McGraw-Hill/Irwin ©2011 The McGraw-Hill Companies, All Rights Reserved Chapter 6 Percents and Their Applications

Convert decimals to percents (including rounding percents), percents to decimals, and fractions to percents 2. Convert percents to fractions Percent and Their Applications #6 Learning Unit Objectives Conversions LU6.1

List and define the key elements of the portion formula 2. Solve for one unknown of the portion formula when the other two key elements are given 3. Calculate the rate of percent decreases and increases Percent and Their Applications #6 Learning Unit Objectives Application of Percents -- Portion Formula LU6.2

6-4 Table Bag of M&M’s Decimal Percent ColorFraction (hundredth)(hundredth) Yellow Yellow % 55 Red Red % 55 Blue Blue % 55 Orange Orange % 55 Brown Brown % 55 Green Green % 55 Total Total % 55 = 1

6-5 Converting Decimals to Percents.66 66% 8 800% 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

6-6 Converting Decimals to Percents % Step 1. Move decimal point 2 places to the right. You are multiplying by 100. If necessary add zeros.

6-7 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. Delete digits to the right of the identified digit. 1 %

6-8 Rounding Percents % % = Step 1 Step 2 Step 3

6-9 Converting Percents to Decimals 66% % 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.

6-10 Converting Fractional Percents to Decimals % Step 1. Convert a single fraction percent to its decimal equivalent by dividing the numerator by the denominator. 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 %

6-11 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. 20% 1515

6-12 Converting a Whole Percent (or a Fractional Percent) to a Fraction 156% 1 1%81%8 Step 1. Drop the percent symbol. Step 2. Multiply the number by 1/100. Step 3. Reduce to lowest terms

6-13 Converting Percents to Decimals 12.5% /2% 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 fractional equivalent and continue with Steps 1 to

6-14 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

6-15 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? Rate = Portion Base R = $320, 000 $400,000 R = 80%

6-16 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 B = $320, B = $400, ,000 is 80% of base ( )

6-17 Calculating Percent Decreases and Increases Step 1. Find the difference between amounts (such as advertising costs). Step 2. Divide step 1 by the original amount (the base): R = P / B. Be sure to express your answer in percent.

6-18 Rate of Percent Increase Rate = Portion Diff. between old and new TV price Base Old TV amount Rate = 2.40 oz oz Rate =.15 or 15% Increase Sheila Leary went to her local supermarket and bought the bag of M&M’s® shown in Figure 6.1. The bag gave its weight as 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.

6-19 Rate of Percent Decrease Rate = Portion Diff. between old and new TV price Base Old TV amount Rate = 4 oz oz Rate =.25 or 25% 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?