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8VHSDUHQWKHVHVEUDFNHWVRUEUDFHVLQQXPHULFDOH[SUHVVLRQV
NS 2.1*2$
Add, subtract,
multiply, and divide with decimals; add with
DQGHYDOXDWHH[SUHVVLRQVZLWKWKHVHV\PEROV
UNDERLYING SKILLS AND CONCEPTS:
negative integers; subtract positive integers from negative
integers; and verify the reasonableness of the results.
computation with whole numbers
computation with integers
Order of Operations
Mathematicians use parentheses to show
what operations to do first.
Step 1: Do all operations in
Parentheses.
P. E. M. D. A. S.
(2 " 5) & (3 " 4) ! 22 $ ?
10 & 12 ! 4 $ ?
22 ! 4 $ 18
Step 2: Evaluate Exponents.
Step 3: Do Multiplication and Division
in order from left to right.
Step 4: Do Addition and Subtraction in
order from left to right.
1
Was the expression evaluated using
order of operations?
17 ! 5 " 9 # 3 $ 36
Hint: No exponents, no parentheses.
So, go to Step 3:
17 ! 45 # 3 =? 36
3
Place parentheses to show the order of
operations used to get 36.
(17 ! 5) " (9 # 3) $ 36
page 102
Place parentheses to show correct order of
operations.
x $ !5 & 3 " 42 & 81 # 9
Step 1: Evaluate exponents
Step 2: Do multiplication and division.
17 ! 42 # 4 % 36
No. Order of operations was not used.
17 ! 5 " 9 # 3 $ 36
2
!5 & 3 " (42) & 81 # 9
17 ! 15 # 4 =? 36
E x am p l E
E x am p l E
!5 & (3 " (42)) & (81 # 9)
Step 3: Do addition and subtraction last.
(4 " 3) & (7 " 2) ! 42 $ n
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Chapter 9 – Lesson 3
E – © CSL Associates, Inc. All rights reserved.
E x am p l E
Name
P RAC T I C E
Evaluate each expression. Use order of operations. Show each step.
1. 24 3 8
2. 125 5 5 10
24 24
0
25 5 10
20 10
30
3. (16 12) 12 4 (12)
4. 27 33 0 5
(4) 12 4 (12)
48
27 27 0 5
4 (12)
27 27 0
12
24
12
00
0
A
B
C
D
(16 4) (12 3) (16 4) 12 3
Do parentheses. Then
divide before subtracting.
(5 5) 9 3 (10 9) 3
?
So, 10 3 1 3
72 40 10 72 (40 10)
7
1
3
3 5 4 3 3 (5 4) 3
Math
Reasoning
Order of Operations
MR 2.2
6. Write an equation that will let
you find the area of the figure.
Use parentheses and exponents
where you can. Then solve.
A 52 (8 4) (8 6) 2
A 25 32 (48 2)
3 in.
A 57 24
A 81 sq in.
8 in.
5 in.
A 25 32 24
5 in.
E – © CSL Associates, Inc. All rights reserved.
Choose the best answer. Explain how you decided.
5. Which equation is NOT true?
4 in.
Chapter 9 – Lesson 3
6 in.
page 103
MCX94.HW.CL.G5.FM&Lesson.v211
8/2/04
18:02
Page 70
Name
…at home!
P RAC T I C E
Evaluate each expression. Use order of operations. Show each step.
1. 25 3 6
2. 145 5 5 10
25 18
29 5 10
7
29 5
34
3. (18 12) 12 4 (12)
4. 8 23 0 2
(6) 12 4 (12)
72 4 (12)
00
12
30
0
18
Choose the best answer. Explain how you decided.
5. Which equation is NOT true?
A
B
C
D
(16 4) (9 3) (16 4) 9 3
Do parentheses. Then
divide before subtracting.
(4 4) 6 3 (8 6) 3
?
So, 8 2 2 3
72 30 10 72 (30 10)
6
2
3
3 6 4 3 3 (6 4) 3
Math
Reasoning
Order of Operations
MR 2.2
6. Write an equation that will let
you find the area of the figure.
Use parentheses and exponents
where you can. Then solve.
1 (52) (8 4) 1 (8 6)
A 2
2
1 (5 5) (8 4) 1 (8 6)
A 3 in.
2
2
25 32 48
A 5 in.
8 in.
2
5 in.
page 70
4 in.
2
73
A 32 2
6 in.
1 sq in.
A 68 2
Home Resource and Homework
Chapter 9 Lesson 3
E – © CSL Associates, Inc. All rights reserved.
8 8 0 2
MCX94TEG5CH01_32.v7.4.2 2/24/01 19:44 Page 191
Name
P RAC T I C E
Evaluate each expression. Use order of operations. Show each step.
1. 24 3 8
2. 125 5 5 10
24 24
0
25 5 10
20 10
30
3. (16 12) 12 4 (12)
4. 27 33 0 5
(4) 12 4 (12)
48
27 27 0 5
4 (12)
27 27 0
12
24
12
00
0
A
B
C
D
(16 4) (12 3) (16 4) 12 3
Do parentheses. Then
divide before subtracting.
(5 5) 9 3 (10 9) 3
?
So, 10 3 1 3
72 40 10 72 (40 10)
7
1
3
3 5 4 3 3 (5 4) 3
Math
Reasoning
Order of Operations
MR 2.2
6. Write an equation that will let
you find the area of the figure.
Use parentheses and exponents
where you can. Then solve.
A 52 (8 4) (8 6) 2
A 25 32 (48 2)
3 in.
A 57 24
A 81 sq in.
8 in.
5 in.
A 25 32 24
5 in.
E – © CSL Associates, Inc. All rights reserved.
Choose the best answer. Explain how you decided.
5. Which equation is NOT true?
4 in.
Chapter 9 – Lesson 3
6 in.
Student Book Page
page 103
Name
…at home!
P RAC T I C E
Evaluate each expression. Use order of operations. Show each step.
1. 25 3 6
2. 145 5 5 10
25 18
29 5 10
7
29 5
34
3. (18 12) 12 4 (12)
4. 8 23 0 2
(6) 12 4 (12)
72 4 (12)
00
12
30
0
18
Choose the best answer. Explain how you decided.
5. Which equation is NOT true?
A
B
C
D
(16 4) (9 3) (16 4) 9 3
Do parentheses. Then
divide before subtracting.
(4 4) 6 3 (8 6) 3
?
So, 8 2 2 3
72 30 10 72 (30 10)
6
2
3
3 6 4 3 3 (6 4) 3
Math
Reasoning
Order of Operations
MR 2.2
6. Write an equation that will let
you find the area of the figure.
Use parentheses and exponents
where you can. Then solve.
3 in.
1
1
A (5 5) (8 4) (8 6)
2
2
8 in.
48
25
A 32 2
2
5 in.
5 in.
page 70
1
1
A (52) (8 4) (8 6)
2
2
4 in.
73
A 32 2
6 in.
1
A 68 sq in.
2
Home Resource and Homework
Chapter 9 Lesson 3
E – © CSL Associates, Inc. All rights reserved.
8 8 0 2