Answer:
(b) 237₉
Explanation:
You want the difference 721₉ -473₉ using base-9 arithmetic.
Difference
The difference is computed in the usual way, except that each "borrow" gives you 9 units, instead of 10.
(7·9² +2·9 +1) -(4·9² +7·9 +3) = (7 -4)·9² +(2 -7)·9 +(1 -3)
= 3·9² +(-5)·9 +(-2) . . . . . . . . . digit by digit subtraction
= 2·9² +(9 -5)·9 +(-2) . . . . . . . . borrow from 9² place
= 2·9² +4·9 +(-2) . . . . . . . . . . . . simplify
= 2·9² +3·9 +(9-2) = 237₉ . . . . . borrow from 9s place, and simplify
Sum
You can also "subtract by adding", just as you might in base-10 arithmetic.
473₉ +6 = 480₉ . . . . . . . . carry into the 9s place
480₉ +10₉ = 500₉ . . . . . . . carry into the 9² place
500₉ +200₉ = 700₉ . . . . . . finish the sum to get 700₉
We want a total of 721₉, so we need to add 21₉ more to the sum amounts we have already added.
216₉ +21₉ = 237₉ ⇒ 473₉ +237₉ = 721₉
The difference is 721₉ -473₉ = 237₉.
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Additional comment
As you know, in base-9 arithmetic, 8 + 1 = 10₉. Of course, every addition fact has two corresponding subtraction facts: 10₉ -8 = 1; 10₉ -1 = 8.
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