copyright © 2011 pearson education, inc. publishing as prentice hall. 10.5 order of operations
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Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
10.5
Order of Operations
Martin-Gay, Basic Mathematics, 4e 22
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Simplifying Expressions p 679
Order of Operations
1. Perform all operations within parentheses ( ), brackets [ ], or other grouping symbols such as square roots or fraction bars.
2. Evaluate any expressions with exponents.
3. Multiply or divide in order from left to right.
4. Add or subtract in order from left to right.
Martin-Gay, Basic Mathematics, 4e 33
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example p 679
Simplify.
2
24 19 3 24 19 9
52
43 9 Add from left to right.
Exponent
Martin-Gay, Basic Mathematics, 4e 44
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example p 679
Simplify.
8 3
4
24
4
6
Multiply in the numerator
divide
Why is the answer positive?
Martin-Gay, Basic Mathematics, 4e 55
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example 679
Simplify.
22 35 7 1
23
25 49 1
24 1
1117755
Martin-Gay, Basic Mathematics, 4e 66
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example p 680
Simplify.
4 6 9 6 49
4 3 6 7
12 6 7
18 7
25
parens 49634
squareroot
multiply
add
subtract
)7(18
Martin-Gay, Basic Mathematics, 4e 77
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example p 680
Simplify.
4 53 5 2 6.3 3 5 12 6.3
3 5 2 6.3
3 3 6.3
9 6.3
2.7
parens
bracketsmultiply
brackets add
multiply
subtract
Martin-Gay, Basic Mathematics, 4e 88
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Practice 4 p 679
Simplify.
exponent
exponent
exponent
523 1)4(2
9
18
52 1)4(8
51168 1168
Martin-Gay, Basic Mathematics, 4e 99
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Practice 5 p 680
Simplify.
grouping
exponent
multiply
9)12()82(2
324
27
9)12()6(2 3)12()6(2
3)12(12
)3(24
Martin-Gay, Basic Mathematics, 4e 1010
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Practice 6 p 680
Simplify.
grouping
exponent
multiply
32)3(4)5(
823
15
32)3(4)5( 8)3(4)5(
8)3(20
Martin-Gay, Basic Mathematics, 4e 1111
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example p 681
The graph shows the monthly normal temperatures for Barrow, Alaska. Use this graph to find the average of the temperatures for the months January through May.
continued
Martin-Gay, Basic Mathematics, 4e 1212
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
continued
14 16 14 1 20av
5erage
There are 5 months from
January through May.
25
5
5
The average of the temperatures is 5 F.
Martin-Gay, Basic Mathematics, 4e 1313
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
DONE
Martin-Gay, Basic Mathematics, 4e 1414
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Practice 7 p 680
Simplify.
parensadd
bracketsmultipy
brackets add
multiply
subtract
9.753524 9.72524
9.71024
9.784
9.732
9.39
Martin-Gay, Basic Mathematics, 4e 1515
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example
Simplify.
1 3 3
5 5 8
1 3
5 5
3
8
3
20
8
3
5
2
85
321
4
parens
multiply