![]() We read the digits down the left side and then towards the right on the bottom to generate the final answer: 783996.Īlthough the process at first glance appears quite different from long multiplication, the lattice method is actually algorithmically equivalent. 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. 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. Step 2 Next, make a grid for so that each digit has a box. Write the digits for the first factor going across the page, and the second digits on the left going down the page. If the product is less than 10, we enter a zero above the diagonal. Lattice Multiplication: Step 1 Take each factor and break it down into digits. 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. Illustrated above is theīefore 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. Of cells (the most significant digit is put at the top). The right side of the lattice so that each digit is a (trailing) header for one row So that each digit is the header for one column of cells (the most significant digit The multiplicand is placed along the top of the lattice If we are multiplying an -digit number byĪn -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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