Percents and Their Applications Chapter Three McGraw-Hill/Irwin Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.

Learning unit objectives LU 3-1: Conversions Convert decimals to percents (including rounding percents), percents to decimals, and fractions to percents. Convert percents to fractions. LU 3-2: 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.

Table 3.1 - Bag of M&M’s Decimal Percent Color Fraction (hundredth) (hundredth) Yellow 18 .33 32.73% 55 Red 10 .18 18.18% Blue 9 .16 16.36% Orange 7 .13 12.73% Brown 6 .11 10.91% Green 5 .09 9.09% Total 55 1.00 100.00% 55 = 1

Converting Decimals to Percents Step 1. Move decimal point 2 places to the right. You are multiplying by 100. If necessary, add zeros. Step 2. Add a percent symbol at the end of the number. 800 % .66 66 % 8 Step 2 Step 2 Step 1 Step 1

Rounding Percents Step 1. When you convert from a fraction or decimal, be sure your answer is in percent before rounding. Step 2. Identify the specific digit. If the digit to the right of the identified digit is 5 or greater, round the identified digit. Step 3. Delete digits to the right of the identified digit. 18 55 .3272727 32.72727% 32.73% 3-5

Converting Percents to Decimals Step 1. Drop the percent symbol. Step 2. Move decimal point 2 places to the left. You are dividing by 100. If necessary, add zeros. 66% 66 .66 824.4% 824.4 8.244 3-6

Converting Fractional Percents to Decimals Step 1. Convert a single fractional percent to its decimal equivalent by dividing the numerator by the denominator. If necessary, round the answer. Step 2. 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 3. Drop the percent symbol; move the decimal point two places to the left (this divides the number by 100). 1 % 5 7 % 3 4 1 / 5 = .0020 31 / 4 = .20 .0775 07.75 3-7

Converting Fractions to Percents Step 1. Divide the numerator by the denominator to convert the fraction to a decimal. Step 2. Move decimal point 2 places to the right; add the percent symbol. 3 4 1 5 75% 3 / 4 = 1 / 5 = 20% .75 .20 3-8

Converting a Whole Percent (or a Fractional Percent) to a Fraction Step 1. Drop the percent symbol. Step 2. Multiply the number by 1/100. Step 3. Reduce to lowest terms. 156% 156 156 X 1 /100 = 14 25 156 100 56 100 1 = 1 1% 8 1 8 1 800 1 X 8 1 /100 = 3-9

Converting a mixed or decimal Percent to a fraction Step 1. Drop the percent symbol. Step 2. Change the mixed percent to an improper fraction. Step 3. Multiply the number by 1/100. Step 4. Reduce to lowest terms. Note: If you have a mixed or decimal percent, change the decimal portion to its fractional equivalent and continue with Steps 1 to 4. 12 1 2 % = 25 2 X 1 100 = 1 8 25 200 = 12 1 2 % = 12.5% = 25 2 X 1 100 = 1 8 25 200 = 3-10

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) 3-11

Base (B) x Rate (R) = Portion (P) 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®? Base (B) x Rate (R) = Portion (P) $400,000 x .80 = P P = $320,000 3-12

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 Rate = $320, 000 $400,000 R = 80% Rate = 3-13

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®? 320,000 is 80% of base (1.00 -- .20) Portion Rate $320,000 .80 B = $400,000 Base = Base = 3-14

Calculating Percent increases and decreases Step 1. Find the difference between amounts (such as sales). Step 2. Using the formula B x R = P, solve for R. Be sure to express your answer in percent. 3-15

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 2.40 oz 16.00 oz Rate = Rate = .15 or 15% increase 3-16

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 Difference between old and new amount Old amount 4 oz 16.00 oz Rate = Rate = .25 or 25% decrease 3-17