• 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
Homework Problems 6.2
1 a.
c.
e.
f.
h.
l.
n.
p.
18 is 4% of 450
$1211.80 is 83% of $1460
0.8625 is 0.25% of 345
240 is 120% of 200
30 is 85.7% of 35
175 is 145.8% of 120
480 is 20% more than 400
70 is 100% more than 35
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?
HW problems 6.2
13. 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
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%: 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.
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.
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.
To calculate grades
•
•
•
•
In-class tests 3
Explorations, Class Notes, etc
Homework
Final Exam
40%
25%
10%
25%