Basic Mathematics for College Students

1.9 Order of Operations 109

SECTION 1.9 STUDY SET

VOCABULARY

Fill in the blanks.

1. Numbers are combined with the operations of
   addition, subtraction, multiplication, and division to
   create.


2. To evaluatethe expression means to find its
   .


3. The grouping symbols are called ,
   and the symbols are called.


4. The expression above a fraction bar is called the
   . The expression below a fraction bar is
   called the.


5. In the expression the
   parentheses are the most grouping symbols
   and the brackets are the most grouping
   symbols.


6. To find the of a set of values, we add
   the values and divide by the number of values.

CONCEPTS

7. List the operations in the order in which they should
   be performed to evaluate each expression.You do not
   have to evaluate the expression.
   a.
   b.
   c.
   d.


8. List the operations in the order in which they should
   be performed to evaluate each expression.You do not
   have to evaluate the expression.
   a.
   b.
   c.
   d.


9. Consider the expression In the
   numerator, what operation should be performed first?
   In the denominator, what operation should be
   performed first?


10. To find the mean (average) of and
    3, we add the values and divide by what number?

NOTATION

11. In the expression what symbol serves as

a grouping symbol? What does it group?

60  5  2

5  2  40

,

15, 33, 45, 12, 6, 19,

5 5(7)

(5 20  82 ) 28

.

16  4  2

16  2  4

50  40  8

50  8  40

(74)^2

7  42

15  90 (22)^3

5(2)^2  1

9 6[86(41)],

[ ]

( )

2  5  4

12. Use brackets to write in clearer
    form.

Fill in the blanks.

13. We read the expression as “16 minus the
    of 4 plus 9.”


14. We read the expression as “The cube of the
    of 8 minus 3.”

Complete each solution to evaluate the expression.

15.

16.

17.

18.

Evaluate each expression.See Example 1.

19. 
    
    
    
    20. 
        
    
    
    
    


20. 
    
    
    
    22. 
        
    
    
    
    

Evaluate each expression.See Example 2.

23. 
    
    
    
    24. 
        
    
    
    
    


24. 
    
    
    
    26. 
        
    
    
    
    

Evaluate each expression.See Example 3.

27. 
    
    
    
    28. 
        
    
    
    
    


28. 
    
    
    
    30. 
        
    
    
    
    

Evaluate each expression.See Example 5.

31. a. 32. a.
    b. b.


32. a. 34. a.
    b. 51 (168) b. 73 (359)

51  16  8 73  35  9

26 (29) 37 (411)

26  2  9 37  4  11

252  3 6(2)6 264  4 7(4)2

192  4 4(2)3 455  7 3(4)5

32  9  3  31 62  5  8  27

52  6  3  4 66  8  7  16

6  32  41 5  42  32

3  52  28 4  22  11

GUIDED PRACTICE





3

12  5  3

32  2  3



12 

 6



 36 

  42

[4(27)] 42 C 4 1 2 D 42



 2 

2 (5 6 2)  2  15  2



 28 

7  4 5(2)^2  7  4  51 2

(83)^3

16 (49)

2(12(54))