Basic Mathematics for College Students

18 Chapter 1 Whole Numbers

To find the sum of three whole numbers, we add two of them and then add the

sum to the third number. In the following examples, we add in two ways. We

will use the grouping symbols ( ), called parentheses,to show this. It is standard

practice to perform the operations within the parentheses first. The steps of the

solutions are written in horizontal form.

3  4  7

The Language of Mathematics In the following example, read (3 4)  7

as “The quantityof 3 plus 4,” pause slightly, and then say “plus 7.” Read 3 

(4 7) as, “3 plus the quantityof 4 plus 7.” The word quantity alerts the reader

to the parentheses that are used as grouping symbols.

Method 1: Group 3 and 4

 14

( 3  4 ) 7  7  7 Because of the

parentheses,

add 3 and 4

first to get 7.

Then add 7 and

7 to get 14.

Method 2: Group 4 and 7

 14

3 ( 4  7 ) 3  11 Because of the

parentheses,

add 4 and 7

first to get 11.

Then add 3 and

11 to get 14.

 

Either way, the answer is 14. This example illustrates that changing the grouping when

adding numbers doesn’t affect the result. This property is called the associative

property of addition.

Success Tip In Example 3, the digits in each place value column were added

from top to bottom. To check the answer, we can instead add from bottom to top.

Adding down or adding up should give the same result. If it does not, an error

has been made and you should re-add. You will learn why the two results should

be the same in Objective 2, which follows.

To check,

add

bottom

to top

1 7 , 8 0 2

9 , 8 3 5

6 9 2

 7 , 2 7 5

1 7 , 8 0 2

First add

top to

bottom

2 Use properties of addition to add whole numbers.

Have you ever noticed that two whole numbers can be added in either order because

the result is the same? For example,

2  8 10 and 8  2  10

This example illustrates the commutative property of addition.

Commutative Property of Addition

The order in which whole numbers are added does not change their sum.

For example,

6  5  5  6

The Language of Mathematics Commutative is a form of the word commute,

meaning to go back and forth.Commuter trains take people to and from work.

Same result