Base-12 Arithmetic Operations

Performing arithmetic in base-12 requires internalizing a new set of multiplication facts while leveraging the superior divisibility of twelve. Addition in Base-12 Carrying occurs at 12 instead of 10. Example: 9 + 5 = 12 (decimal) = 10 (base-12) X + 3 = 13 (decimal) = 11 (base-12) E + E = 22 (decimal) = 1X (base-12) Multiplication Table Highlights 12 x 12 = 100 (base-12) = 144 (decimal) 6 x 2 = 10 (base-12) - exactly one dozen 4 x 3 = 10 (base-12) - four threes make twelve The base-12 times table is more regular than base-10 because 12 has 6 factors (1,2,3,4,6,12) vs 4 for 10 (1,2,5,10). Division Advantages In base-12, division by 2, 3, 4, 6 always terminates: 1/2 = 0.6 1/3 = 0.4 1/4 = 0.3 1/6 = 0.2 In decimal, 1/3 = 0.333... (repeating). Base-12 eliminates this imprecision for the most common fractions. Subtraction with Borrowing Borrowing in base-12 means borrowing 12 (a dozen) instead of 10: 20 - 7 = 19 (base-12) means 24 - 7 = 17 (decimal) = 15 (base-12)