Math 101Application of Mathematics Lecture 7 Percents and Their Applications
Learning Objectives • Convert decimals to 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.
Percent Percents are the result of expressing numbers as part of 100. Example: 10% = 10 out of 100
Converting Decimals to Percents Problem: Convert .579 to a percentage Step 1 - Move the decimal point two places to the right. .579 = 57.9 Step 2 - Add a percent symbol at the end of the number. 57.9%
Converting Decimals to Percents – cont. Problem: Convert .7329 to a percentage Step 1 - Move the decimal point two places to the right. .7329 = 73.29 Step 2 - Add a percent symbol at the end of the number. 73.29%
Rounding Percents Problem: Convert 23/27 to a rounded percentage to the nearest hundredth percent Step 1 - Convert the fraction to a decimal; then make a percentage. 23/27 = .8518518 = 85.18518% Step 2 - Identify the specific digit being rounded. If the digit to the right of the identified digit is 5 or greater, round up the identified digit. The identified digit is 8 (hundredth place); since the digit to the right of the 8 is 5 or more, the digit is rounded up to a 9. Step 3 - Delete digits to the right of the identified digit. 85.19%
Rounding Percents – cont. Problem: Convert 12/13 to a rounded percentage to the nearest thousandth percent Step 1 - Convert the fraction to a decimal; then make a percentage. 12/13 = .92307692 = 92.307692% Step 2 - Identify the specific digit being rounded. If the digit to the right of the identified digit is 5 or greater, round up the identified digit. The identified digit is 7 (thousandth place); since the digit to the right of the 7 is 5 or more, the digit is rounded up to a 8. Step 3 - Delete digits to the right of the identified digit. 92.308%
Converting Percents to Decimals Problem: Convert 5% (5.%) to a decimal. Step 1 - Drop the percent symbol. 5. Step 2 - Move the decimal point two places to the left. .05
Converting Percents to Decimals – cont. Problem: Convert 33% (33.%) to a decimal. Step 1 - Drop the percent symbol. 33. Step 2 - Move the decimal point two places to the left. .33
Converting Fractional Percents to Decimals Problem: Convert 8 1/4% to a decimal Step 1 - Convert a single fractional percent to its decimal equivalent by dividing the numerator by the denominator. Then combine the whole number and the fractional percent. 1/4% = .25% 8 1/4% = 8.25% Step 2 - Drop the percent symbol; move the decimal point two places to the left. 8.25% = .0825
Converting Fractional Percents to Decimals – cont. Problem: Convert 22 3/8% to a decimal Step 1 - Convert a single fractional percent to its decimal equivalent by dividing the numerator by the denominator. Then combine the whole number and the fractional percent. 3/8% = .375% 22 3/8% = 22.375% Step 2 - Drop the percent symbol; move the decimal point two places to the left. 22.375% = .22375
Converting Fractions to Percents Problem: Convert 3/10 to a percentage. Step 1 - Divide the numerator by the denominator to convert the fraction to a decimal. 3/10 = .3 Step 2 - Move the decimal point two places to the right; add the percent symbol. .3 = 30%
Converting Fractions to Percents – cont. Problem: Convert 2/5 to a percentage. Step 1 - Divide the numerator by the denominator to convert the fraction to a decimal. 2/5 = .4 Step 2 - Move the decimal point two places to the right; add the percent symbol. .4 = 40%
Converting a Whole Percent (or a Fractional Percent) to a Fraction Problem: Convert 234% to a fraction Step 1 - Drop the percent symbol. 234 Step 2 - Multiply the number by 1/100 1/100 X 234 = 234/100 Step 3 - Reduce to lowest terms 234/100 = 2 34/100 = 2 17/50
Converting a Whole Percent (or a Fractional Percent) to a Fraction – cont. Problem: Convert 1278% to a fraction Step 1 - Drop the percent symbol. 1278 Step 2 - Multiply the number by 1/100 1/100 X 1278 = 1278/100 Step 3 - Reduce to lowest terms 1278/100 = 12-78/100 = 12-39/50
Converting a Mixed or Decimal Percent to a Fraction Problem: Convert 37 1/2% to a fraction Step 1 - Drop the percent symbol. 37 1/2 Step 2 - Change the mixed number to an improper fraction. 75/2 Step 3 - Multiply the number by 1/100. 1/100 X 75/2 = 75/200 Step 4 - Reduce to lowest terms. 75/200 = 3/8
Converting a Mixed or Decimal Percent to a Fraction- cont. Problem: Convert 15-3/5% to a fraction Step 1 - Drop the percent symbol. 15-3/5 Step 2 - Change the mixed number to an improper fraction. 78/5 Step 3 - Multiply the number by 1/100. 1/100 X 78/5 = 78/500 Step 4 - Reduce to lowest terms. 78/500 = 39/250
Terms and Key Formula Base (B) Number equal to 100% or the whole amount Rate (R) Percent equal to the Portion divided by the Base Portion (P) Number equal to some percentage of the Base Portion (P) = Base (B) x Rate (R)
Solving for Portion Problem: Computer sales are 70% of the total sales. Total sales are $100,000. What are the sales of the non-computer sales?
Solving for Portion - continued Step 1 - Set up the formula. P = $100,000 X .30 Step 2 - Calculate portion (sale of non-computers). P = $30,000 Portion (P) = Base (B) x Rate (R)
Solving for Rate Problem: Sales of computers are $60,000. Total sales are $300,000. What is the percent of computer sales compared to total sales?
Solving for Rate - continued Step 1 - Set up the formula. R = $60,000 $300,000 Step 2 - Calculate rate (percent of computer sales to total sales). R = 20% Portion (P) = Base (B) x Rate (R)
Solving for Base Problem: Computer sales are 20% of total sales. Sales of non-computer items are $300,000. What are the total sales of all items?
Solving for Base - continued Step 1 - Set up the formula. B = $300,000 .80 Step 2 - Calculate the base. B = $375,000 Portion (P) = Base (B) x Rate (R)
Calculating Percent Decrease Problem: ABC Company decreases the price of its product from $1,000 to $800. What is the percentage decrease? Formula: Rate = Portion(difference between old and new price) Base (old price) R = $1,000 - $800 $1,000 R = $200 $1,000 R = 20% Portion (P) = Base (B) x Rate (R)
Calculating Percent Increase Problem: ABC Company increases the price of its product from $1000 to $1,500. What is the percentage increase? Formula: Rate = Portion(difference between old and new price) Base (old price) R = $1,500 - $1,000 $1,000 R = $500 $1,000 R = 50% Portion (P) = Base (B) x Rate (R)
