1. April 28, 2009 “Nobody can go back and start a new beginning, but anyone can start today and make a new ending.” ~Maria Robinson

2. Final Exam Tuesday, May 12 11am – 1pm In our usual classroom Cumulative (covers material from entire semester). As always, you may use a calculator and/or manipulatives from your own pack.

3. April 28, 2009 Section 6.1 (finish) Exploration 6.3 Section 6.2 – Percents Course evaluations

4. 6.1 (cont’d) Ratios and Rates If a : b = c : d, then a/b = c/d. If a/b = c/d, then a : b = c : d. Example: 35 boys : 50 girls = 7 boys : 10 girls 5 miles per gallon = 15 miles using 3 gallons

5. 6.1 (cont’d) Proportional word problems: Start easy: I can buy 3 candy bars for $2.00. So, at this rate, 6 candy bars should cost… 9 candy bars should cost… 30 candy bars should cost… 1 candy bar should cost… this is called a unit rate.

6. 6.1 (cont’d) Proportional word problems: Here’s another. 7 small drinks cost as much as 5 large drinks. At this rate… How much should 14 small drinks cost? How much should 21 small drinks cost? How much should 15 large drinks cost?

7. 6.1 (cont’d) Ratios are not the same as fractions The ratio of males to females is 3 : 2. That means 3/5 of the people are male, and 2/5 of the people are female. The ‘whole’ is the group of 5 people.

8. 6.1 (cont’d) Ratios are not the same as fractions The mixture is 3 parts water and 1 part green dye. That means that 3/4 of the mixture is water and 1/4 of the mixture is green dye. The ‘whole’ is the mixture, which consists of 4 total parts.

9. 6.1 (cont’d) Ratios are not the same as fractions A school’s enrollment increases by 25 students per year. This one can be expressed as a fraction – sort of: 25 students/1 year. There is no ‘whole’, though, since the two quantities being compared have different units!

10. Exploration 6.3 Do Part 1.

11. 6.1 (cont’d) Reciprocal unit ratios Suppose I tell you that 4 doodads can be exchanged for 3 thingies. How much is one thingy worth? 4 doodads/3 thingies means 1 1/3 doodads per thingy. How much is one doodad worth? 3 thingies/4 doodads means 3/4 thingy per doodad.

12. 6.1 (cont’d) To solve a proportion: If a/b = c/d, then ad = bc. Show that this is true:

13. 6.1 (cont’d) To set up a proportion: Ex: I was driving behind a slow truck at 25 mph for 90 minutes. How far did I travel? Set up equal rates: miles/minute 25 miles/60 minutes = x miles/90 minutes. Solve: 25 × 90 = 60 × x; x = 37.5 miles.

14. 6.1 (cont’d) Strange looking problems: Ex: I see that 1/4 of the balloons are blue, and there are 6 more red balloons than blue. Let x = number of blue balloons, and so x + 6 = number of red balloons. Also, the ratio of blue to red balloons is 1 : 3 Proportion: x/(x + 6) = 1/3 Alternate way to think about it. 2x + 6 = 4x x x + 6

15. 6.1 (cont’d) Which rates are (equivalent) proportional? Ex: 1.6/10 mph 2.1/0.6 mph 3.2.1/3.5 mph 4.31.5/52.5 mph 5.240/400 mph 6.18.42/30.7 mph 7.60/100 mph

16. 6.2 – Percents Percent means per hundred. 50% means 50 per hundred, or 50/100. 95% means 95 per hundred, or 95/100. 2% means 2 per hundred, or 2/100. 315% means 315 per hundred, or 315/100.

17. 6.2 (cont’d) Percents you should know: 1 = 100% 1/4 = 25%, 1/2 = 50%, 3/4 = 75% 1/5 = 20%, 2/5 = 40%, 3/5 = 60%, 4/5 = 80% 1/8 = 12.5%, 3/8 = 37.5%, 5/8 = 62.5%, 7/8 = 87.5% 1/10 = 10%, 2/10 = 20%, etc…

18. 6.2 (cont’d) Fractions, decimals, percents To write fractions as decimals or percents: a/b means a ÷ b. Divide, and write the answer to get the decimal. Then, multiply by 100 to get the percent. Ex: 48/60 = 48 ÷ 60 = 0.8 = 80% You try: 4/9, 4 3/20

19. 6.2 (cont’d) Fractions, decimals, percents To write decimals as fractions or percents: Consider using expanded form, then combine fractions and simplify. To write a percent, multiply by 100. Ex: 0.09 = 9/100 = 9% You try: 7.007, 0.59

20. 6.2 (cont’d) Fractions, decimals, percents To write a percent as a decimal, divide by 100. From there, you can convert the decimal to a fraction. Ex: 591% = 5.91 = 5 91/100 You try: 3%, 62%, 0.4%

21. 6.2 (cont’d) What happens if... What if you have 3 2/5% Rewrite 2/5 as 0.4. So 3 2/5% = 3.4%

22. Homework Link to online homework list: http://math.arizona.edu/~varecka/302AhomeworkS09. htm *Note: approximate grades are posted on D2L.