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Lattice Method of Multiplication
Lattice multiplication, a variations of today's
standard long multiplication were introduced into
Europe by Fibonacci (whose correct name is
Leonardo of Pisa). It requires the preparation of a
lattice (
a grid drawn on paper) which guides the
calculation and separates all the multiplications from
A lattice is first constructed to fit
the size of the numbers being
multiplied.
multiplying a 3-digit number
by a 2-digit number.
multiplying a 2-digit number
by a 2-digit number.
multiplying a 3-digit number
by a 3-digit number.
During the multiplication phase, the lattice is filled in
with two-digit products of the corresponding digits
labeling each row and column: the tens digit goes in the
top-left corner.
During the addition phase, the lattice is summed on the
diagonals.

Finally, if a carry phase is necessary, the answer as
shown along the left and bottom sides of the lattice is
converted to normal form by carrying ten's digits as in