  ## Encyclopedia > Multiplication table

Article Content

# Multiplication table

A multiplication table is used to define a 'multiplication' operation for an algebraic system. Multiplication tables as they are used to teach schoolchildren multiplication are a grid where rows and columns are headed by the numbers to multiply, and the entry in each cell is the product of the column and row headings:
 9×9=81 9×8=72 9×7=63 9×6=54 9×5=45 9×4=36 9×3=27 9×2=18 8×8=64 8×7=56 8×6=48 8×5=40 8×4=32 8×3=24 8×2=16 7×7=49 7×6=42 7×5=35 7×4=28 7×3=21 7×2=14 6×6=36 6×5=30 6×4=24 6×3=18 6×2=12 5×5=25 5×4=20 5×3=15 5×2=10 4×4=16 4×3=12 4×2=8 3×3=9 3×2=6 2×2=4

This table does not give the ones and zeros. That is because:

• Anything times zero is zero.
• Anything times one is itself. For example, 5×1=5.

Adding a number to itself is the same as multiplying it by two. For example, 7+7=14, which is the same as 7×2.

Multiplication tables can define 'multiplication' operations for groups, fields, rings, and other algebraic systems.

The following table is an example of a multiplication table for the unit octonions (see octonion, from which this example is taken).

 · 1 e1 e2 e3 e4 e5 e6 e7 1 1 e1 e2 e3 e4 e5 e6 e7 e1 e1 -1 e4 e7 -e2 e6 -e5 -e3 e2 e2 -e4 -1 e5 e1 -e3 e7 -e6 e3 e3 -e7 -e5 -1 e6 e2 -e4 e1 e4 e4 e2 -e1 -e6 -1 e7 e3 -e5 e5 e5 -e6 e3 -e2 -e7 -1 e1 e4 e6 e6 e5 -e7 e4 -e3 -e1 -1 e2 e7 e7 e3 e6 -e1 e5 -e4 -e2 -1

All Wikipedia text is available under the terms of the GNU Free Documentation License

Search Encyclopedia
 Search over one million articles, find something about almost anything!

Featured Article
 Eurofighter ... (33%), Daimler-Benz (33%), Alenia[?] of Italy (21%), and CASA of Spain (13%). Over the next five years, design work continued, aided by data from the British ...  This page was created in 37.3 ms