chapter 6
DESCRIPTION
Chapter 6. Section 5. Complex Fractions. Simplify a complex fraction by multiplying numerator and denominator by the least common denominator (Method 2). Simplify rational expressions with negative exponents. 6.5. 2. The quotient of two mixed numbers can be written as a fraction. - PowerPoint PPT PresentationTRANSCRIPT
Objectives
1
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Complex Fractions
Simplify a complex fraction by multiplying numerator and denominator by the least common denominator (Method 2).
Simplify rational expressions with negative exponents.
6.5
2
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Complex Fractions.
The quotient of two mixed numbers can be written as a fraction.
Complex FractionA fraction with fractions in the numerator and/or denominator is called a complex fraction.
1 12 3
2 4
1 12 2
2 2 1 1
3 34 4
12
21
34
Numerator of complex fractionMain fraction barDenominator of complex fraction
Slide 6.5-3
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Objective 1
Simplify a complex fraction by multiplying numerator and denominator by the least common denominator. (Method 2 in our Text)
Slide 6.5-9
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Solution:
2 13 44 19 2
Simplify each complex fraction.
2 1
3 44 1
9
36
236
24 9
16 18
15
34
62
43
a
a
a
a
2 6
3 4
a
a
62
43
a
a
Slide 6.5-11
Simplifying Complex Fractions (Method 2)CLASSROOM EXAMPLE 4
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
This technique utilizes the Fundamental Law of Fractions.
Method 2 from our Text
Simplifying a Complex Fraction
Step 1: Find the LCD of all fractions within the complex fraction.
Step 2: Multiply both the numerator and denominator of the complex fraction by this LCD using the distributive property as necessary. Write in lowest terms.
Slide 6.5-10
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Simplify the complex fraction.
2 2
2 2
2 3
4 1a b ab
a b ab
Solution:
2 2
22
2
2 2
2
2 3
4 1
a b ab
aa
bb
b
a
a
b
2 3
4
b a
ab
Slide 6.5-12
Simplifying a Complex Fraction (Method 2)CLASSROOM EXAMPLE 5
LCD = a2b2
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Solution:1 2
1 22 1
2 3
a b
b a
Simplify the complex fraction.
2 3
1 2 8
a b a
a a b
Slide 6.5-8
Simplifying a Complex Fraction CLASSROOM EXAMPLE 3
LCD = (a+1)(b-2)(a+3)
1 2
1 22 1
2 3
a b
b a
(a+1)(b-2)(a+3)
(a+1)(b-2)(a+3)
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Simplify each complex fraction.
1 21
41
x x
x
2
2
2 34
4 916
xxxx
2 34
2 3 2 3
4
44
4
44
x x
x x
xx
x x
x x
4
2 3
2 3
2 3
x
x
x
x
4
2 3
x
x
1 2 1
11
14
x xx
x
x
x x
1 2
4
x x
x
3 1
4
x
x
Slide 6.5-13
Deciding on a Method and Simplifying Complex Fractions
Solution:
CLASSROOM EXAMPLE 6
Note: One term distribute once, two terms distribute twice
Ex 1
Ex 2
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Simplify rational expressions with negative exponents.
Objective 2
Slide 6.5-10
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
2 1
1 35
a b
a b
Simplify the expression, using only positive exponents in the answer.
2
3
1 1
1 5a b
a b
LCD = a2b3
22
33
3
2
1 1
1 5
a
a
bb
b
a
ba
2 3 2 3
2 3 2 3
2
3
1 1
1 5a b
a b
a b a b
a b a b
3 2 2
3 25
b a b
ab a
Slide 6.5-11
CLASSROOM EXAMPLE 7
Simplifying Rational Expressions with Negative Exponents
Solution:
Negative exponent means take the reciprocal of the base.