Chapter 6 - Percents and their applications. In this chapter, the learning objectives are: 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.
Chapter 6 Percents and Their Applications McGrawHill/Irwin ©2011 The McGrawHill Companies, All Rights Reserved #6 Percent and Their Applications Learning Unit Objectives LU6.1 Conversions Convert decimals to percents (including rounding percents), percents to decimals, and fractions to percents Convert percents to fractions 62 #6 Percent and Their Applications Learning Unit Objectives LU6.2 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 63 and increases Table 6.1 Bag of M&M’s Decimal Color Yellow Fraction (hundredth) 18 .33 55 Red 10 .18 55 Blue 9 .16 Blue 55 Orange 7 .13 55 Brown 6 .11 55 Green 5 .09 55 Total 55 1.00 55 = 1 64 Percent (hundredth) 32.73% 18.18% 16.36% 12.73% 10.91% 9.09% 100.00% 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 66 65 66% 800% Converting Decimals to Percents Step 1. Move decimal point 2 places to the right. You are multiplying by 100. If necessary add zeros .42.5 425 66 42.5% 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 % 17 67 0588235 0588235 5.88% Rounding Percents 3272727 ep St 2 p St e 0 0 0 55 = 18 55 32.73727% 32.73% 68 3 p e St 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% 69 824.4% 66 8.244 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 % 610 3 7 % 0025 0775 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 611 75% 20% 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% 612 14 15 1% 1 800 Converting Percents to Decimals 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 4 12.5% 613 12 1/2% 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 = $320,000 614 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? Rate = Portion Base R = $320, 000 $400,000 615 R = 80% 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) Base = Portion Rate B = $320,000 .80 616 B = $400,000 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 617 Rate of Percent 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 18.40 ounces, which was 15% more than a regular 1pound 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 Diff . between old and new TV price Base Old TV amount Rate = 2.40 oz 16.00 oz Rate = .15 or 15% Increase 618 Rate of Percent Decrease The increase in the price of sugar caused the M&M/Mars company to decrease the weight of each 1pound bag of M&M’s® to 12 ounces. What is the rate of percent decrease? Rate = Portion Diff . between old and new TV price Base Old TV amount Rate = 4 oz 16.00 oz Rate = .25 or 25% Decrease 619 ... Step 2. Add a percent symbol at the end of the number 66 6 5 66 % 800% Converting Decimals to Percents Step 1. Move decimal point 2 places to the right. You are multiplying by 100. If necessary add zeros .42.5 425 6 6 42.5% Rounding Percents... Step 2. Move decimal point 2 places to the left, You are dividing by 100. If necessary add zeros 66 % 6 9 824.4% 66 8.244 Converting Fractional Percents to Decimals Step 1. Convert a single fraction percent to its decimal ... rounding percents), percents to decimals, and fractions to percents Convert percents to fractions 6 2 #6 Percent and Their Applications Learning Unit Objectives LU6.2 Application of Percents Portion Formula List and define the key elements of the