1. Percents Section 2-9

2. Goals Goal To solve percent problems using proportions. To solve percent problems using the percent equation. Rubric Level 1 – Know the goals. Level 2 – Fully understand the goals. Level 3 – Use the goals to solve simple problems. Level 4 – Use the goals to solve more advanced problems. Level 5 – Adapts and applies the goals to different and more complex problems.

3. Vocabulary Percent

4. Definition Another common application of proportions is percents. Percent - a ratio that compares a number to 100. Example:

5. To find the fraction equivalent of a percent write the percent as a ratio with a denominator of 100. Then simplify. To find the decimal equivalent of a percent, divide by 100. Percent

6. Fraction Decimal 100% 40% 25% 20%50% 60% 75% 80% 10% Some Common Equivalents The greatest percent shown in the table is 100% or 1. But percents can be greater than 100%. For example, 120% = = 1.2. You can also find percents that are less than 1%. For example, 0.5% = = 0.005.

7. Solving Percent Problems Two Methods 1)The Percent Proportion 2)The Percent Equation

8. Percent Proportion Method #1

9. Percent Equation part = percent% ∙ whole Method #2

10. Find 30% of 80. Method 1 Use a proportion. 100x = 2400 x = 24 30% of 80 is 24. Check 30% is the same as, and of 80 is 24. Use the percent proportion. Let x represent the part. Find the cross products. Since x is multiplied by 100, divide both sides by 100 to undo the multiplication. Example: Finding the Part

11. Example 1B: Finding the Part Find 120% of 15. Method 2 Use an equation. x = 120% of 15 x = 1.20(15) x = 18 120% of 15 is 18. Write an equation. Let x represent the part. Write the percent as a decimal and multiply. Example: Finding the Part

12. Find 20% of 60. Method 1 Use a proportion. 100x = 1200 x = 12 20% of 60 is 12. Let x represent the part. Find the cross products. Since x is multiplied by 100, divide both sides by 100 to undo the multiplication. Check 20% is the same as, and of 60 is 12. Your Turn:

13. Find 210% of 8. Method 2 Use an equation. x = 210% of 8 x = 2.10(8) x = 17 210% of 8 is 16.8. Write an equation. Let x represent the part. Write the percent as a decimal and multiply. Your Turn:

14. Method 2 Use an equation. Write an equation. Let x represent the part. Write the percent as a decimal and multiply. Find 4% of 36. x = 4% of 36 x =.04(36) 4% of 36 is 1.44. x =1.44 Your Turn:

15. What percent of 45 is 35? Round your answer to the nearest tenth. Method 1 Use a proportion. Use the percent proportion. Let x represent the percent. 45x = 3500 x ≈ 77.8 35 is about 77.8% of 45. Find the cross products. Since x is multiplied by 45, divide both sides by 45 to undo the multiplication. Example: Finding the Percent

16. 230 is what percent of 200? Method 2 Use a equation. 230 = x 200 230 = 200x 1.15 = x 230 is 115% of 200. Write an equation. Let x represent the percent. Write the decimal as a percent. This answer is reasonable; 230 is more than 100% of 200. Since x is multiplied by 200, divide both sides by 200 to undo the multiplication. The answer is a decimal. 115% = x Example: Finding the Percent

17. What percent of 35 is 7?. Method 1 Use a proportion. Use the percent proportion. Let x represent the percent. 35x = 700 x = 20 7 is 20% of 35. Find the cross products. Since x is multiplied by 35, divide both sides by 35 to undo the multiplication. Your Turn:

18. 27 is what percent of 9? Method 2 Use an equation. 27 = x 9 27 = 9x 3 = x 27 is 300% of 9. Write an equation. Let x represent the percent. Write the whole number as a percent. This answer is reasonable; 27 is more than100% of 9. Since x is multiplied by 9, divide both sides by 9 to undo the multiplication. The answer is a whole number. 300% = x Your Turn:

