Lecture Practical business math procedures (11/e) - Chapter 6: Percents and their applications

After completing this chapter, students will be able to: Convert decimals to percents (including rounding percents), percents to decimals, and fractions to percents; convert percents to fractions; list and define the key elements of the portion formula; solve for one unknown of the portion formula when the other two key elements are given; calculate the rate of percent decreases and increases.

Percents and Their Applications McGraw­Hill/Irwin Chapter Six Copyright © 2014 by The McGraw­Hill Companies, Inc. All rights reserved Learning unit objectives LU 6-1: Conversions Convert decimals to percents (including rounding percents), percents to decimals, and fractions to percents Convert percents to fractions LU 6-2: Application of Percents—Portion Formula List and define the key elements of the portion formula Solve for one unknown of the portion formula when the other two key elements are given Calculate the rate of percent decreases and increases 6­2 Table 6.1 - Bag of M&M’s Color Yellow Red Blue Orange Brown Green Total Decimal Percent Fraction (hundredth) (hundredth) 55 10 55 55 55 18 33 18 32.73% 18.18% 55 16 16.36% 13 12.73% 11 10.91% 55 55 55 = 09 9.09% 1.00 100.00% 6­3 Converting Decimals to Percents Step Move decimal point places to the right You are multiplying by 100 If necessary, add zeros Step Add a percent symbol at the end of the number 66 % 66 Step Step 800 % Step Step 6­4 Rounding Percents Step When you convert from a fraction or decimal, be sure your answer is in percent before rounding Step Identify the specific digit If the digit to the right of the identified digit is or greater, round the identified digit Step Delete digits to the right of the identified digit % 0588235 0588235 5.88% 17 6­5 Rounding Percents p e St 55 18 55 18 00 00 3272727 St e p = 32.73727% 32.73% ep t S 6­6 Converting Percents to Decimals Step Drop the percent symbol Step Move decimal point places to the left You are dividing by 100 If necessary, add zeros 66% 824.4% 66 824.4 66 8.244 6­7 Converting Fractional Percents to Decimals Step Convert a single fraction percent to its decimal equivalent by dividing the numerator by the denominator Step If a fractional percent is combined with a whole number (mixed fractional percent) convert the fractional percent first Then combine the whole number and the fractional percent Step Drop the percent symbol; move the decimal point two places to the left (this divides the number by 100) % 1/4 = 0025 25 3% 31 / = 07.75 0775 6­8 Converting Fractions to Percents Step Divide the numerator by the denominator to convert the fraction to a decimal Step Move decimal point places to the right; add the percent symbol 75% 3/4 = 75 1/5 = 20% 20 6­9 Converting a Whole Percent (or a Fractional Percent) to a Fraction Step Drop the percent symbol Step Multiply the number by 1/100 Step Reduce to lowest terms 156% 156 156 X /100 = 156 100 1% = 56 100 X1 /100 = 14 25 800 6­10 Converting Percents to Decimals Step Drop the percent symbol Step Change the mixed percent to an improper fraction Step Multiply the number by 1/100 Step Reduce to lowest terms Note: If you have a mixed or decimal percent, change the decimal portion to fractional equivalent and continue with Steps to 12 12.5% = % = 12 % = 25 X 25 = 100 X 1 25 = 200 = 25 200 = 6­11 Solve Percents with the Portion Formula   When solving problems involving portion, base, or rate, you must give two of these elements Portion (P) = Base (B) x Rate (R) 6­12 Solving for Portion Sales of Milk Chocolate M&M’s® are 80% of total M&M’s® sales Total M&M’s® sales are $400,000 What are the sales of Milk Chocolate M&M’s®? Portion (P) = Base (B) x Rate (R) P = $400,000 x 80 P = $320,000 6­13 Solving for Base Sales of Peanut and other M&M’s® chocolate candies are 20% of total M&M’s® sales Sales of Milk Chocolate M&M’s® sales are $320,000 What are the total sales of all M&M’s®? Base = Portion Rate $320,000 80 320,000 is 80% of base (1.00 - 20) Base = B = $400,000 6­14 Solving for Rate Sales of Milk Chocolate M&M’s® are $320,000 Total M&M’s® sales are $400,000 What is the percent of Milk Chocolate M&M’s® sales compared to total M&M’s® sales? Portion Base $320, 000 $400,000 Rate =R = 80% Rate = 6­15 Calculating Percent Decreases and Increases Step Find the difference between amounts (such as advertising costs) Step Divide step by the original amount (the base): R = P / B Be sure to express your answer in percent 6­16 Rate of Percent Increase Sheila Leary went to her local supermarket and bought a bag of M&M’s® The bag gave its weight as 18.40 ounces, which was 15% more than a regular 1-pound bag of M&M’s® Sheila, who is a careful shopper, wanted to check and see if she was actually getting a 15% increase Rate = Portion Base Difference between old and new amount Old amount Rate = 2.40 oz 16.00 oz Rate = 15 or 15% increase 6­17 Rate of Percent Decrease The increase in the price of sugar caused the M&M/Mars company to decrease the weight of each 1-pound bag of M&M’s® to 12 ounces What is the rate of percent decrease? Rate = Portion Base Rate = Difference between old and new amount Old amount oz 16.00 oz Rate = 25 or 25% decrease 6­18 ... objectives LU 6-1 : Conversions Convert decimals to percents (including rounding percents) , percents to decimals, and fractions to percents Convert percents to fractions LU 6-2 : Application of Percents? ??Portion... supermarket and bought a bag of M&M’s® The bag gave its weight as 18.40 ounces, which was 15% more than a regular 1-pound bag of M&M’s® Sheila, who is a careful shopper, wanted to check and see if... identified digit % 0588235 0588235 5.88% 17 6­5 Rounding Percents p e St 55 18 55 18 00 00 3272727 St e p = 32.73727% 32.73% ep t S 6­6 Converting Percents to Decimals Step Drop the percent symbol Step