1. To calculate grades In-class tests 340% Explorations, Class Notes, etc25% Homework10% Final Exam25%

3. 1. Suppose the ratio of men to women in a room is 2:3. –A. If there are 10 more women than men, how many men are in the room? –B. If there are 24 men i. How many women are in the room? ii. If 12 more men enter the room, how many women must enter to keep the ratio of men to women the same?

4. 2. The ratio of men to women graduating with math PhDs is 3:1. At our math department, we have 5 female regular faculty, and 62 male regular faculty. –A. Is our department on track? –B. How many women would need to enter the department in order for the ratio of men to women will reflect the ratio graduating with PhDs?

5. Percent 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

6. Easy Percents--just know these 1 = 100% 1/3 = 33.3%, 2/3 = 66.6% 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..

7. 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. Example: 48/60 = 48 ÷ 60 = 0.8 = 80% You try: 4/9, 4 3/20

8. Fractions, Decimals, Percents To write decimals as fractions or percents: Read the decimal without the word “point.” Simplify if necessary. To write a percent, multiply by 100. Example: 0.09 = 9/100 = 9% You try: 7.007, 0.59

9. Fractions, Decimals, Percents To write a decimal, divide by 100. To write a fraction, read the decimal without the word “point.” Simplify if necessary. Example: 591% = 5.91 = 5 91/100 You try: 3%, 62%, 0.4%

10. What happens if… What if you have 3 2/5% Rewrite 2/5 as 0.4. So 3 2/5% = 3.4%

11. Ways to estimate A newspaper story reports that 8% of 7968 students work full time. Strategy 1: Use 10% as a benchmark 10% of 7968 is 796.8, or about 797. Strategy 2: Use 1% as a benchmark 1% of 7968 is 79.68, or about 80. So 8% is 8 1%: 8 80 = 640.

12. Ways to estimate Strategy 3: find a close number: 7968 is about 8000: 10% of 8000 is 800; 8 1% is 8 80 = 640. Strategy 4: find a range. 8% is between 10% and 5%. 5% of 8000 is 400. 10% of 8000 is 800. So 8% of 7968 is between 400 and 800.

13. For exact answer: Write and solve a proportion. Percent = part = is 100 whole of 8 = x --> 8 7968 = 100x 100 7968 63744 = 100x 637.44 = x About 637 students work full time.

14. For most problems Write the percent problem as a proportion; then solve.

15. Example My friend makes 68 baskets a week, and wants to sell no more than 30%. What is the maximum number of baskets she can sell? Part = Percent = Is Whole 100 Of 30 = x --> 30 68 = 100x 100 68 About 20.

16. Try this on your own My son has 72 stuffed animals on his bed, but he generally only sleeps with 4 at a time. What percent of his animals does he sleep with? 4 = x --> 4 100 = 72x. X = 18% 72 100

17. Example There is a 20% off sale at the mall. I’ve wanted this really cool sweater that is $120, but couldn’t afford it. How much less is the price with the sale? What is the sale price? If the sale is 20% off, then the sweater is going to cost 100 - 20 = 80% of the original price. New price: $96. Savings: $24. Can you explain how to do this in your head?

18. Example The college bookstore makes a profit by charging students 25% more than the book actually cost wholesale. If your book cost $140, how much did the bookstore pay for it? The bookstore pays 100%, and you pay 100 + 25 = 125%. 100% = $x --> 100 140 = 125x 125% $140

19. Example In the course of a year, there has been a decrease of 0.5% in the number of cacti in a certain zip code. If there had been about 640,000 cacti at the beginning of the year, how many are left now? 100% in the beginning; 100 - 0.5 = 99.5% now. 100 = 640,000 --> 100x = 99.5 640000 99.5 x About 636,800 cacti are left.