Page 17 - ArithBook5thEd ~ BCC

standing for 7 tens +15 ones. It looks funny (as if 15 were a digit), but it doesn’t change thevalue of
the minuend, which is still 7 × 10 + 15 = 85. We represent the borrowing operation like this:

{7}{15}
8 5
− 4 6

Ignoring the original minuend, we have 15 − 6= 9 for the ones place, and 7 − 3= 4 for the tens place,
as follows:

{7}{15}
8 5
− 4 6
3 9

The difference is 39. We can check this by verifying that the difference + the subtrahend = the original
minuend:
39

+4 6
85

Sometimes you have to go more than one place to the left to borrow successfully. This happens
when the next higher place has a 0 digit – there is nothing to borrow from.
Example 11. Find the difference:

207
− 69

Solution. In the ones column we can’t take 9 from 7, so we need to borrow from a higher place. We
can’t borrow from the tens place, because it has 0 tens. But we can borrow from the hundreds place.
We borrow 1 hundred, and convert it into 9 tens and 10 ones. The minuend is now represented as
{1}{9}{17},standing for 1 hundred +9 tens +17 ones, (as if 17 were a digit). We represent the
borrowing as before:

{1}{9}{17}
2 0 7

− 6 9
Ignoring the original minuend, we have 17 − 9= 8 for the ones place, 9 − 6= 3 for the tens place, and
1 − 0= 1 for the hundreds place:

{1}{9}{17}
2 0 7

− 6 9
1 3 8

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