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 1 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 1 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 3 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 4 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 5 Graphing Positive and Negative Fractions Graph each fraction on the number line. 4 7 (a) 1 -1

Graphing Positive and Negative Fractions EXAMPLE 5 Graphing Positive and Negative Fractions Graph each fraction on the number line. 1 7 (b) – 1 -1

Graphing Positive and Negative Fractions EXAMPLE 5 Graphing Positive and Negative Fractions Graph each fraction on the number line. 6 7 (c) – 1 -1

Finding the Absolute Value of Fractions EXAMPLE 6 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 7 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, = 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. a 5 – 8 a 1 9 1 – 4 1 .

Using Division to Simplify Fractions EXAMPLE 8 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 8 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