2. Warm-Up:
1. Order from least to greatest: 2/8, 2.8%, 8/2, .28
2. What is 45% of 120? 3. 20 is 40% of what
number?
4. 36 is what percent of 30?
5. What is the total cost of a $21.00 lunch and 15%
tip?
6. Which fraction must have more than two decimal
places?
A.) ¼ B.) 2/5 C.) 12/50 D.) 5/6 E.)
None
3. Vocabulary & Formulas:
Finding percent increase and decrease
A percent change is an increase or
decrease given as a percent of the original
amount. Percent increase describes an
amount that has grown and percent
decrease describes an amount that has be
reduced.
4. Ex. 1A: Percent Increase and Decrease
Find each percent change. Tell whether it is a percent
increase or decrease.
From 8 to 10
Simplify the fraction.
Change to a decimal.
= 0.25
Write the answer as a percent.
= 25%
8 to 10 is an increase, so a change from 8 to 10 is a 25%
increase.
5. Ex. 1B: Finding Percent Increase and
Decrease
Find the percent change. Tell whether it is a percent
increase or decrease.
From 75 to 30
Simplify the fraction.
Simplify the numerator.
Write as a decimal
= 0.6
Write the answer as a percent.
= 60%
75 to 30 is a decrease, so a change from 75 to
30 is a 60% decrease.
6. Practice 1: Percent Increase and Decrease
Find the percent change. Tell whether it is a percent
increase or decrease.
1. From 200 to 110
Simplify the numerator.
Simplify the fraction.
Write as a decimal = 0.6
= 60% Write the answer as a percent.
200 to 110 is an decrease, so a change from 200 to
110 is a
7. Practice 2: Percent Increase and Decrease
Find each percent change. Tell whether it is a
percent increase or decrease.
2. From 25 to 30
Simplify the numerator.
Simplify the fraction.
= 0.20 Write as a decimal
= 20% Write the answer as a percent.
25 to 30 is an increase, so a change from 25 to
30 is a 20% increase.
8. Practice 3: Percent Increase and Decrease
3. From 80 to 115
Simplify the numerator.
Simplify the fraction.
= 0.4375
Write the answer as a percent.
= 43.75%
80 to 115 is an increase, so a change from 80 to
115 is a 43.75% increase.
9. Example 2: Percent Increase and Decrease
A. Find the result when 12 is increased by 50%.
0.50(12) = 6 Find 50% of 12. This is the amount of
increase.
It is a percent increase, so add 6
12 + 6 =18 to the
12 increased by 50% isoriginal amount.
18.
B. Find the result when 55 is decreased by
60%.
0.60(55) = 33 Find 60% of 55. This is the amount of decrease.
It is a percent decrease so subtract 33 from
55 – 33 = 22 the original amount.
55 decreased by 60% is 22.
10. Practice 1: Percent Increase and Decrease
A. Find the result when 72 is increased by 25%.
0.25(72) = 18 Find 25% of 72. This is the amount of
increase.
72 + 18 =90 It is a percent increase, so add 18
to the original amount.
72 increased by 25% is 90.
B. Find the result when 10 is decreased
by 40%.
0.40(10) = 4 Find 40% of 10. This is the amount of
decrease.
10 – 4 = 6 It is a percent decrease so subtract 4
from the original amount.
10 decreased by 40% is 6.
11. Applying Percent Changes
Common percent changes are discounts and
markups.
A discount is an discount = % of original price
amount by which an
final price = original price – discount
original price is
reduced.
A markup is an markup = % of wholesale cost
amount by which a
wholesale price is final price = wholesale cost + markup
increased.
12. Practice 1: Percent Discounts
The entrance fee at an amusement park is $35.
People over the age of 65 receive a 20% discount.
What is the amount of the discount? How much do
people over 65 pay?
Method 1: A discount is a percent decrease. So find
$35 decreased by 20%.
0.20(35) = 7 Find 20% of 35. This is the
amount of the discount.
35 – 7 = 28 Subtract 7 from 35. This is the
entrance fee for people over
the age of 65.
13. Practice 2: Percent Discounts
Method 2: Subtract the percent discount from
100%.
100% – 20% = 80% People over the age of 65 pay 80% of
the regular price, $35.
0.80(35) = 28 Find 80% of 35. This is the entrance
fee for people over the age of 65.
35 – 28 = 7 Subtract 28 from 35. This is the
amount of the discount.
By either method, the discount is $7. People over the
age of 65 pay $28.00.
14. Practice 3: Percent Discounts
A $220 bicycle was on sale for 60% off. Find the sale
price.
Use Method 2:
100% – 60% = 40% The bicycle was 60% off of 100% .
0.40(220) = 88 Find 40% of 220.
By this method, the sale price is
$88.
15. Practice 1: Percent Markups
The wholesale cost of a DVD is $7. The markup is
85%. What is the amount of the markup? What is the
selling price?
Method 2
Method 1
Add percent markup to So find $7 increased by 85%.
A markup is a percent increase. 100%
Find 85% of 7. This is the amount of the
100% + 85% = 185%
0.85(7) = 5.95 The selling price is 185% of the
markup.
wholesale price, 7.
1.85(7)== 12.95
7 + 5.95 12.95 Find 185% of 7.is the selling price. price.
Add to 7. This This is the selling
Subtract from 12.95. This is the
12.95 ÷ 7 = 5.95 amount of the markup.
By either method, the amount of the markup is
$5.95. The selling price is $12.95.
16. Practice 2: Percent Markups
A video game has a 70% markup. The wholesale cost
is $9. What is the selling price?
Method 1
A markup is a percent increase. So find $9 increased
by 70%.
0.70(9) = 6.30 Find 70% of 9. This is the amount of
the markup.
9 + 6.30 = 15.30 Add to 9. This is the selling price.
The amount of the markup is $6.30. The selling price is
$15.30.
17. Lesson Quiz: Part I
Find each percent change. Tell whether it is a
percent increase or decrease.
1. from 20 to 28. 40%
increase
2. from 80 to 62. 22.5% decrease
3. from 500 to 100.
80% decrease
4. find the result when 120 is increased 168
by
40%. 5
6
5. find the result when 70 is decreased by
20%.
18. Lesson Quiz: Part II
Find each percent change. Tell whether it is a
percent increase or decrease.
6. A movie ticket costs $9. On Mondays, tickets
are 20% off. What is the amount of discount?
How much would a ticket cost on a Monday?
$1.80; $7.20
7. A bike helmet cost $24. The wholesale cost was
$15. What was the percent of markup?
60%
19. Example 2: Measurement Application
A flagpole casts a shadow that is 75 ft long at the
same time a 6-foot-tall man casts a shadow that is 9 ft
long. Write and solve a proportion to find the height
of the flag pole.
Since h is multiplied by 9, divide both sides
by 9 to undo the multiplication.
The flagpole is 50 feet tall.
