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3 × 5 = 15 4 × 5 = 20 5 × ... Hypercomplex number multiplication tables show the non-commutative results of multiplying two hypercomplex imaginary units.
The multiplication of whole numbers may be thought of as repeated addition; ... [15] [verification needed] ... for huge numbers; Multiplication table;
It requires memorization of the multiplication table for ... 26 15 13 18 17 13 09 00 ... multiplication of two numbers could be thought of as a product of two ...
Mathematical tables are lists of numbers showing the results of a calculation with varying arguments.Trigonometric tables were used in ancient Greece and India for applications to astronomy and celestial navigation, and continued to be widely used until electronic calculators became cheap and plentiful in the 1970s, in order to simplify and drastically speed up computation.
As with the 2 × 2 complex representation above, complex numbers can again be produced by constraining the coefficients suitably; for example, as block diagonal matrices with two 2 × 2 blocks by setting c = d = 0. Each 4×4 matrix representation of quaternions corresponds to a multiplication table of unit quaternions.
Common tools in early arithmetic education are number lines, addition and multiplication tables, counting blocks, and abacuses. [186] Later stages focus on a more abstract understanding and introduce the students to different types of numbers, such as negative numbers, fractions, real numbers, and complex numbers.