How to Use the Chinese Grid Method

The Chinese Grid method of multiplication (also known as lattice multiplication) is a technique for multiplying large numbers together without having to add large results or keep track of digits. Numbers of any size can be solved simply by making a grid and following a simple procedure. Unlike the more common methods of multiplication, you don't have to add large numbers together at the end to obtain your product. The only steps involved are multiplying and then adding a series of single-digit numbers.

Making the Grid

• 1

  Draw a rectangular grid. Make as many rows as there are digits in the first number. Make as many columns as there are digits in the second number.

• 2

  Draw a series of diagonal lines through the grid from the top-right corner to the bottom-left corner so that each square in the grid is bisected by a diagonal line. Extend the diagonal line about an inch past the border of the grid.

• 3

  Write the digits of the first number to the right of the grid, placing each digit directly to the right of a row.

• 4

  Write the digits of the second number above the grid, placing each digit directly above a column.

• 5

  Calculate the product of the first digit of the first number and the first digit of the second number. Put the answer where the digits intersect at the top-left corner of the grid-- the tens digit above the diagonal (write "0" if the product is less than 10), and the ones column below the diagonal.

• 6

  Calculate the product of the first digit of the first number and every other digit of the second number, again placing the answer at the corresponding location on the leftmost column.

• 7

  Repeat Steps 5 and 6 for the remaining digits of the first number, filling in the corresponding column with the corresponding products of the digits.

Calculating the Product

• 1

  Place the digit on the bottom-right diagonal underneath the rightmost column of the grid. This is the ones digit of your answer.

• 2

  Add up the digits of the diagonal directly above the bottom-right digit. Place the ones digit of the sum in the extension of this diagonal outside the grid. Carry the tens digit (if there is one) to the next diagonal going up.

• 3

  Repeat Step 2 for the remaining diagonals, making sure to add any carried digits.

• 4

  Write the digits out from top to bottom of the left row, and then left to right of the bottom row. These are the digits of the product, in order.