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Leslie also recommended that young pupils memorize the multiplication table up to 50 × 50. The illustration below shows a table up to 12 × 12, which is a size commonly used nowadays in English-world schools.
In this section, numerals are in decimal. For example, "10" means 9+1, and "12" means 9+3. The Dozenal Society of America argues that if a base is too small, significantly longer expansions are needed for numbers; if a base is too large, one must memorise a large multiplication table to perform arithmetic.
Their multiplication tables were not the tables that one might expect by analogy to decimal multiplication tables. Instead, they kept only tables for multiplication by certain "principal numbers" (the regular numbers and 7). To calculate other products, they would split one of the numbers to be multiplied into a sum of principal numbers.
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It requires memorization of the multiplication table for single digits. This is the usual algorithm for multiplying larger numbers by hand in base 10. A person doing long multiplication on paper will write down all the products and then add them together; an abacus-user will sum the products as soon as each one is computed.
Multiplication by a positive number preserves the order: For a > 0, if b > c, then ab > ac. Multiplication by a negative number reverses the order: For a < 0, if b > c, then ab < ac. The complex numbers do not have an ordering that is compatible with both addition and multiplication. [30]