Reteach 1-6
Name
Date
LESSON
1-6
Class
Reteach
Order of Operations
When an expression contains more than one operation, the operations must be
performed in a certain order.
I. Evaluate powers (exponents).
II. Perform multiplication and division in order from left to right.
III. Perform addition and subtraction in order from left to right.
2
Simplify 4 ! 7 " 2 # 5 ! 3.
4 2 ! 7 " 2 • 5 ! 3 Identify powers.
16 ! 7 " 2 • 5 ! 3 Evaluate 4 2.
16 ! 7 " 2 • 5 ! 3 Identify multiplication and division.
16 ! 7 " 10 ! 3
23 " 10 ! 3
Evaluate 2 # 5.
Start at the left and perform each addition and subtraction in order.
13 ! 3
16
Fill in the blanks to simplify each expression.
1. 3 ! 5 • 4 " 2
3!
20
"2
23
"2
21
2
2. 20 " 4 ! 3
20 "
16
!3
4
!3
7
3. 6 ! 12 $ 4 " 8
6!
3
"8
9
"8
1
Simplify each expression.
4. 6 $ 2 • 4 " 3
9
7. 3 ! 3 $ 3 ! 3
7
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
2
5. 18 $ 3 " 5 ! 2
"1
8. 7 2 ! 4 2 • 3
6. 3 ! 5 • 3 " 8 $ 2
14
9. 6 ! 10 $ 2 • 5 " 1
97
46
30
Holt Algebra 1
Name
LESSON
1-6
Date
Class
Reteach
Order of Operations continued
Expressions can also include grouping symbols. Parentheses ( ),
brackets [ ], and braces { } are the most common grouping symbols.
Operations inside grouping symbols must always be done first.
If there are grouping symbols inside other grouping symbols,
evaluate the innermost group first.
2
Simplify the expression 6 " 3(5 " 1) ! 2.
6 2 " 3(5 " 1) ! 2
62 " 3 • 4 ! 2
36 " 3 • 4 ! 2
36 " 12 ! 2
24 ! 2
Evaluate 5 " 1.
Evaluate 6 2.
Evaluate 3 # 4.
Add and subtract from left to right.
26
The symbols shown at right are also
treated as grouping symbols.
Symbol
Example
Absolute-value
#2 " 3#
Radical
!!!
$3 ! 6
Fraction Bar
2
!7
_____
4"1
Simplify each expression.
2
10. 2 ! 6 (8 " 5) $ 2
!3 ! 2 " !4 ! 3 " ! 5 2
11. __________________
6 " 22
13
30
12. 4 ! 3 " # 2 " 6 # ! 5 "
16
13. If a right triangle has legs of lengths a and b, then the length of its hypotenuse can be
!
found using the expression $a 2 ! b 2 . Find the length of the hypotenuse of a right triangle
whose legs measure 11 cm and 14 cm. Round your final answer to the nearest tenth.
17.8 cm
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
47
Holt Algebra 1
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