In each of these problems, each bottom digit is less than the corresponding top digit. This may not always be the case. We will examine the case where the bottom digit is greater than the corresponding top digit in the next section.
Subtraction involving borrowing
Minuend and subtrahend
It often happens in the subtraction of two whole numbers that a digit in the
minuend (top number) will be less than the digit in the same position in the
subtrahend (bottom number). This happens when we subtract 27 from 84.
We do not have a name for
. We need to rename 84 in order to continue. We'll do so as follows:
Our new name for 84 is 7 tens + 14 ones.
Notice that we converted 8 tens to 7 tens + 1 ten, and then we converted the 1 ten to 10 ones. We then had 14 ones and were able to perform the subtraction.
Borrowing
The process of
borrowing (converting) is illustrated in the problems of Sample Set C.
Sample set c
Practice set c
Perform the following subtractions. Show the expanded form for the first three problems.
Borrowing more than once
Sometimes it is necessary to
borrow more than once . This is shown in the problems in
[link] .
Sample set d
Perform the Subtractions. Borrowing more than once if necessary
- Borrow 1 ten from the 4 tens. This leaves 3 tens.
- Convert the 1 ten to 10 ones.
- Add 10 ones to 1 one to get 11 ones. We can now perform
.
- Borrow 1 hundred from the 6 hundreds. This leaves 5 hundreds.
- Convert the 1 hundred to 10 tens.
- Add 10 tens to 3 tens to get 13 tens.
- Now
.
-
.
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- Borrow 1 ten from the 3 tens. This leaves 2 tens.
- Convert the 1 ten to 10 ones.
- Add 10 ones to 4 ones to get 14 ones. We can now perform
.
- Borrow 1 hundred from the 5 hundreds. This leaves 4 hundreds.
- Convert the 1 hundred to 10 tens.
- Add 10 tens to 2 tens to get 12 tens. We can now perform
.
- Finally,
.
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Practice set d
Perform the following subtractions.
Borrowing from zero
It often happens in a subtraction problem that we have to borrow from one or more zeros. This occurs in problems such as
-
and
-
We'll examine each case.
Borrowing from a single zero.
Consider the problem
Since we do not have a name for
, we must borrow from 0.
Since there are no tens to borrow, we must borrow 1 hundred. One hundred = 10 tens.
We can now borrow 1 ten from 10 tens (leaving 9 tens). One ten = 10 ones and 10 ones + 3 ones = 13 ones.
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Now we can suggest the following method for borrowing from a single zero.
Borrowing from a single zero
To borrow from a single zero,
- Decrease the digit to the immediate left of zero by one.
- Draw a line through the zero and make it a 10.
- Proceed to subtract as usual.