1-6 The Order of Operations
Name
Date
Evaluate: 7 • (33 5 • 3) 4 3
Compute within parenthesis first;
7 • (27 5 • 3) 4 3
evaluate the exponent.
7 • (27 15) 4 3
Within parentheses, multiply.
7 • (12) 4 3
Within parentheses, subtract.
84 4 3
Multiply from left to right.
21 3
Divide.
24
Add.
Remember:
Order of Operations
1. Grouping Symbols: parentheses ( ),
brackets [ ], braces { }, fraction bar ––
2. Exponents.
3. Multiply or divide from left to right.
4. Add or subtract from left to right.
7 • (33 5 • 3) 4 3 24
Evaluate each expression.
1. 24 16 6 • 5 92
24 16 6 • 5 81
24 16 30 81
8 30 81
38 81
43
4. |19 | • 5 (3 1)2
|19 | • 5 – (4)2
|19 | • 5 – 16; 19 • 5 – 16
95 – 16; 79
Copyright © by William H. Sadlier, Inc. All rights reserved.
7. 11 (23) 4 42 • (8 5)
11 (8) 4 16 • 3
11 2 16 • 3; 11 2 48
9 48; 57
10. 15 51 | 1 3 | • 4
1
|2 | • 4
5
75 2 • 4; 75 8
67
15 2. 32 15 7 • 2 82
32 15 7 • 2 64
32 15 14 64
17 14 64
31 64
33
5. 5 • (3 6) )
25 5 | 32 |
6. 7 • (8 2) 16 2 | 53 |
7 • (6) 16 2 | 125 |
42 4 2 125; 42 2 125
40 125; 165
9. 9 31 | 4 6 | • 9
8. 17 (33) 3 23 • (7 2)
9 31 |2 | • 9
1
9 2 • 9; 27 2 • 9
3
27 18; 45
17 (27) 3 8 • 5
17 9 8 • 5; 17 9 40
26 40; 66
11. 24 • 120 3(6 2)2
12. 30 • 150 4(5 1)2
30 • 1 4(6)2; 30 • 1 4(36)
30 • 1 144; 30 144
114
24 • 120 3(6 2)2
24 • 1 3(8)2; 24 • 1 3(64)
24 192; 168
14. 8[2(3.5 21) | 2.5 7 |]
1
(0.5)]; 4[3(2) (0.5)]
2
4(6 0.5); 4(5.5);
22
(
|27 | • 3 – (6)2
|27 | • 3 – 36; 27 • 3 – 36
81 – 36
45
5 • (9) 25 5 | 9 |
45 5 5 9; 45 1 9
44 9; 53
13. 4[3(1.5 21) | 4.5 5 |]
4[3 1.5 3. |27 | • 3 (4 2)2
1
(4.5)]; 8[2(4) (4.5)]
2
8[8 4.5); 4(3.5);
14
(
8[2 3.5 Lesson 1-6, pages 12–13.
)
Chapter 1
11
For More Practice Go To:
Evaluate each expression. Write the answer in simplest form.
2
(
)3
15. 1 2 42 82
[3 • (5 3)] 5
(1)3 16 8 1 2
;
(3 • (2))2 25 (6)2 25
(2)2 36 9
44
;
[2(2)]2 9 [(4)]2 9
1
1
36 25; 11
8
8
;
16 9 7
81 4 3 ) 6 11
763
18.
(9 64) |5 | 55 5
;
13
11 11
;
2 2
(
100 5 3 ) 3 20
495
(10 125) |23 | 115 23
5 5
2
;
10
5 1
;
10 2
(
)|
[
(
)2] |
19. 7 3 • 2 82 4 •4 3 15 3
9 • (2 3 )
(
)
[
(
)2]
20. 24 2 • 5 62 7 •5 10 32 16
7 • (4 2 )
[7 3 • (10)2] | 4 • (3 5) |
;
81 • (2 81)
[7 3 • (100)] | 4 • (2) |
81 • (83)
[7 300] | 8 | 293 8 285
95
;
;
;
2241
6723
6723
6723
[24 2 • (11)2] | 7 • (10 2) |
;
49 • (4 32)
[24 2 • (121)] | 7 • (8) |
49 • (36)
[24 242] | 56 | [218] 56 162
9
;
;
;
98
1764
1764
1764
21. Insert grouping symbols to make the answer
correct. Then evaluate the expression to justify
your work.
22. Insert grouping symbols to make the answer
correct. Then evaluate the expression to justify
your work. (Hint: Use absolute value bars.)
|4 9| 32 8
6
11
7 (11 13)2
(9 3) •(4 6)(12 3) 20
?
?
(12) • (2) (4) –20; 24 4 20;
20 20 True
|5 | 9 8 ? 6 5 9 8 ? 6
;
;
11
11
74
7 (2)2
?
6 6
6
14 8
;
True
11 11 11
11
23. Use four 4s, any of the four operations, and grouping symbols to
write expressions that are equal to 0 through 10. For example:
(4 4) (4 4) 0
Possible answers: 4 4 4 4 0; (4 4) (4 4) 1; 4 4 4 4 2;
(4 4 4) 4 3; 4 4 • (4 4) 4; (4 4 • 4) 4 5; 4 (4 4) 4 6;
44 4 4 7; 4 4 4 4 8; 4 4 4 4 9
(44 4) 4 10
12
Chapter 1
Copyright © by William H. Sadlier, Inc. All rights reserved.
(
17.
2
(
)2
16. 3 5 62 92
[2 • (4 6)] 3