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

Percents and their Applications in Business Chapter 6 Percents and their Applications in Business Copyright © 2003 by South-Western

Chapter 6, Percents and Their Applications in Business Outline Section I: Understanding and Converting Percents 6-1 Converting percents to decimals and decimals to percents. 6-2 Converting percents to fractions and fractions to percents. Section II: Using the Percentage Formula to Solve Business Problems 6-3 Solving for the portion. 6-4 Solving for the rate. 6-5 Solving for the base. 6-6 Determining rate of increase or decrease.

Chapter 6, Percents and Their Applications in Business (Cont.) Outline Section III: Solving Other Business Problems Involving Percents 6-6 Determining rate of increase or decrease. 6-7 Determining amounts in increase or decrease situations. 6-8 Understanding and solving problems involving percentage points.

Section I, Understanding and Converting Percents 6-1 Converting Percents to Decimals and Decimals to Percents Steps for Converting percent to a decimal: Step 1. Remove the percent sign Step 2. Divide by 100. Step 3. If the percent is a fraction, such as 3/8%, or a mixed number, such as 4 3/4%, first change the fraction to a decimal, then follow Steps 1 and 2 above. Step 4. If the percent is a fraction such sa 2/3%, which converts to repeating decimal, .66666, round the decimal to hundredths, .67, then follow Steps 1 and 2 above. 2/3 % = .67 % = .0067

EVERYBODY’S BUSINESS LEARNING TIP To divide a number by 100, move the decimal point two places to the left. Add zeros as needed. Remember, if there is no decimal point, it is understood to be to the right of the digit in the ones place. (24 = 24.)

Steps for Converting A Decimal or Whole Number to a Percent Step 1. Multiply by 100. Step 2. Add a percent to the number. Step 3. If there are fractions involved, such as ¾, convert them to decimals first, then proceed with Steps 1 and 2 above. ¾ = .75 = 75%

6-2 Converting a Percent to A Fraction Steps for Converting a Percent to a Fraction: Step 1 Remove the percent sign. Step 2. (If the percent is a whole number)Write a fraction with the percent as the numerator and 100 as the denominator, If that fraction is improper, change it to a mixed number. Reduce to lowest terms. or Step 2. (If the percent is a fraction)Multiply the number by 1/100 and reduce to lowest terms. Step 2. (If the percent is a decimal) Convert it to a fraction and multiply by 1/100. Reduce to lowest terms.

Steps for Converting Fractions or Mixed Numbers to Percents Step 1. Change the fraction to a decimal by dividing the numerator by the denominator. Step 2. Multiply by 100. (Move the decimal point two places to the right. Add zeros as needed.) Step 3. Write a percent sign after the number.

Section II, Using the Percentage formula to Solve Business Problems Steps of Solving Percentages Problems Step 1. Identify the two knowns and the one unknown. Step 2. Choose the formula that solves for that unknown. Step 3. Solve the equation by substituting the known values for the letters in the formula.

EVERYBODY’S BUSINESS 12 400 48 LEARNING TIP SHORTCUT Remember to use the % key on your calculator. 12 400 48 % X =

Section III, Solving Other Business Problems Involving Percents 6-6 Determining Rate of Increase or Decrease Step 1. Identify the original and the new amounts, and find the difference between them. Step 2. Using the rate formula, R = P divided by B, substitute the difference from Step 1 for the portion, and the original amount for the base. Step 3. Solve the equation for R. Remember, you answer will be in decimal form, which must be converted to a percent.

6-7 Determining Amounts in Increase of Decrease Situations Steps for Determining the new Amount After a Percentage Change: Step 1. In the formula Portion = rate X Base, substitute the original amount, or starting point, for the base. Step 2a. If the rate of change is an increase, add that rate to 100% to determine the rate. Step 2b. If the rate of change is a decrease, subtract that rate form 100% to determine the rate. Step 4. Solve the equation for the portion.

EVERYBODY’S BUSINESS LEARNING TIP Remember, if the rate of change is increase, add that rate to 100%. If that rate of change is a decrease, subtract that rate from 100%.

Steps for Determining the Original amount before a percentage Change: Step 1. In the formula Base = Portion divided by rate, substitute the new amount for the portion. Step 2a. If the rate of change is an increase, add that rate to 100% to determine the rate. Step 2b. If the rate of change is a decrease, subtract that rate from 100% to determine the rate. Step 3. Solve the equation for the base.

EVERYBODY’S BUSINESS LEARNING TIP Calculating percentage points is an application of the rate formula, Rate = Portion divided by Base, with the change in percentage points as the portion and original percentage points as the base.

Chapter 6 Portion = Rate x Base Rate = Portion  Base Base = Portion  Rate Copyright © 2003 by South-Western