# Columbus State Community College

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Columbus State Community College
Chapter 4 Section 1 Introduction to Signed Fractions

Introduction to Signed Fractions
Use a fraction to name the part of a whole that is shaded. Identify numerators, denominators, proper fractions, and improper fractions. Graph positive and negative fractions on a number line. Find the absolute value of a fraction. Write equivalent fractions.

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

Using Fractions to Represent Part of One Whole
EXAMPLE Using Fractions to Represent Part of One Whole Use fractions to represent the shaded and unshaded portions of each figure. 5 9 (a) 4 9

Using Fractions to Represent Part of One Whole
EXAMPLE Using Fractions to Represent Part of One Whole Use fractions to represent the shaded and unshaded portions of each figure. (b) 9 14 5 14

Using Fractions to Represent More than One Whole
EXAMPLE 2 Using Fractions to Represent More than One Whole Use a fraction to represent the shaded parts. 1 4 1 4 1 4 1 4 1 4 1 4 1 4 (a) 1 1 4 7 4 An area equal to 7 of the parts is shaded, so is shaded.

Using Fractions to Represent More than One Whole
EXAMPLE 2 Using Fractions to Represent More than One Whole Use a fraction to represent the shaded parts. 1 3 1 3 1 3 1 3 1 3 (b) 1 1 3 5 3 An area equal to 5 of the parts is shaded, so is shaded.

The 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.

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.

Identifying Numerators and Denominators
EXAMPLE Identifying Numerators and Denominators Identify the numerator and denominator in each fraction. 3 8  Numerator (a)  Denominator 9 5  Numerator (b)  Denominator

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.

Classifying Types of Fractions
EXAMPLE Classifying Types of Fractions Identify all proper and improper fractions in this list. 2 3 5 4 7 2 1 9 3 5 6 1 9 Recall that the numerator of an improper fraction is greater than or equal to the denominator. Recall that the numerator of a proper fraction is smaller than the denominator.

Graphing Positive and Negative Fractions
EXAMPLE Graphing Positive and Negative Fractions Graph each fraction on the number line. 4 7 (a) 1 -1

Graphing Positive and Negative Fractions
EXAMPLE Graphing Positive and Negative Fractions Graph each fraction on the number line. 1 7 (b) – 1 -1

Graphing Positive and Negative Fractions
EXAMPLE Graphing Positive and Negative Fractions Graph each fraction on the number line. 6 7 (c) – 1 -1

Finding the Absolute Value of Fractions
EXAMPLE Finding the Absolute Value of Fractions Find each absolute value: 3 4 | and 3 4 space 3 4 space 1 –1 The distance from 0 to and from 0 to is space, so = = 3 4 |

Equivalent Fractions Equivalent Fractions Fractions that represent the same number (the same point on a number line) are 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. a b a • c b • c = a b a ÷ c b ÷ c = or .

Writing Equivalent Fractions
EXAMPLE Writing Equivalent Fractions Write as an equivalent fraction with a denominator of 24. 5 6 5 • ? 6 • ? 5 • 4 6 • 4 20 (a) = = 24 7 8 7 • ? 8 • ? 7 • 3 8 • 3 21 (b) = = 24

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, = and = 1. Also recall that when any number is divided by 1, the result is the number. That is, = a. For example, = and = – 4. a 5 – 8 a 1 9 1 – 4 1 .

Using Division to Simplify Fractions
EXAMPLE Using Division to Simplify Fractions Simplify each fraction by dividing the numerator by the denominator. 2 2 2 (a) Think of as 2 ÷ 2. The result is 1, so = 1. 32 4 32 4 (b) Think of as – 32 ÷ 4. The result is – 8, so is – 8. 32 4 Keep the negative sign.

Using Division to Simplify Fractions
EXAMPLE Using Division to Simplify Fractions Simplify each fraction by dividing the numerator by the denominator. 8 1 8 1 8 1 (c) Think of as 8 ÷ 1. The result is 8, so = 8.

Note on Rational Numbers: Positive and Negative Fractions
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. a b a b 8 1

Introduction to Signed Fractions
Chapter 4 Section 1 – Completed Written by John T. Wallace