Basic Mathematics for College Students

139

Complete the solution by subtracting in the thousands column (1  1 0) and
bringing down the 4 in the ten thousands column.

13 9

The difference is 40,728.

4 0 , 7 2 8

4 2

1

, 4

3

0

10

3

13

 1 , 6 7 5

728

Borrow 1 thousand from 2 in the thousands column and change the 2 to 1.

Add the borrowed 10 to the digit 3 in the hundreds column of the minuend

to get 13. Then subtract in the hundreds column: 13  6 7.

4 2

1

, 4

3

0

10

3

13

 1 , 6 7 5

1.3 Subtracting Whole Numbers 33

13 9

4 0 ,728

4 2

1

, 4

3

0

10

3

13

 1 , 6 7 5

Your solution should

look like this:

Check subtractions using addition.

Every subtraction has a related addition statement.For example,

because

because

because

These examples illustrate how we can check subtractions. If a subtraction is done
correctly,the sum of the difference and the subtrahend will always equal the minuend:

Difference subtrahend minuend

100  1  99 99  1  100

25  15  10 10  15  25

9  4  5 5  4  9

3

The Language of Mathematics To describe the special relationship between

addition and subtraction, we say that they are inverse operations.

EXAMPLE (^6) Check the following subtraction using addition:
Strategy We will add the difference (1,728) and the subtrahend (1,954) and
compare that result to the minuend (3,682).
WHY If the sum of the difference and the subtrahend gives the minuend, the
subtraction checks.
Solution
The subtraction to check Its related addition statement
Since the sum of the difference and the subtrahend is the minuend, the subtraction
is correct.

1

1

,7 2

1

8

 1 , 9 5 4

3 , 6 8 2

difference

 subtrahend

minuend

3 , 6 8 2

 1 , 9 5 4

1 , 7 2 8

3 , 6 8 2

 1 , 9 5 4

1 , 7 2 8

Self Check 6

Check the following subtraction

using addition:

Now TryProblem 39

9 , 7 8 4

 4 , 7 9 2

4 , 8 9 2



Estimate differences of whole numbers.

Estimation is used to find an approximate answer to a problem.

4

EXAMPLE (^7) Estimate the difference: 89,070 5,431
Strategy We will use front-end rounding to approximate the 89,070 and 5,431.
Then we will find the difference of the approximations.
Self Check 7
Estimate the difference:
Now TryProblem 43

64,2597,604