The final product is composed of the digits outside the lattice which were just calculated. We continue summing the groups of numbers between adjacent diagonals, and also between the top diagonal and the upper left corner. We place the 9 just below theīottom of the lattice and carry the 1 into the sum for the next diagonal group. Next we sum the numbers between the previous diagonal and the next higher diagonal. We place the sum along the bottom of the lattice below the rightmost column. Since this is the only number below this diagonal, the first sum is 6. This number is bounded by the corner of the lattice and the first diagonal. We start at the bottom half of the lower right corner cell (6). We sum the numbers between every pair of diagonals and also between the first (and last) diagonal and the corresponding corner of the lattice. ![]() Now we are ready to calculate the digits of the product. If the product is less than 10, we enter a zero above the diagonal. The tens digit of the product is placed above the diagonal that passes through the cell, and the units digit is put below that diagonal. Now we calculate a product for each cell by multiplying the digit at the top of the column and the digit at the right of the row. īefore the actual multiplication can begin, lines must be drawn for every diagonal path in the lattice from upper right to lower left to bisect each cell. IllustratedĪbove is the lattice configuration for computing. ![]() Header for one row of cells (the most significant digit is put at the top). Is placed along the right side of the lattice so that each digit is a (trailing) Of cells (the most significant digit is put at the left). Is placed along the top of the lattice so that each digit is the header for one column If we are multiplying an -digit number by an -digit number, the size of the lattice is. In this approach, a lattice is first constructed, sized to fit the numbersīeing multiplied. The lattice method is an alternative to long multiplication for numbers.
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