To calculate grades

• In-class tests 3 40%

• Explorations, Class Notes, etc 25%

• Homework 10%

• Final Exam 25%

• 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 will reflect the ratio graduating with PhDs?

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

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..

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%

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 benchmark10% of 7968 is 796.8, or about 797.

• Strategy 2: Use 1% as a benchmark1% of 7968 is 79.68, or about 80. So 8% is 8 • 1%: 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.

For most problems

• Write the percent problem as a proportion; then solve.

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.

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

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?

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 = 125x125% $140

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.