1. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Hawkes Learning Systems: Introductory Algebra Section 3.7: Percents and Applications

2. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Objectives o Change decimals to percents. o Change percents to decimals. o Find percents of numbers. o Find fractional parts of numbers. o Solve word problems involving decimals, fractions, and percents.

3. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Changing Decimals to Percents To Change a Decimal to a Percent 1)Move the decimal two places to the right. 2)Add the % symbol. (These two steps have the effect of multiplying by 100 and then dividing by 100. Thus the number is not changed. Just the form is changed.)

4. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 1: Decimals and Percents Change each decimal to an equivalent percent. a.b. a. 0.214b. 3.6c. 0.002d. 0.4 Solutions: Continued on the next slide…

5. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 1: Decimals and Percents (cont.) c.d. Solutions:

6. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Changing Percents to Decimals To Change a Percent to a Decimal 1)Move the decimal two places to the left. 2)Delete the % symbol.

7. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 2: Decimals and Percents Change each percent to an equivalent decimal. a.b. a. 53%b. 48.5%c. 0.6%d. 2% Solutions: Continued on the next slide…

8. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 2: Decimals and Percents (cont.) c.d. Solutions:

9. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Decimal/Percentage Relationships A decimal that is: 1)less than 0.01 is less than 1%. 2)between 0.01 and 0.10 is between 1% and 10%. 3)between 0.10 and 1.00 is between 10% and 100%. 4)more than 1.00 is more than 100%.

10. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. The Basic Formula R · B = A R = RATE or percent (as a decimal or fraction) B = BASE (number we are finding the percent of) A = AMOUNT or percentage (a part of the base) “of” means to multiply (the raised dot · is used in the formula) “is” means equals (=) The relationship among R, B, and A, is given in the formula R · B = A.

11. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 3: Using R · B = A Find 42.5% of 140. Solution: In this problem, R = 42.5% and B = 140. A = R · B A = 0.425 · 140 A = 59.5

12. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 4: Using R · B = A The amount 18.75 is 37.5% of what number? Solution: In this problem A = 18.75 and R = 37.5%.

13. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Basic Steps for Solving Word Problems 1.Understand the problem: a. Read the problem. b. Understand all the words. c. If it helps, restate the problem in your own words. d. Be sure that there is enough information. 2.Devise a plan using, for example, one or all of the following: a. Guess, estimate, or make a list of possibilities. b. Draw a picture or diagram. Continued on the next slide…

14. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Basic Steps for Solving Word Problems (cont.) c. Use a variable and form an equation. 3.Carry out the plan: a. Try all the possibilities you have listed. b. Study your picture or diagram for insight into the solution. c. Solve any equations that you may have set up. 4.Look back over the results: a. Can you see an easier way to solve the problem? Continued on the next slide…

15. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Basic Steps for Solving Word Problems (cont.) b. Does your solution actually work? Does it make sense in terms of the wording of the problem? Is it reasonable? c. If there is an equation, check your answer in the equation.

16. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 5: Discount and Sales Tax A new combination printer/scanner that normally sells for $300 is now on sale at 18% off. a) What is the discount amount? b) What is the sale price? a) Here, the base price B = 300 and the rate R = 0.18. Solutions:

17. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 5: Discount and Sales Tax A new combination printer/scanner that normally sells for $300 is now on sale at 18% off. a) What is the discount amount? b) What is the sale price? b) Solutions:

18. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 6: Discount and Sales Tax In the previous example, the final sale price of the printer/scanner was found to be $246. If there is also a 8% sales tax, what will the final amount of the purchase be? Solution: First, find the amount of the sales tax. Continued on the next slide…

19. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 6: Discount and Sales Tax (cont.) Solution: Second, add the sales tax to the discounted amount.

20. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 7: Percent of Profit Calculate the percent of profit per amount invested. a. $400 profit made by investing $800. b. $250 profit made by investing $625. Solutions: a. b.