19. 38% of what number is 85? Round your answer to the nearest tenth. Method 1 Use a proportion. Use the percent proportion. 38x = 8500 x = 223.7 38% of about 223.7 is 85. Let x represent the whole. Find the cross products. Since x is multiplied by 38, divide both sides by 38 to undo the multiplication. Example: Finding the Whole

20. 20 is 0.4% of what number? Method 2 Use an equation. 20 = 0.4% of x 20 = 0.004 x 5000 = x Write an equation. Let x represent the whole. Write the percent as a decimal. Since x is multiplied by 0.004, divide both sides by 0.004 to undo the multiplication. 20 is 0.4% of 5000. Example: Finding the Whole

21. 120% of what number is 90? Method 1 Use a proportion. Use the percent proportion. 120x = 9000 x = 75 120% of 75 is 90. Let x represent the whole. Find the cross products. Since x is multiplied by 120, divide both sides by 120 to undo the multiplication. Your Turn:

22. Method 2 Use an equation. 48 is 15% of what number? 48 = 15% of x 48 = 0.15 x 320 = x Write an equation. Let x represent the whole. Write the percent as a decimal. Since x is multiplied by 0.15, divide both sides by 0.15 to undo the multiplication. 48 is 0.15% of 320. Your Turn:

23. The serving size of a popular orange drink is 12 oz. The drink is advertised as containing 5% orange juice. How many ounces of orange juice are in one serving size? Use the percent proportion. 100x = 60 x = 0.6 A 12 oz orange drink contains 0.6 oz of orange juice. Let x represent the percent. Since x is multiplied by 100, divide both sides by 100 to undo the multiplication. Example: Application

24. Use the information above to find the number of karats in a bracelet that is 42% gold. Round your answer to the nearest whole number. Use the percent proportion. Let x represent the number of karats. 100x = 1008 x = 10.08 A ring that contains 42% gold is about 10 karats. Since x is multiplied by 100, divide both sides by 100 to undo the multiplication. Your Turn:

25. Simple Interest Paid Annually Time in years Interest rate per year as a decimal Principal Simple interest A common application of percents is simple interest. Interest - the amount of money charged for borrowing money, or the amount of money earned when saving or investing money. Principal - the amount borrowed or invested. Simple Interest - interest paid only on the principal. Definition

26. Find the simple interest paid for 3 years on a $2500 loan at 11.5% per year. I = Prt Write the formula for simple interest. I = (2500)(0.115)(3) Substitute known values. Write the interest rate as a decimal. I = 862.50 The amount of interest is $862.50. Multiply. Example: Simple Interest Application

27. After 6 months, the simple interest earned on an investment of $5000 was $45. Find the interest rate. I = Prt Write the formula for simple interest. 45 = 2500r 0.018 = r The interest rate is 1.8%. Substitute the given values. Multiply 5000. Since r is multiplied by 2500, divide both sides by 2500 to undo the multiplication. Example: Simple Interest Application

28. Helpful Hint When you are using the formula I= Prt to find simple interest paid annually, t represents time in years. One month is year.

29. Find the simple interest earned after 2 years on an investment of $3000 at 4.5% interest earned annually. I = Prt Write the formula for simple interest. I = 270 The interest earned is $270. Substitute the given values. Multiply. I = (3000)(0.045)(2) Your Turn:

30. The simple interest paid on a loan after 6 months was $306. The annual interest rate was 8%. Find the principal. I = Prt Write the formula for simple interest. The remaining principal is $7650. Substitute the given values. 306 = (P)(0.08) 306 =.04P 7650 = P Multiply 0.08. Since P is multiplied by 0.04, divide both sides by 0.04. Your Turn:

31. Joke Time Why are there so many Smiths in the phone book? They all have phones. Why did the algebra student get so excited after they finished a jigsaw puzzle in only 6 months? Because on the box it said from 2-4 years. Why did the algebra student climb the chain-link fence? To see what was on the other side.

32. Assignment 2.9 Exercises Pg. 154 – 156: #10 – 48 even