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Question

Reduce 7215 from scale twelve to scale ten by working in scale ten, and verify the result by working in the scale twice.

Solution
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In scale of ten
7215
12
---------
86
12
--------
1033
12
--------
12401
Thus the result is 12401 in each case.
7215 in scale twelve means 7×123+2×122+1×12+5 in scale ten. The calculation is most readily effected by writing this expression in the form [(7×12+2)×12+1]×12+5; thus we multiply 7 by 412 and add 2 to the product; then we multiply 86 by 12 and add 1 to product; then 1033 by 12 and add 5 to product.

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