Final Exam info

Tuesday December 14th

2 – 4 PM

Math East 141

• 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. 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?

Per cent

• Meaning

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

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

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

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%

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..

What happens if…

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

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% and 8 • 80 = 640.

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.

For exact answer:• Write and solve a proportion.

Percent = part = is 100 whole of 8 = x --> 8 • 7968 = 100x100 7968

63744 = 100x 637.44 = x

About 637 students work full time.

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.

Exploration 6.5

• #1-7

Exploration 6.7

• Part 1, #1-3.

Try this on your own

• My grandson 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?

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?

• Can you explain how to do this in your head?

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?

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?

• In 2008 and 2009, many people saw their retirement accounts go down over the last year by as much as 50%.

• By what percent would their accounts have to increase to get back to where they were before the downturn?

To calculate grades

• In-class tests 3 50%• Explorations, Class Notes,

attendance, etc 15%• Homework 10%• Final Exam 25%

Homework Problems 6.21 a. 18 is 4% of 450

c. $1211.80 is 83% of $1460e. 0.8625 is 0.25% of 345f. 240 is 120% of 200h. 30 is 85.7% of 35l. 175 is 145.8% of 120n. 480 is 20% more than 400p. 70 is 100% more than 35

HW problems 6.22. 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?

HW problems 6.213. Approximately 2.32 million, or

2,320,000, Americans are homeless.– Estimate?

HW problems 6.2

16. The original price of the computer was $2200.

20.After two years, the teacher’s salary will be $30,941.

30. 1: 200 or 1 out of 200