Multiplication in Base Twelve
The duodecimal multiplication table works in a similar way as the decimal table you learned in primary school. To use it, find the first number to be multiplied at the top row, then find the second number to be multiplied in the leftmost column. Run your finger right along the row that is headed by the second number until you are directly under the first number in the top row. This is the product of the two numbers. Example: 7 × 9 = 53;. In words, we can say “seven times nine is five dozen three”. Five dozen three is sixty-three.
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
X |
E |
10 |
|
2 |
4 |
6 |
8 |
X |
10 |
12 |
14 |
16 |
18 |
1X |
20 |
|
3 |
6 |
9 |
10 |
13 |
16 |
19 |
20 |
23 |
26 |
29 |
30 |
|
4 |
8 |
10 |
14 |
18 |
20 |
24 |
28 |
30 |
34 |
38 |
40 |
|
5 |
X |
13 |
18 |
21 |
26 |
2E |
34 |
39 |
42 |
47 |
50 |
|
6 |
10 |
16 |
20 |
26 |
30 |
36 |
40 |
46 |
50 |
56 |
60 |
|
7 |
12 |
19 |
24 |
2E |
36 |
41 |
48 |
53 |
5X |
65 |
70 |
|
8 |
14 |
20 |
28 |
34 |
40 |
48 |
54 |
60 |
68 |
74 |
80 |
|
9 |
16 |
23 |
30 |
39 |
46 |
53 |
60 |
69 |
76 |
83 |
90 |
|
X |
18 |
26 |
34 |
42 |
50 |
5X |
68 |
76 |
84 |
92 |
X0 |
|
E |
1X |
29 |
38 |
47 |
56 |
65 |
74 |
83 |
92 |
X1 |
E0 |
|
10 |
20 |
30 |
40 |
50 |
60 |
70 |
80 |
90 |
X0 |
E0 |
100 |
Here are a few additional examples:
3 × 7 = 19; (three times seven is one dozen nine). Decimally, twelve plus nine is twenty-one.
X × 5 = 42; (ten times five is four dozen two). In base ten, four twelves plus two equal fifty.
9² = 69; (nine squared is six dozen nine). Decimally, six twelves plus nine equal eighty-one.
18; × 4 = 40; + 28; = 68; (one dozen eight times four equals four dozen plus two dozen eight, which is six dozen eight). Decimally, twenty times four is eighty.
Read more about duodecimal multiplication through this Fundamental Operations in the Duodecimal System. Compare the dozenal multiplication table with others in Multiplication Tables of Various Bases.
