Basic Mathematics for College Students

30 Chapter 1 Whole Numbers

Solution

We start at the right and subtract the ones digits and then the tens digits, and write

each difference below the horizontal bar.

Tens column

Vertical form

Ones column

The answer (difference)

Difference of the ones digits: Think 9  7 2.

Difference of the tens digits: Think 5  2 3.

The difference is 32.





5 9

 2 7

3 2



EXAMPLE (^2) Subtract 235 from 6,496.
Strategy We will translate the sentence to mathematical symbols and then
perform the subtraction. We must be careful when translating the instruction to
subtract one numberfrom another number.
WHY The order of the numbers in the sentence must be reversed when we
translate to symbols.
Solution
Since 235 is the number to be subtracted, it is the subtrahend.

6,496  235

To find the difference, we write the subtraction in vertical form and subtract the

digits in each column, working from right to left.

Bring down the 6 in the thousands column.

When 235 is subtracted from 6,496, the difference is 6,261.



6 , 4 9 6

 2 3 5

6 , 2 6 1

 

Subtract 235 from 6,496.

Self Check 2

Subtract 817 from 1,958.

Now TryProblem 23

Subtract whole numbers with borrowing.

If the subtraction of the digits in any place value column requires that we subtract a

larger digit from a smaller digit, we must borrow or regroup.

2

EXAMPLE (^3) Subtract:
Strategy As we prepare to subtract in each column, we will compare the digit in
the subtrahend (bottom number) to the digit directly above it in the minuend (top
number).

3 2

 1 5

Self Check 3

Subtract:

Now TryProblem 27

8 3

 3 6

Caution! When subtracting two numbers, it is important that we write them

in the correct order, because subtraction is notcommutative. For instance, in

Example 2, if we had incorrectly translated “Subtract 235 from 6,496”as

235 6,496, we see that the difference is not 6,261. In fact, the difference is not

even a whole number.