Chapter 2 Multiplying and Dividing Fractions

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Chapter 2Multiplying and Dividing Fractions
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Chapter Outline

• Introduction to Fractions and Mixed Numbers
• Factors and Prime Factorization
• Simplest Form of a Fraction
• Multiplying Fractions
• Dividing Fractions

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2.1
Introduction to Fractions and Mixed Numbers
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Section Objectives

• Identifying Numerators and Denominators and
  Reviewing Division Properties for 0 and 1
• Writing Fractions to Represent Shaded Areas of
  Figures
• Identifying Proper Fractions, Improper Fractions,
  and Mixed Numbers
• Writing Mixed Numbers as Improper Fractions
• Writing Improper Fractions as Mixed Numbers or
  Whole Numbers

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Identifying Numerators and Denominators and
Reviewing Division Properties for 0 and 1
SOLUTION
EXAMPLE
Simplify .
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 5
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Writing Fractions to Represent Shaded Areas of
Figures
EXAMPLE
Write a fraction to represent the shaded part of
the following rectangle.
SOLUTION
4 Parts Considered
7 Equal Parts
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 6
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Identifying Proper Fractions, Improper Fractions,
and Mixed Numbers
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 7
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Writing Mixed Numbers as Improper Fractions
(step 1)
(step 1)
(step 2)
(step 2)
(step 3)
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 8
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Writing Improper Fractions as Mixed Numbers or
Whole Numbers
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 9
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2.2
Factors and Prime Factorization
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Section Objectives

• Finding Factors of Numbers
• Identifying Prime and Composite Numbers
• Finding Prime Factorizations

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Finding Factors of Numbers
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 12
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Identifying Prime and Composite Numbers
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 13
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Finding Prime Factorizations
because 42 is not a prime number we must divide
it by a prime number.
because 21 is not a prime number we must divide
it by a prime number.
because 7 is a prime number we can now write the
prime factorization of 84.
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 14
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2.3
Simplest Form of a Fraction
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Section Objectives

• Writing Fractions in Simplest Form
• Determining Whether Two Fractions Are Equivalent
• Solving Problems by Writing Fractions in Simplest
  Form

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Writing Fractions in Simplest Form
Both have a common factor of 2.
There are no more common factors.
The simplest form of is
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 17
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Determining Whether Two Fractions Are Equivalent
EXAMPLE
Determine whether are
equivalent.
SOLUTION
Since both have a common
simplified form of they are equivalent.
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 18
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Determining Whether Two Fractions Are Equivalent
EXAMPLE
Determine whether are
equivalent by cross multiplying.
SOLUTION
Since the cross products are not equal,
are not equivalent.
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 19
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Solving Problems by WritingFractions in Simplest
Form
EXAMPLE
There are 5280 feet in a mile. What fraction of
a mile is represented by 2640.
SOLUTION
Both 2640 and 5280 have a common factor of 2640.
The fraction of a mile represented by 2640 is
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 20
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2.4
Multiplying Fractions
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Section Objectives

• Multiplying Fractions
• Multiplying Fractions and Mixed Numbers or Whole
  Numbers
• Solving Problems by Multiplying Fractions

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Multiplying Fractions
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 23
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Multiplying Fractions and Mixed Numbers or Whole
Numbers
EXAMPLE
Multiply 10 by
SOLUTION
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 24
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Solving Problems by Multiplying Fractions
EXAMPLE
An estimate for the measure of an adults wrist
is of the waist size. If Jorge has a
34-inch waist, estimate the size of his wrist.
SOLUTION
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 25
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2.5
Dividing Fractions
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Section Objectives

• Finding Reciprocals of Fractions
• Dividing Fractions
• Dividing Fractions and Mixed Numbers
• Solving Problems by Dividing Fractions

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Finding Reciprocals of Fractions
90
10
9



1
90
9
10
11
1
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 28
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Dividing Fractions

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3
5
3
5
2
5






16
2
8
2
8
3
8
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 29
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Dividing Fractions and Mixed Numbers
EXAMPLE
Divide
SOLUTION
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 30
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Solving Problems by Dividing Fractions
EXAMPLE
If there are grams of fat in 4 ounces
of lean hamburger meat, how many grams of fat are
in an ounce?
SOLUTION
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 31