Chapter 1 Section 1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

Chapter Chapter 11Section Section 11

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley


Fractions

Learn the definition of factor.Write fractions in lowest terms.Multiply and divide fractions.Add and subtract fractions.Solve applied problems that involve fractions.Interpret data in a circle graph.

11

44

33

22

66

55

1.11.11.11.1


Definitions

Natural numbers: 1, 2, 3, 4,…,

, ,NumeratorFraction BarDenominator

Ex. The improper fraction can be written , a mixed number.

1

2

2

3

15

7

12

5

22

5

Whole numbers: 0, 1, 2, 3, 4,…,

Fractions:

Proper fraction: has a value of less then 1; the numerator is smaller than or equal to the denominator.

Improper fraction: has a value of greater then 1; the numerator is larger than the denominator.

Mixed number: is a combination of a whole number and a fraction.

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Objective 11

Learn the definition of factor.

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Learn the definition of factor.

In the statement 2 × 9 = 18, the numbers 2 and 9 are called factors. Other factors of 18 include 1, 3, 6, and 18. The number 18 in this statement is called a product.

The number 18 is factored by writing it as a product of two or more numbers.

Ex. 6 ·3, 18 × 1, (2)(9), or 2(3)(3)

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Learn the definition of factor. (cont’d)

A natural number greater than 1 is prime if its products include only 1 and itself.

Ex. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37,…

A natural number greater than 1 that is not prime is called a composite number.

Ex. 4, 6, 8, 9, 10, 12,…

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EXAMPLE 1

Starting with the smallest prime factor is not necessary. No matter which prime factor is started with the same prime factorization will always be found.

Write 90 as the product of prime factors.

Solution:

2 45 2 3 15 2 3 3 5

Factoring Numbers

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Objective 22

Write fractions in lowest terms.

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A fraction is in lowest terms, when the numerator and denominator have no common factors other than 1.

Basic Principle of Fractions:If the numerator and denominator are multiplied or divided by the same nonzero number, the fraction remains unchanged.

Writing fractions in lowest terms.

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Writing a Fraction in Lowest Terms:

Step 1: Write the numerator and the denominator as the product of prime factors.

Writing fractions in lowest terms. (cont’d)

Step 2: Divide the numerator and denominator by the greatest common factor, the product of all

factors common to both.

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EXAMPLE 2

When writing fractions in lowest terms, be sure to include the factor 1 in the numerator or an error may result.

Write in lowest terms.

Solution:

=

12

20

3 4

45

3

5

Writing Fractions in Lowest Terms

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Objective 33

Multiply and divide fractions.

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Multiply and divide fractions.

Multiplying Fractions:

If and are fractions, then · = .a

b

a

b

c

d

c

d

a c

b d

That is, to multiply two fractions, multiply their numerators and then multiply their denominators.

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Dividing Fractions:

If and are fractions, then ÷ = .a

b

a

bc

d

c

da d

b c

Multiply and divide fractions. (cont’d)

That is, to divide two fractions, is to multiply its reciprocal; the fraction flipped upside down.

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EXAMPLE 3

Find each product, and write it in lowest simple terms.

Solution:

2

3

7 3 2

3 2 7

2

3

1 33 1

3 4

10 7

3 4

5 7

3

2

22

35

6

55

6

7 12

9 14

or

Multiplying Fractions

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EXAMPLE 4

Find each quotient, and write it in lowest terms.

Solution:

or9 3

10 5

3 53

2 5 3

9 5

10 3

3

2

11

2

3 12 3

4 3

11 10

4 3 11 3

4 10

33

40

Dividing Fractions

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Objective 44

Add and subtract fractions.

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Add and subtract fractions.

Adding Fractions:

If and are fractions, then + = .a

b

c

b

a

b

c

b

a c

b

That is, to find the sum, the result of adding the numbers, having the same denominator, add the numerators and keep the same denominator.

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Add and subtract fractions. (cont’d)

If the fractions do not share a common denominator. The least common denominator (LCD) must first be found as follows:

Step 1: Factor each denominator.

Step 2: Use every factor that appears in any factored form. If a factor is repeated, use the largest number of repeats in the LCD.

Step 3: Find the number that can be multiplied by the denominator to get the LCD and multiply the

numerator and denominator by that number.

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Add and subtract fractions. (cont’d)

Subtracting Fractions:

If and are fractions, then .a

bc

b

a c a c

b b b

If fractions have different denominators, find the LCD using the same method as with adding fractions.

That is, to find the difference, the result of subtracting the numbers, between two fractions having the same denominator subtract the numerators and keep the same denominator.

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EXAMPLE 5

Find the sum , and write it in lowest terms.

Solution:

1 5

9 9

1 5

9

6

9

3

2

3

3

2

3

Adding Fractions with the Same Denominator

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Find each sum, and write it in lowest terms.

EXAMPLE 6

7 2

30 45

21 4

90

25

90

5

3 3

5

2 5

5

18

5 14 2

6 3 29 14

6

43

6

17

6or

Adding Fractions with DifferentDenominators

Solution:

3 2

3 2

7 2

30 45

29 7

6 23

2

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EXAMPLE 7 Subtracting Fractions

Find each difference, and write it in lowest terms.

EXAMPLE 7

3 1

10 4

3 13 1

8 2

6 5

20

1

20

27 12

8

15

8

71

8or

Solution:2 5

2

3 1

0 51 4

27 3

8 42

4

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Objective 55

Solve applied problems that involve fractions.

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22

14200

500

galft

ft

EXAMPLE 8

A gallon of paint covers 500 ft2. To paint his house, Tran needs enough paint to cover 4200 ft2. How many gallons of paint should he buy?

Solution:

Tran needs to buy 9 gallons of paint.

22 500

42001

ftft

gal 4200

500

gal

142

05

00

10

gal

42

.5

gal2

85

Adding Fractions to Solve an Applied Problem

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Objective 66

Interpret data in a circle graph.

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EXAMPLE 9

In November 2005, there were about 970 million Internet users world wide.

Using a Circle Graph to Interpret Information

How many actual Internet users were there in Europe?

Estimate the number of Internet users in Europe.

Which region had the second-largest number of Internet Users in November 2005?

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Solution:

a) Europe

b)

c)

EXAMPLE 9 Solutions

31000 300

10million million

3970 291

10million million

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Chapter 1 Section 1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

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Transcript of Chapter 1 Section 1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.