In the subtraction shown, , and are digits. What is the value of
Solution
We work from right to left as we would if doing this calculation by hand. In the units column, we have giving 1. Thus, . (There is no borrowing required.) In the tens column, we have giving 1. Since 1 is larger than 0, we must borrow from the hundreds column. Thus, gives 1, which means . In the hundreds column, we have but we have already borrowed 1 from , so we have giving 0. Therefore, we must be subtracting 9 from 9, which means that should be 10, which is not possible. We can conclude, though, that and that we have borrowed from the 6. In the thousands column, we have or . This gives , which is correct. Finally, .
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