Ch 4 Sec 1: Slide #1

Columbus State Community College

Chapter 4 Section 1

Introduction to Signed Fractions

Ch 4 Sec 1: Slide #2

Introduction to Signed Fractions

1. Use a fraction to name the part of a whole that is shaded.

2. Identify numerators, denominators, proper fractions, and improper fractions.

3. Graph positive and negative fractions on a number line.

4. Find the absolute value of a fraction.

5. Write equivalent fractions.

Ch 4 Sec 1: Slide #3

Fractions

Fractions

A fraction is a number of the form where a and b are integers and b is not 0.

ab

Ch 4 Sec 1: Slide #4

Using Fractions to Represent Part of One Whole

Use fractions to represent the shaded and unshaded portions of each

figure.

(a)

EXAMPLE 1 Using Fractions to Represent Part of One Whole

59

49

Ch 4 Sec 1: Slide #5

Using Fractions to Represent Part of One Whole

Use fractions to represent the shaded and unshaded portions of each

figure.

(b)

EXAMPLE 1 Using Fractions to Represent Part of One Whole

514

914

Ch 4 Sec 1: Slide #6

Using Fractions to Represent More than One Whole

Use a fraction to represent the shaded parts.

(a)

EXAMPLE 2 Using Fractions to Represent More than One Whole

14

1

14

14

14

14

14

14

An area equal to 7 of the parts is shaded, so is shaded.14

74

Ch 4 Sec 1: Slide #7

Using Fractions to Represent More than One Whole

Use a fraction to represent the shaded parts.

(b)

EXAMPLE 2 Using Fractions to Represent More than One Whole

13

1

13

13

13

13

An area equal to 5 of the parts is shaded, so is shaded.13

53

Ch 4 Sec 1: Slide #8

The Numerator and Denominator

Numerator and Denominator

The denominator of a fraction shows the number of equal parts in the whole, and the numerator shows how many parts are being considered.

Ch 4 Sec 1: Slide #9

Fraction Bar

NOTE

Recall that a fraction bar, –, is a symbol for division and division by 0 is undefined. Therefore a fraction with a denominator of 0 is also undefined.

Ch 4 Sec 1: Slide #10

Identifying Numerators and Denominators

Identify the numerator and denominator in each fraction.

(a)

EXAMPLE 3 Identifying Numerators and Denominators

38

Numerator Denominator

(b) 95

Numerator Denominator

Ch 4 Sec 1: Slide #11

Proper and Improper Fractions

Proper and Improper Fractions

If the numerator of a fraction is smaller than the denominator, the fraction is a proper fraction. A proper fraction is less than 1.

If the numerator of a fraction is greater than or equal to the denominator, the fraction is an improper fraction. An improper fraction is greater than or equal to 1.

Ch 4 Sec 1: Slide #12

Recall that the numerator of a proper fraction is smaller than the

denominator.

23

19

35

Recall that the numerator of an improper fraction is greater than or

equal to the denominator.

Classifying Types of Fractions

Identify all proper and improper fractions in this list.

EXAMPLE 4 Classifying Types of Fractions

54

72

61

99

Ch 4 Sec 1: Slide #13

0 1-1

Graphing Positive and Negative Fractions

Graph each fraction on the number line.

EXAMPLE 5 Graphing Positive and Negative Fractions

(a) 47

Ch 4 Sec 1: Slide #14

0 1-1

Graphing Positive and Negative Fractions

Graph each fraction on the number line.

EXAMPLE 5 Graphing Positive and Negative Fractions

(b) – 17

Ch 4 Sec 1: Slide #15

0 1-1

Graphing Positive and Negative Fractions

Graph each fraction on the number line.

EXAMPLE 5 Graphing Positive and Negative Fractions

(c) – 67

Ch 4 Sec 1: Slide #16

Finding the Absolute Value of Fractions

EXAMPLE 6 Finding the Absolute Value of Fractions

0 1–1

Find each absolute value: . 34| | and –

34| |

34

space34

space

The distance from 0 to and from 0 to is space,

so = = .34| | –

34| |

34

–34

34

34

Ch 4 Sec 1: Slide #17

Equivalent Fractions

Equivalent Fractions

Fractions that represent the same number (the same point on a

number line) are equivalent fractions.

Ch 4 Sec 1: Slide #18

Writing Equivalent Fractions

Writing Equivalent Fractions

If a, b, and c are numbers (and b and c are not 0), then

In other words, if the numerator and denominator of a fraction are

multiplied or divided by the same nonzero number, the result is an

equivalent fraction.

ab

a • cb • c

=ab

a ÷ cb ÷ c

=or .

Ch 4 Sec 1: Slide #19

24

Writing Equivalent Fractions

EXAMPLE 7 Writing Equivalent Fractions

Write as an equivalent fraction with a denominator of 24.

56

20= =

5 • ?6 • ?5 • 46 • 4

(a)

2478

21= =

7 • ?8 • ?7 • 38 • 3

(b) – – –

Ch 4 Sec 1: Slide #20

Division Properties

Division Properties

If a is any number (except 0), then = 1. In other words, when a

nonzero number is divided by itself, the result is 1.

For example, = 1 and = 1.

Also recall that when any number is divided by 1, the result is the

number. That is, = a.

For example, = 9 and = – 4.

55

.

– 8– 8

aa

a1

91

– 41

Ch 4 Sec 1: Slide #21

Using Division to Simplify Fractions

EXAMPLE 8 Using Division to Simplify Fractions

Simplify each fraction by dividing the numerator by the denominator.

22

Think of as 2 ÷ 2. The result is 1, so = 1.(a)22

22

324

Think of as – 32 ÷ 4.

The result is – 8, so is – 8.

(b) – 324

–

324

–

Keep the negative sign.

Ch 4 Sec 1: Slide #22

Using Division to Simplify Fractions

EXAMPLE 8 Using Division to Simplify Fractions

Simplify each fraction by dividing the numerator by the denominator.

81

Think of as 8 ÷ 1. The result is 8, so = 8.(c)81

81

Ch 4 Sec 1: Slide #23

Note on Rational Numbers: Positive and Negative Fractions

NOTE

The title of this chapter is “Rational Numbers: Positive and Negative

Fractions.” Rational numbers are numbers that can be written in the

form , where a and b are integers and b is not 0.

Remember an integer can be written in the form (8 can be

written as ).

So rational numbers include all the integers and all the fractions.

ab a

b81

Ch 4 Sec 1: Slide #24

Introduction to Signed Fractions

Chapter 4 Section 1 – Completed

Written by John T. Wallace