4.2 Percents of Increase and Decrease - Big Ideas Learning
English
Spanish
4.2 Percents of Increase and Decrease
STATE STANDARDS
MA.7.A.1.2
percent of increase?
What is a percent of decrease? What is a
1 ACTIVITY: Percent of Decrease Mica
Each year in the Columbia River Basin, adult salmon swim up river to streams to lay eggs and hatch their young.
To go up the river, the adult salmon use fish ladders. But, to go down the river, the young salmon must pass through several dams.
There are electric turbines at each of the eight dams on the main stem of the Columbia and Snake Rivers. About 88% of the young salmon pass through these turbines unharmed.
Revelstoke
Duncan
Keenlyside
Canada
Chief Grand Albeni Joseph Coulee Falls
Libby
U.S. Hungry
Seattle
Wells Rocky
Reach
a R Lower Monumental
Noxon Horse Kerr
Columbi
Rock Island
Little Goose
Montana
Wanapum
Lower Granite
Priest Rapids
Dworshak
The Dalles McNarry
Portland
Bonneville Oregon
Ice Harbor
John
Day
Oxbow
Brownlee
Hell's Canyon
Jackson Lake Boise Projects
Willamette R.
Corps of Engineers Dams
Dams owned by others
Idaho
Snake R.
Copy and complete the table and the bar graph to show the number of young salmon that make it through the dams.
Dam
0
1
2
3
4
5
6
7
8
Salmon 1000 880 774
88% of 1000 = 0.88 1000 88% of 880 = 0.88 880
= 880
= 774.4 774
Number of Salmon
Surviving Salmon
1200
1000
800
600
400
200
0
0
1
2
3
4
5
6
7
8
Dams
164 Chapter 4 Percents
English
Spanish
2 ACTIVITY: Percent of Increase
From 2000 to 2006, the population of Florida increased about 2% each year. Copy and complete the table and the bar graph using this pattern. Predict the population in 2015.
For 2007:
2% of 18,000,000 = 0.02 18,000,000
= 360,000
18,000,000 + 360,000 = 18,360,000
2006 Population 18,000,000
2006 Population
Increase
2007 Population
Year 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
Population 18,000,000 18,360,000
Population
2008 2010 2013
Population of Florida
26,000,000 24,000,000 22,000,000 20,000,000 18,000,000 16,000,000 14,000,000 12,000,000 10,000,000
8,000,000 6,000,000 4,000,000 2,000,000
0 2006 2007
2009
2011 2012
Year
2014 2015
3. In Activity 1, by what percent does the number of young salmon decrease with each dam?
4. Describe real-life examples of a percent of decrease and a percent of increase.
5. IN YOUR OWN WORDS What is a percent of decrease? What is a percent of increase?
Use what you learned about percent of increase and percent of decrease to complete Exercises 13 ?18 on page 168.
Section 4.2 Percents of Increase and Decrease 165
English
Spanish
4.2 Lesson
Lesson Tutorials
Key Vocabulary percent of change,
p. 166 percent of increase,
p. 166 percent of decrease,
p. 166
A percent of change is the percent that a quantity changes from the original amount.
percent
of
change
=
amount of change ----
original amount
Percents of Increase and Decrease When the original amount increases, the percent of change is called a percent of increase.
percent of increase = -- new amoun-- t - origin-- al amount
original amount
When the original amount decreases, the percent of change is called a percent of decrease.
percent of decrease = -- original am-- ount - ne-- w amount
original amount
EXAMPLE 1 Finding a Percent of Increase
The table shows the number of hours you spent online last weekend. What is the percent of change in your online time from Saturday to Sunday?
Day Saturday Sunday
Hours Online 2 4.5
The number of hours on Sunday is greater than the number of hours on Saturday. So, the percent of change is a percent of increase.
percent
of
increase
=
new amount - original amount ------
original amount
= -- 4.5 - 2
2
=
2.5 --
2
Substitute. Subtract.
= 1.25, or 125%
Write as a percent.
Your online time increased 125% from Saturday to Sunday.
Find the percent of change. Round to the nearest tenth of a percent, if necessary.
1. 10 inches to 25 inches
2. 57 people to 65 people
166 Chapter 4 Percents
English
Spanish
EXAMPLE 2 Finding a Percent of Decrease
The bar graph shows a softball player's home run totals. What was the percent of change from 2007 to 2008?
Softball
The number of home runs decreased from 2007 to 2008. So, the percent of change is a percent of decrease.
2005
18
2006
10
2007
28
2008
20
0 5 10 15 20 25 30 35
Home Runs
percent
of
decrease
=
original amount - new amount ------
original amount
= -- 28 - 20
28
Substitute.
=
8 --
28
Subtract.
0.286, or 28.6%
Write as a percent.
The number of home runs decreased about 28.6%.
Season
Exercises 4?11
3. What was the percent of change from 2005 to 2006?
EXAMPLE 3 Standardized Test Practice
You have 250 songs on your MP3 player. You delete 20% of the songs. How many songs are left?
A 50
B 150
C 200
D 300
Find the amount of decrease.
20% of 250 = 0.2 250
= 50
Write as multiplication. Multiply.
The decrease is 50 songs. So, there are 250 - 50 = 200 songs left.
The correct answer is C .
Exercises 13?22
4. WHAT IF? After deleting the 50 songs in Example 3, you add 10% more songs. How many songs are on the MP3 player?
Section 4.2 Percents of Increase and Decrease 167
English
Spanish
4.2 Exercises
Help with Homework
1. VOCABULARY How do you know whether a percent of change is a percent of increase or a percent of decrease?
2. NUMBER SENSE Without calculating, which has a greater percent of increase? 5 bonus points on a 50-point exam 5 bonus points on a 100-point exam
3. WRITING What does it mean to have a 100% decrease?
93++4(-+(6-9(3)-=+)9=3()-=1)=
Identify the percent of change as an increase or decrease. Then find the percent of change. Round to the nearest tenth of a percent, if necessary.
1 2 4. 12 inches to 36 inches
5. 75 people to 25 people
6. 50 pounds to 35 pounds
7. 24 songs to 78 songs
8. 10 gallons to 24 gallons
9. 72 paper clips to 63 paper clips
10. 16 centimeters to 44.2 centimeters
11. 68 miles to 42.5 miles
12. ERROR ANALYSIS Describe and correct the error in finding the percent increase from 18 to 26.
-- 26 - 18 0.31 = 31% 26
Find the new amount. 3 13. 8 meters increased by 25%
15. 50 points decreased by 26% 17. 68 students increased by 125% 19. 62 kilograms decreased by 32%
14. 15 liters increased by 60% 16. 25 penalties decreased by 32% 18. 1000 grams decreased by 94% 20. 124 ounces decreased by 67%
21. ERROR ANALYSIS Describe and correct the error in using the percent of change to find a new amount.
25 is decreased by 40%.
40% of 25 = 0.4 25 = 10
So, 25 + 10 = 35.
22. VIDEO GAME Last week, you finished Level 2 of a video game in 32 minutes. Today, you finish Level 2 in 28 minutes. What is your percent of change?
168 Chapter 4 Percents
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