Lattice multiplication is a very neat way of multiplying non-single digit quantities. It eliminates the need of switching to and from multiplication and addition. In Lattice multiplication, all multiplication is done before the addition is done. The process is fairly simple:
1. Create a matrix with the number of columns equal to the number of digits of the first number and the number of rows equal to the number of digits of the second number. In the example above, there first and second number both have 2 digits, hence the 2 x 2 matrix.
2. Draw a diagonal in each cell starting from the upper right corner down to the lower left corner.
3. Each row correspond to a digit of the second number and Each column correspond to a digit of the first number. To get the value of each cell, simply multiply the corresponding column value times the column value then the first digit of the product is put on the upper left triangle while the second digit of the product is put on the lower right triangle. We are ensured that there are only 2 digits for any product since the only possible value for each column and each row only ranges from 0 to 9. This means that the maximum result of any product is 9 times 9 or 89. In cases that the product of the cell is only one digit, the product is put on the lower right triangle and zero is put on the upper left triangle. For example, Column 1, row 1 correspond to the digits 2 times 4 and the product is 8. 8 is put on the lower right triangle and zero is put on the upper right triangle.
4. The addition is done. Each diagonal represent a digit in the result. the lower right diagonal is the ones place, the diagonal just above the lower right corner represents the tens place, the diagonal just below the upper left corner represents the hundreds place, and the upper left corner represents the thousands place. To get the result, add the digits in the diagonal and carry over the first digit of the product to the next diagonal.
In the example, there is only one element in the diagonal so we know that the value in the ones place is 6. The digits in the tens diagonal are 8, 5, and 6 which have a sum of 19 that makes the value of the tens place as 9 and 1 is carried over to the hundreds diagonal. The hundreds diagonal have the digits 2, 8, 1, and the carried over 1 from the tens place resulting a sum of 12, this makes the value of hundreds to be 2 and 1 is carried over to the thousands place. The thousands place only have 0 and 1 carried over from the hundreds place which makes the value of the thousands place to be 1. This makes the product of 27 and 48 to be 1296.
Full video:
Lattice Multiplication at KhanAcademy.org
An explanation of why it works:
Why Lattice multiplication works
