagonal. The 1 gets added to the next diagonal.

2

5

1

54 x 97 = 5,238

Now, try these two examples on your own. The grids are drawn for you. Don’t go on to the next slide until you’ve given these problems a try. Look back to previous slides if you need help.

1.) 26 x 4 =

2 6

4

2.) 31 x 62 =

3 1

6

2

See if you got the answers!

1.)

2 6

4248

01

0 4

1

3 1

6

2

2.)

18

06

0

06

29

1

2 2

1

26 x 4 = 104 31 x 62 = 1,922

Now that you’ve learned lattice multiplication, you

can practice with any numbers of your choice!

Good luck!