One of the most important concepts to understand in order to become a proficient abacist is that of complementary numbers.

RULE: Give a number, whenever the sum of any two numbers equals the given number, the two numbers are said to be complementary.

When adding or subtracting two numbers on the abacus, the concept of complementary numbers makes it easy to manipulate the beads. For abacists, the important complements are for the numbers 5 and 10.

For example, the complementary numbers for 5 are 1+4, 2+3, 3+2 and 4+1.

The complementary numbers for 10 are 1+9, 2+8, 3+7, 4+6, 5+5, 6+4, 7+3, 8+2 and 9+1.

See the Addition General Procedure, Cases 1 and 2 for an explanation of how complementary numbers are used when adding on the abacus.

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