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Operations and Computation
Lattice Multiplication Method
The lattice method for multiplying numbers has been used
for hundreds of years. It is very easy to use if you know the
basic multiplication facts. Study the examples below.
Use the lattice method to multiply 3 45.
4
5
The box with squares and diagonals is called a lattice.
Write 45 above the lattice.
Write 3 on the right side of the lattice.
3
4
5
1
5
4
5
1
1
2
4
5
5
2
1
3
Multiply 3 5.
Write the answer as shown.
3
Multiply 3 4.
Write the answer as shown.
3
Add the numbers along each diagonal,
starting at the right.
5
1
1
3
5
Read the answer. 3 45 135
Use the lattice method. Multiply 4 713.
7
2
0
8
2
8
70
1
seventy
3
1
4
5
2
2
4
4 713 2,852
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Operations and Computation
The numbers along a diagonal may add up to a 2-digit
number. When this happens . . .
◆ Write the 1s digit.
◆ Add the 10s digit to the sum along the diagonal above.
Use the lattice method. Multiply 7 89.
8
5
9
6
3
6
2
7
The sum along one diagonal is 6 6 12.
Write the 1s digit of 12.
7
Add the 10s digit of 12 to the sum along
the diagonal above.
This sum is 6.
3
8
51
9
6
3
6
6
2
3
Read the answer. 7 89 623
Use the lattice method. Multiply 34 26.
2
6
0
1
8
6
0
2
8
2
4
3
Write 26 above the lattice.
Write 34 on the right side of the lattice.
4
Multiply 3 6. Then multiply 3 2.
Multiply 4 6. Then multiply 4 2.
6
11
3
8
0 6
0 2
4
4
8 8
8
4
0
Write the answers as shown in the lattice.
Add the numbers along each diagonal
starting at the right.
For the sum 18, write 8. Then add 1 to the
sum along the diagonal above.
Read the answer. 34 26 884
seventy-one
71
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Operations and Computation
The search for ways to record computation
started in India, perhaps about the eleventh
century. The lattice method of multiplication
was probably passed on from the Hindus
to the Arabians. The Arabians then passed
it on to the Europeans. Fifteenth-century
writers in western Europe included it in
their printed books.
Did You Know
In the late 1500s, John
Napier invented a set
of numbered rods
that could be used to
multiply numbers.
The rods were strips of
wood or bone, called
Napier’s Bones. Using
these rods to multiply
is almost the same as
using the lattice method.
The first printed arithmetic book appeared
in Italy in 1478. Luca Pacioli listed eight
different ways to do multiplication in this
book. He called one of the ways “lattice
multiplication.” The name suggests the
gratings that were placed in windows to
keep people from looking through them.
1.
3
2.
6
5
7
1
4
3
3 517 4 36 3.
6
4
4.
4
7
7
8
3
64 8 Check your answers on page 338.
72
seventy-two
?
47 73