11-8 Mixed Expressions and Complex Fractions

Algebra 1 Glencoe McGraw-Hill Linda Stamper

A mixed number is the sum of an integer and a fraction. A mixed expression is the sum of a monomial and a rational expression.

3x3x

3

21

221

2

Changing mixed expressions to rational expressions is similar to changing mixed number to improper fractions.

Write the mixed number as a rational expression.

Write the problem.3x

63

3x6

3

3x3x

3x6

3x9x3

3x69x3

3x15x3

Use the LCD to write with a common denominator.Distribute and combine like terms.

Write the mixed number as a rational expression.

y584y

6y

Example 1

Example 2 105x

517x15

y584y

6y

84y84y

8y4y40y02

84y6y 2

8y4y4620y 2

4y22

y2310y2 2

4y2y2310y 2

105x517x

15

105x015x

105x517x

105x105x15

105x

5x17150x75

105x5x17150x75

105x145x58

If a fraction has one or more fractions in the numerator or denominator, it is called a complex fraction.

numerical complex fraction

dcba

3251

You simplify an algebraic complex fraction in the same way that you simplify a numerical complex fraction.

algebraic complex fraction

Rewrite in arithmetic form.

Use reciprocal to rewrite as multiplication.

Simplify.

32

51

23

51

103

32

51

Multiply.

Change the mixed number to an improper fraction.

16

37

14

61

31

2

61

37

2

Rewrite in arithmetic form.

Use reciprocal to rewrite as multiplication.

Simplify a complex fraction involving a monomial.

a

yx

ayx

3

2

22

Multiply.

2

a

yx

ayx

3

222

yx

a

ayx

2

322

1

ya2

Write the problem.

igh

bbhg

3

23

Simplify.

b

igh

bhg

2

3

3Example 3

2

33

b

ighbhg

ih

bg2

2

rn

p16m

rp

n24m

4

2

2

53Example 4

c

ba

c

ba

4

4

2

5Example 5

rn

p16m

rp

n24m4

2

2

53

p16m

rn

rp

n24m2

4

2

53

3

9

2p

n3m

4

4

2

5

c

ba

c

ba

4

4

2

5

ba

c

c

ba

3

24

b

ca

Rewrite in arithmetic form.Use reciprocal to rewrite as multiplication.

Simplify a complex fraction involving polynomials.

3a 2a

15a

Multiply.

Simplify the numerator.

3a 2a

152a2aa

3a 2a

152aa2a2

3a 2a

15a2a2

3a 2a

5a3a

Factor.

1 3a

2a5a3a

3a

12a

5a3a

2a5a

82bb

23b

b

2

Simplify.

Example 6

12c 7c

10c6c21

2

Example 7

82bb

23b

b

2

Simplify.

4b3b3

Example 6

82bb 3b3b2

3bb

2

82bb 3b6b2

3bb

2

82bb 3b6b3

2

4b2b 3b2b3

1

4b2b 3b2b3

4b2b

13b2b3

12c 7c

10c6c21

2

Simplify.

7c3c

Example 7

12c 7c

10c6c27c7c 2

12c 7c

3c5c2 2

12c 7c

1c23c

1

12c7c

1c23c

12c

17c

1c23c

11-A9 Pages 623-624 #12–20,25-33.