Contemporary Mathematics for Business and Consumers Third Edition By: Robert A. Brechner COPYRIGHT © 2003 by South-Western, a division of Thomson Learning. Thomson LearningTM is a trademark used herein under license. ALL RIGHTS RESERVED. No part of this work covered by the copyright hereon may be reproduced or used in any form or by any means–graphic, electronic, or mechanical, including photocopying, recording, taping, Web distribution or information storage and retrieval systems–without the written permission of the publisher. For permission to use material from this text or product, contact us by Tel (800) 730-2214 Fax (800) 730-2215 http://www.thomsonrights.com

Chapter 2 Fractions Copyright © 2003 by South-Western

Outline CHAPTER 2 Fractions SECTION I: Understanding and Working with Fractions 2-1 Distinguishing among the various types of fractions. 2-2 Converting improper fractions to whole or mixed numbers. 2-3 Converting mixed numbers to improper fractions. 2-4 Reducing fractions to lowest terms using a. Inspection and the rules of divisibility. b. The greatest common divisor method. 2-5 Raising fractions to higher terms. SECTION II: Addition and Subtraction of Fractions 2-6 Determining the least common denominator (LCD) of two or more fractions. 2-7 Adding fractions and mixed numbers.

CHAPTER 2 Fractions (cont.) Outline SECTION II: Addition and Subtraction of Fractions 2-8 Subtracting factions and mixed numbers SECTION III: Multiplication and Division of Fractions 2-9 Multiplying fractions and mixed numbers. 2-10 Dividing fractions and mixed numbers.

KEY TERMS Chapter 2, Section I Numerator : The number on top of the division line of a fraction. It represents the divided in the division. In the fraction ¼, 1 is the denominator. Denominator: The number on the bottom of the division line of a fraction. It represents the divisor in the division. In the fraction 1/4 , 4 is the denominator. Division line: The horizontal or slanted line separating the numerator from the denominator. The symbol representing “divided by” in a fraction. In the fraction ¼, the line between the 1 and the 4 is the division line. Common or Proper fraction: A fraction in which the numerator is smaller to or less than the numerator. Represents one whole unit or more. The fraction 4/1 is an improper fraction. Mixed Number: A number that combines a whole number with a proper fraction. The fraction 101/4 is a mixed number.

Everybody’s Business Learning Tip Answer: 1/9, 12, 3 1/2 A complex fraction is one in which the numerator of the denominator, or both, are fractions Examples: 2/3 9 7/8 6 ¾ 1/4 Answer: 1/9, 12, 3 1/2

2-2 Converting Improper Fractions to Whole or Mixed Numbers Steps for Converting Improper Fractions to Whole or Mixed Numbers. Step 1. Divide the Numerator of the improper fraction by the denominator. Step 2a. If there is no remainder, the improper fraction becomes a whole number. Step 2b. If there is a remainder, write the whole number and then write the fraction. Whole number = Remainder Divisor

2-3 Converting Mixed Numbers to Improper Fractions Steps for Converting a Mixed Number to an Improper Fraction: Step 1. Multiply the denominator by the whole number. Step 2. Add the numerator to the product from Step 1. Step 3. Place the total from Step 2 as the “new” numerator. Step 4. Place the original denominator as the “new” denominator.

2-4 Reducing Fractions to Lowest Terms Steps for Determining the Greatest Common Divisor of a Fraction: Step 1. Divide the number of the fractin into the denominator. Step 2. Take the remainder from Step 1 and divide it into the divisor from Step 1. Step 3. Repeat this division process until the remainder is either 0 or 1. If the remainder is 0, the last divisor is the greatest common divisor. If the remainder is 1, the fraction cannot be reduced and is therefore in lowest terms

2-5 Raising Fractions to Higher Terms Steps for Raising A Fraction To A New Denominator: Step 1. Divide the original denominator into the new denominator. The resulting quotient is the common multiple that raises the fraction. Step 2. Multiply the numerator and the denominator of the original fraction by the common multiple.

Section II, Addition And Subtraction of Fractions 2-6 Determining the last Common Denominator (LCD) of Two or More Fractions Steps for Finding the Least Common Denominator of Two or More Fractions: Step 1. Write all the denominators in a row. Step 2. Find a prime number that divides evenly into any of the denominators. Write that prime number to the left of the row, and divide. Place all quotients and undivided numbers in the next row down. Step 3. Repeat this process until the new row contains all ones. Step 4. Multiply all the prime numbers oin the left together to get the LCD of the fractions.

Answer to fraction problems should always be reduced to lowest terms EVERYBODY’S BUSINESS Learning Tip Answer to fraction problems should always be reduced to lowest terms

2-7 Adding Fractions with the Same Denominator Steps for Adding Like Fractions: Step 1. Add all the numerators and place the total over the original denominator. Step 2. If the result is a proper fraction, reduce it to lowest terms. Step 3. If the result is an improper fraction, convert it to a whole or a mixed number.

Adding Fractions With Different Denominators Steps for Adding Unlike Fractions: Step 1. Find the least common denominator of the unlike fractions. Step 2. Raise all fractions to the terms of the LCD, making them like fractions. Step 3. Follow the same procedure used for adding like fractions.

Adding Mixed Numbers Steps for Adding Mixed Numbers: Step 1. Add the fractional parts. If the sum is an improper fraction, convert it to a mixed number. Step 2. Add the whole number. Step 3. Add the fraction from Step 1 to the whole number from Step 2. Step 4. Reduce the sum to lowest terms.

2-8 Subtracting Fractions and Mixed Numbers Steps for Subtracting Like Fractions: Step 1. Subtract the numerators and place the difference over the original denominator. Step 2. Reduce the fractions to lowest terms. Steps for Subtracting Unlike Fractions: Step 1. Find the least common denominator. Step 2. Raise each fractin to the denominator of the LCD. Step 3. Follow the same procedure used to subtract like fractions.

Subtracting Mixed Numbers Steps for Subtracting Mixed Numbers: Step 1. If the fractions of the mixed numbers have the same denominator, subtract them and reduce to lowest terms. Step 2. If the fractions do not have the same denominator, raise them to the denominator of the LCD, and subtract. Step 3. Subtract the whole numbers. Step 4. Add the difference of the whole numbers and the difference of the fractions.

SECTION III, Multiplications and Division of Fractions 2-9 Multiplying Fractions: Step 1. Multiply all numerators to form the new numerator. Step 2. Multiply all the denominators to form the new denominator. Step 3. If necessary, reduce the answers to lowest terms.

SECTION III, Multiplications and Division of Fractions 2-9 Steps for Applying Cancellation: Step 1. Find a common factor that devides evenly into at least one of the denominators and one of the numerators. Step 2. Divide that common factor into the denominator and numerator, thereby reducing it. Step 3. Repeat this process until there are no more common factors. Step 4. Multiply the fractions as before.

Multiplying Mixed Numbers 2-9 Steps for Multiplying Mixed Numbers: Step 1. Convert all mixed numbers to improper fractions. Step 2. Multiply as before, using cancellation wherever possible.. Step 3. If the answer is an improper fraction, convert it to a whole or mixed number. Step 4. Reduce to lowest terms..

2-10 Dividing Fractions and Mixed Numbers Steps for Dividing Fractions: Step 1. Identify the fraction that is the divisor, and invert. Step 2. Change the”divide by” sign, to a “multiplied by” sign x. Step 3. Multiply the fractions. Step 4. Reduce the answer to lowest terms.

The number after the “divide sign” is the divisor. EVERYBODY’S BUSINESS Learning Tip The number after the “divide sign” is the divisor. This is the number that gets inverted when dividing.