1. 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?

2. 2. The ratio of men to women graduating with math PhDs is 3:1
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 to reflect the ratio graduating with PhDs?

3. Per cent
Meaning

4. 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

5. 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, /20

6. 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: = 9/100 = 9%
You try: , 0.59

7. Homework Problems 6.2 a. 18 is 4% of 450 c. $1211.80 is 83% of $1460
e is 0.25% of 345
f is 120% of 200
h is 85.7% of 35
l is 145.8% of 120
n is 20% more than 400
p is 100% more than 35

8. HW problems 6.2
2. An estimate would be that her take-home pay is about 80% of her gross pay. The exact answer is that her take-home pay is 77 1/3% of her gross pay.
8. The second dress costs less than the first. First estimate, then find exact prices.
How?

9. HW problems 6.2
13. Approximately 2.32 million, or 2,320,000, Americans are homeless.
Estimate?

10. HW problems 6.2 16. The original price of the computer was $2200.
After two years, the teacher’s salary will be $30,941.
30. 1: 200 or 1 out of 200

11. 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%, %

12. Easy Percents--just know these
1 = ____%
1/3 = ____%, 2/3 = ____%
1/4 = ____%, 1/2 = ____%, 3/4 = ____%
1/5 = ____%, 2/5 = ____%, 3/5 = ____%,
4/5 = ____%
1/8 = ____%, 3/8 = ____%, 5/8 = ____%,
7/8 = ____%
1/10 = ____%, 2/10 = ____%, etc..

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

14. 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.

15. 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 % of 8000 is So 8% of 7968 is between 400 and 800.

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

17. Solving percent problems
Twenty-two percent of a university’s faculty were not born in the U.S. If there are 4320 faculty members, how many were born outside the U.S.?
Write the percent problem as a proportion; then solve.
Write an equation with the given information and a letter to represent the unknown number; then, solve.

18. 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%

19. 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?

20. 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 = 125%.
100% = $x --> 100 • 140 = 125x 125% $140

21. 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; = 99.5% now = 640, > 100x = 99.5 • x About 636,800 cacti are left.

22. To calculate grades In-class tests 3 40%
Explorations, Class Notes, etc 25%
Homework %
Final Exam %