copyright © 2011 pearson education, inc. publishing as prentice hall. 3.5 order, exponents, and the...

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

3.5

Order, Exponents, and the Order of Operations

Martin-Gay, Basic Mathematics, 4ed 22

Comparing Fractions

P 215

5

4

5

2

53 93

Martin-Gay, Basic Mathematics, 4e 33


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



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



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




Practice Problem 3Practice Problem 3

SOLUTIONSOLUTION

Evaluate

2

5

1

2

5

1

5

1

5

1

55

11

25

1

P 216





SOLUTIONSOLUTION

Evaluate

3

3

2

3

3

2

3

2

3

2

3

2

333

222

27

8

P 216





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



Reviewing Operations on Fractions

P 217



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.



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.



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



Using Order of Operations


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





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





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



DONE

copyright © 2011 pearson education, inc. publishing as prentice hall. 3.5 order, exponents, and the...

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