ASIDES
Multiple approaches
Today, we rely more and more on calculators to give us the answers we once worked out on paper or in
our heads. Colin Ledsome CEng FIED looks at how it was done in medieval times
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Today, if you want to multiply two numbers, with more
than one digit, you probably reach for a calculator.
When you fi rst did multiplication by hand at school,
you would learn your multiplication tables, committing
to memory all the results up to 12 x 12.
For larger numbers, you would have laid them out on two lines
and gone through ‘long’ multiplication, taking each digit of
one number in turn and multiplying the other, then adding the
results, eg:
7438
235
1487600
223140
37190
1747930
364
23
7280
1092
8372
or
In the medieval period, they used a different arrangement,
which may have taken up more room, but allowed a teacher to
check each multiplication pair individually. A diamond-shaped
matrix, with additional vertical lines, forms the structure. The
two numbers fi t on the two top lines. Each pair of digits is then
multiplied and the result put in the appropriate cell. Adding the
vertical columns gives the result required on the bottom two
lines. Sometimes, obsolete ways of doing something can teach us
to look at an everyday activity and gain new insight.
8 2
3 1 6 3
4 0 6 2 4 5
7 0 8 0 9 4 0
1 4 1 2 1 5 0
1 2 1 2 0 3
3 3
7 3 5 9
2 0 9 6
0 6 1 8 4
0 1 2 1 2
8 0 8 2
3 7
4 7
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