How do you do lattice multiplication?

Answer 1

Setting up the latticeFirst, draw a grid that has as many rows and columns as the multiplicand and the multiplier. The grid shown here is for multiplying a 4-digit number by a 3-digit number.

Next, draw a diagonal through each box from upper right corner to lower left corner. Continue the line a short way past the grid. (Ms. Thomas describes the process to her students as "corner to corner and out the door.")

Write one factor across the top and the other down the right side, lining up the digits with the boxes.

MultiplicationThe multiplication is performed by multiplying the digits at the head of each row and column. Fill in each square of the grid with the product of the digits above and to its right, recording the products so that the tens are in the upper (diagonal) half of the square and the ones are in the lower half. If the product does not have a tens digit, record a zero in that triangle.

In the example shown here, the highlighted row and column give us 1×5=5, so we write 0 in the upper half of the square and 5 in the lower half.

AdditionNow add the numbers in the grid along the diagonals, starting from the lower right corner. (Ms. Thomas describes this step to her students as "ride the slide.") Carry any tens into the top of the next diagonal.

In this example, the highlighted diagonal gives us 4+2+5+1=12, so we write 2 at the bottom of the diagonal and carry the 1 to the top of the next diagonal to the left.

To find the answer, read the digits starting down the left of the grid and continuing across the bottom. Here, the answer to 2314×157 is 363,298.