1. Warm Up Sept. 12 th Sit in your usual seat with your tracking sheet out and your homework on your desk. Answer the following questions on your OWN sheet of paper. 1.Solve for h: 8(h – 1) = 6h + 4 + 2h 2.There are three consecutive integers whose sum is 39. What are the integers? 3. Membership for the Alpine rock-climbing gym costs $25 per month plus a $125 sign-up fee. Membership for Rocco’s rock-climbing gym costs $30 per month plus a $50 sign-up fee. a)After how many months will the memberships costs the same? b)If you only wanted a one-year membership, which gym would you join?

2. Homework Questions?

3. Finishing Variables on Both Sides…

4. Instead of working with fractions, multiply the entire equation (EVERYTHING!) by the least common denominator (LCD). 1.

5. Special Cases In some equations, the variables cancel out. If this happens while solving, the resulting equation determines the answer. Examples: 1. 2(3w – 7) = 7w + 9 – w

6. Special Cases (cont.) 2.-5(2j – 3) + j = 3(2 – 3j) + 9

7. Working with Ratios and Proportions!

8. Vocabulary A ratio compares 2 numbers by division.

9. Proportions A proportion is an equation that states that 2 ratios are equal. Examples: 1. 2.

10. You try! Try numbers 13 and 14 on your homework sheet.

11. Proportions (cont.) 3. 4.

12. Want some practice? Complete problem 19 and 20 on your homework sheet!

13. Applications 1.An MP3 player that has 2 gigabytes of storage can hold about 500 songs. A similar but larger MP3 has 25 gigabytes of storage. How many songs can the larger MP3 player hold?

14. Applications 2.Josh finished 24 math problems in one hour. At this rate, how many hours will it take him to complete 60 problems?

15. You try! Work on problems 21 and 22 from your homework sheet.

16. Indirect Measurement 1. A girl stands 5 feet tall and casts a shadow that is 2 feet long. An apartment building casts a shadow that is 35 feet long. How tall is the building?

17. Can you do this one? 2. On a map, the distance from Jacksonville to Orlando, FL is 1.25 inches. The map has a scale factor of 1 inch = 110 miles. What is the actual distance from Jacksonville to Orlando?

18. Similar Figures Similar figures have the same shape but not necessarily the same size. We use proportions to find missing lengths of similar figures. 1.In the diagram, ΔABC ~ ΔDEF. What is DE? B E A C D F 1016 12 18

19. You try this one! 1.In the diagram, ΔABC ~ ΔDEF. What is AC? B E A C D F 810 15 27

20. Vocabulary A ratio that compares quantities measured in different units is called a rate. A rate with a denominator of 1 is called a unit rate.

21. Comparing Unit Rates Think about this and discuss with your neighbor… You are shopping for T-shirts. Which store offers the best deal? Why? Store A: $25 for 2 shirts Store B: $45 for 4 shirts Store C: $30 for 3 shirts

22. Converting Units To convert from one unit to another, such as feet to inches, multiply by a conversion factor to produce the desired units. A conversion factor is a ratio of 2 equivalent measures in different units. In other words, we set up a proportion with two equivalent ratios to find our missing unit!

23. Convert the following: 1. 330 min.  hours2. 5 ft. 3 in.  in.

24. Let’s practice! Try problems 1 – 3 on your homework sheet.

25. Converting Rates A student ran 150 feet in 5.8 seconds. At what speed did the student run in miles per minute? (1 mile = 5280 feet; 1 minute = 60 seconds)

26. Let’s practice! Try problems 9 – 11 on your homework sheet.

27. Homework Working with Ratios Worksheet (all problems we did not complete in class)