Percents and Their Applications Chapter 6 Percents and Their Applications

Learning Unit Objectives #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

Learning Unit Objectives #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 and increases

Table 6.1 - 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 .66 66% 8 800%

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 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 .0588235 .0588235 5.88%

Rounding Percents .3272727 Step 1 55 18.000000 = Step 2 18 55 55 18.000000 = Step 2 18 55 32.73727% Step 3 32.73%

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. 824.4% 66% 8.244 .66

Converting Percents to Decimals Drop the percent symbol and move the decimal point 2 places to the left. .95 .00.95 .95% .0095

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). 3 4 7 % 1 % 4 .0775 .0025

Converting Fractional Percents to Decimals Step 1 .20% 5 1.00 = Step 2 1 % 5 .00.20 Step 3 .0020

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. 1 5 20% 3 4 75%

Converting Fractions to Percents .05 Step 1 20 1.00 = Step 2 1 20 .05. Step 3 5%

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 1% 8 156% 14 15 1 800 1

Converting a Whole Percent (or a Fractional Percent) to a Fraction 76 x 1 100 Step 1 Step 2 76% 76 100 Reduce to lowest terms 19 25 Step 3

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% 12 1/2% 1 8 1 8

Converting a Mixed or Decimal Percent to a Fraction 1 2 22 Step 1 Step 2 45 x 1 = 45 2 100 200 22.5% Reduce to lowest terms 9 40 Step 3

Application of Percents - Portion Formula Portion (P) = Base (B) x Rate (R) Assume you received a small bonus check of $100 and your company did not withhold any taxes. Compute taxes assuming a 20% in tax rate. Portion “is” Base “of” Rate “%”

Portion (P)= Base (B) x Rate (R) 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

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%

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 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.

Rate of Percent Decrease Original Price $1,500 Rate = Portion Diff . between old and new TV price Base Old TV amount Rate = $600 ($1,500-$900) $1,500 Rate = .40 or 40% Decrease New Price $900

Rate of Percent Increase Original Price $1,000 Rate = Portion Diff . between old and new TV price Base Old TV amount Rate = $200 ($1,200-$1,000) $1,000 Rate = .20 or 20% Decrease New Price $1,200

Problem 6-59: Solution: $30.50 $4.50 = 677.78%

Problem 6-61: Solution: $24,500 x 1.15 = $28,175

Problem 6-67: Solution: $19.95 $49.95 = 39.94%