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boxmul.txt
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1993-08-13
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*Here's a way to simplify and organize
any multiplication problem. With Box
Multiplication, you can solve prob-
lems of any size and have fun at the
same time.$
Let's try 64 x 12. First, draw a box
and divide it into four squares, one
for each digit, like this.
Put the first number on top. Put
the second number on the right.
Divide each square diagonally.$
We'll start at the top right box.
Multiply 4 x 1 and put the answer,
4, in the box. Put the 4 in the
lower half, where the units go.
There aren't any tens, so leave the
top half of the box empty.$
Next, we'll do the bottom right
box. This time multiply 4 x 2 = 8.
Put the 8 in the lower half of the
box. Again, there is no tens digit,
so we leave the top half empty.$
Now, the lower left box. Multiply
6 x 2 = 12. Put the 2 (units) in
the lower half and the 1 (tens) in
the upper half of the box.$
And now, the last box. 6 x 1 = 6.
There isn't a tens digit, so put
the 6 in the lower half of the box.$
The last step is to add the numbers
in each diagonal row, starting with
the 8 at the lower right. There
isn't anything to add to the 8, so
just put the 8 down below its box.$
Now add the next diagonal row.
4 + 2 = 6
Put the 6 at the left end of the
diagonal row.$
Add the next row diagonally:
6 + 1 = 7
Put the 7 at the left end of the
diagonal row. Read the answer from
around the outside of the box, from
left to right. 64 x 12 = 768.$
Box multiplication works on numbers
of any size. Let's try it with a
bigger example. Let's do 345 x 27.
A 3-digit number is multiplied by a
2-digit number, so we'll need a box
with 6 squares, like this:$
We'll start at the top right:
5 x 2 = 10
Put the 0 in the bottom half of the
box and the 1 in the top half.$
We'll do the bottom row all at once.
5 x 7 = 35, in the lower left box.
4 x 7 = 28, in the lower middle box.
3 x 7 = 21, in the lower left box.$
In the upper left box: 3 x 2 = 6
The 6 goes in the lower half.
In the upper middle box: 4 x 2 = 8
The 8 goes in the lower half.$
Now just add up the diagonal rows
and we'll know the answer. Start at
the bottom right. There's nothing
to add to the 5, so just move it
down.$
Now, the next row up:
0 + 3 + 8 = 11
11 is a two digit number, so put the
ones digit at the end of the row.
Put the other 1 in the next diagonal
row.$
Adding the next row we get:
1 + 8 + 2 + 1 + 1 = 13
Put the 3 at the left end of the
diagonal row, and put the 1 up in
the next diagonal row.$
Finally the last column:
6 + 2 + 1 = 9
Put the 9 down at the end of the row.
Read the answer from the digits
around the outside of the box from
left to right: 345 x 27 = 9,315@