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Math 101 Application of Mathematics

Math 101 Application 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.

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Math 101 Application of Mathematics

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  1. Math 101Application of Mathematics Lecture 7 Percents and Their Applications

  2. 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.

  3. Percent Percents are the result of expressing numbers as part of 100. Example: 10% = 10 out of 100

  4. 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%

  5. 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%

  6. 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%

  7. 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%

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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%

  13. 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%

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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)

  19. 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?

  20. 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)

  21. 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?

  22. 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)

  23. 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?

  24. 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)

  25. 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)

  26. 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)

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