Basic Mathematics for College Students

1.2 Adding Whole Numbers 19

Associative Property of Addition

The way in which whole numbers are grouped does not change their sum.

For example,

(25) 4  2 (54)

The Language of Mathematics Associativeis a form of the word associate,

meaning to join a group. The WNBA (Women’s National Basketball

Association) is a group of 14 professional basketball teams.

EXAMPLE (^4) Find the sum: 98 (2 17)
Strategy We will use the associative property to group 2 with 98.
WHY It is helpful to regroup because 98 and 2 are a pair of numbers that are easily
added.
Solution
We will write the steps of the solution in horizontal form.
Use the associative property of addition to
regroup the addends.
Do the addition within the parentheses first.
 117

 100  17

98 (217)( 98  2 ) 17

Sometimes, an application of the associative property can simplify a calculation.

Whenever we add 0 to a whole number, the number is unchanged. This property
is called the addition property of 0.

Self Check 4

Find the sum: (139 25)  75

Now TryProblems 45 and 49

We can often use the commutative and associative properties to make addition of
several whole numbers easier.

Addition Property of 0

The sum of any whole number and 0 is that whole number. For example,

3  0  3 , 5  0  5 , and 0  9  9

Self Check 5

Add:

a.14 + 7 + 16 + 1 + 2

b.

Now TryProblems 53 and 57

675

204

 435

EXAMPLE (^5) Add: a. 3  5  17  2  3 b.
Strategy We will look for groups of two (or three numbers) whose sum is 10 or
20 or 30, and so on.
WHY This method is easier than adding unrelated numbers, and it reduces the
chances of a mistake.
Solution
Together, the commutative and associative properties of addition enable us to use
any order or grouping to add whole numbers.
a.We will write the steps of the solution in horizontal form.
3 + 5 + 17 + 2 + 3  20 + 10 Think: 3  17 20 and 5  2  3 10.
 30

201

867

 49