Basic Mathematics for College Students

1.3 Subtracting Whole Numbers 31

Some subtractions require borrowing from two (or more) place value columns.

EXAMPLE (^4) Subtract: 9,927  568
Strategy We will write the subtraction in vertical form and subtract as usual. In
each column, we must watch for a digit in the subtrahend that is greater than the
digit directly above it in the minuend.
WHY If a digit in the subtrahend is greater than the digit above it in the minuend,
we need to borrow (regroup) to subtract in that column.
Solution
We write the subtraction in vertical form, so that the corresponding digits are lined
up. Each step of this subtraction is explained separately. Your solution should look
like the last step.
Since 8 in the ones column of 56 8 is greater than 7 in the ones column of 9,92 7 ,we
cannot immediately subtract. To subtract in that column, we must regroup by
borrowing 1 ten from 2 in the tens column. In this process, we use the fact that 1 ten
10 ones.
Since 6 in the tens column of 5 6 8 is greater than 1 in the tens column directly above
it, we cannot immediately subtract. To subtract in that column, we must regroup by
borrowing 1 hundred from 9 in the hundreds column. In this process, we use the fact
that 1 hundred 10 tens.
Borrow 1 ten from 2 in the tens column and change the 2 to 1. Add the
borrowed 10 to the digit 7 in the ones column of the minuend to get 17.
Then subtract in the ones column: 17  8 9.

9 , 9 2

1

7

17

 5 6 8

9

9 , 9 2 7

 5 6 8

Self Check 4

Subtract:

Now TryProblem 33

6,734 356

WHY If a digit in the subtrahend is greater than the digit directly above it in the
minuend, we must borrow (regroup) to subtract in that column.

Solution
To help you understand the process, each step of this subtraction is explained
separately. Your solution need only look like the laststep.
We write the subtraction in vertical form to line up the tens digits and line up
the ones digits.

Since 5 in the ones column of 1 5 is greater than 2 in the ones column of 3 2 ,we
cannot immediately subtract in that column because 2 5 is nota whole number.
To subtract in the ones column, we must regroup by borrowing 1 ten from 3 in the
tens column. In this regrouping process, we use the fact that 1 ten 10 ones.

Subtract in the tens column: 2  1 1.

The difference is 17.

3

2

2

12

 1 5

1 7

Borrow 1 ten from 3 in the tens column and change the 3 to 2. Add the

borrowed 10 to the digit 2 in the ones column of the minuend to get 12. This

step is called regrouping. Then subtract in the ones column: 12  5 7.

3

2

2

12

 1 5

7

3 2

 1 5

Your solution should

look like this:

3

2

2

12

1 5

1 7