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.
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