To calculate grades
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In-class tests 3
Explorations, Class Notes, etc
Homework
Final Exam
40%
25%
10%
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
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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
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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 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.
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 = 100x
100
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
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30 =
100
• About 20.
x --> 30 • 68 = 100x
68
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 = 125x
125%
$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.