Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
3.5
Order, Exponents, and the Order of Operations
Martin-Gay, Basic Mathematics, 4e 33
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Comparing Fractions
The inequality symbols < or > can be used to write the order of numbers.
Comparing FractionsTo determine which of two fractions is greater, Step 1: Write the fractions as like fractions.Step 2: The fraction with the greatest numerator is the greater fraction.
P 215
Martin-Gay, Basic Mathematics, 4e 44
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example 1
Insert < or > to form a true statement.
The LCD of 10 and 7 is 70.
Since 21 > 20, then
3 2
10 7
3 3 21
10 10
7
7 70 10
10
2 2 20
7 7 70
21 20
70 70
3 2
10 7
P 215
Martin-Gay, Basic Mathematics, 4ed 55
Comparing Fractions
Comparing Fractions:
Practice Problem 1
Step 1: Write the fractions as like fractions
Step 2: The fraction with the greater
numerator is the greater fraction.
Practice Problem 2
Step 1: Write the fractions as like fractions
Step 2: The fraction with the greater
numerator is the greater fraction.
11
10
9
8
99
90
99
88
11
11
P 215-216
9
2
5
3
45
10
45
27
9
9
9
9
11
10 &
9
8
9
2 &
5
3
5
5
Martin-Gay, Basic Mathematics, 4e 66
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Evaluating Fractions Raised to Powers
Evaluate each expression.
1.
2.
31
4
1 1 1 1
4 4 4 64
43
5
3 3 3 3 81
5 5 5 5 625
P 216
Martin-Gay, Basic Mathematics, 4e 77
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Evaluating Fractions Raised to Powers
Practice Problem 3Practice Problem 3
SOLUTIONSOLUTION
Evaluate
2
5
1
2
5
1
5
1
5
1
55
11
25
1
P 216
Martin-Gay, Basic Mathematics, 4e 88
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Evaluating Fractions Raised to Powers
Practice Problem 4Practice Problem 4
SOLUTIONSOLUTION
Evaluate
3
3
2
3
3
2
3
2
3
2
3
2
333
222
27
8
P 216
Martin-Gay, Basic Mathematics, 4e 99
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Evaluating Fractions Raised to Powers
Practice Problem 5Practice Problem 5
SOLUTIONSOLUTION
Evaluate
32
3
2
4
1
32
3
2
4
1
3
2
3
2
3
2
4
1
4
1
33344
22211
432
8
P 216
548
8
54
1
1
Martin-Gay, Basic Mathematics, 4e 1010
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Reviewing Operations on Fractions
P 217
Martin-Gay, Basic Mathematics, 4e 1111
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Using the Order of Operations
Order of Operations1. Perform all operations within parentheses ( ), brackets [ ], or other grouping symbols such as square roots or fraction bars, starting with the innermost set.
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 1212
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example
Simplify: 1 1 1
2 6 3
1 1 1 1 1
2 6 3
3
2 6 1
1 3
2 6
3 3
6 6
61
6
Divide first.Multiply by the reciprocal.
Change to like fractions.
Martin-Gay, Basic Mathematics, 4e 1313
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example
Simplify: 22 8 2
3 27 3
2 22 8 2 8
3 27 3
2 8
272
1
3 7
22 26
3 27 4 26
9 27
4 27
9 26 2
2 3 9
9 2 136
13
Add inside ParensLike fractions
Exponent
Multiply by reciprocal.
P 217
Martin-Gay, Basic Mathematics, 4e 1414
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Using Order of Operations
Practice Problem 10Practice Problem 10
SOLUTIONSOLUTION
Use the order of operations to simplify 10
3
7
4
9
2
10
3
7
4
9
2 Divide.
10
3
4
7
9
2
10
3
49
72
Multiply10
3
36
14
1036
314
360
42
60
7
P 217-218
Multiply by reciprocal
Martin-Gay, Basic Mathematics, 4e 1515
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Using Order of Operations
Practice Problem 11Practice Problem 11
SOLUTIONSOLUTION
Use the order of operations to simplify
25
11
5
3
5
22
25
11
5
3
5
22
Subtract.
Exponent
4
25
25
4 1
Divide
25
11
5
5
5
3
5
22
25
11
25
15
5
22
25
4
5
22
25
4
55
22
25
4
25
4
P 217-218
Martin-Gay, Basic Mathematics, 4e 1616
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Using Order of Operations
Practice Problem 12Practice Problem 12
SOLUTIONSOLUTION
Find the average of .24
7 and ,
8
3,
2
1
24
7
8
3
2
1
1
1
24
7
3
3
8
3
12
12
2
1
24
7
24
9
24
12
324
28
24
28
1
3
24
28
3
1
24
28
72
28
18
7
LCM is 24
OR, Simplify 28/24 to 7/6. Divide 7/6 by 3.
18
7
3
1
6
7
1
3
6
7
P 217-218