7-9
7-9 Percent
PercentProblems
Problems
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
11
7-9 Percent Problems
Warm Up
Write each decimal as a percent and
fraction.
1. 0.38
19
38%, __
2. 0.06
3
6%, __
3. 0.2
1
__
20%, 5
Course 1
50
50
7-9 Percent Problems
Problem of the Day
Lucky Jim won $16,000,000 in a lottery.
Every year for 10 years he spent 50%
of what was left. How much did Lucky
Jim have after 10 years?
$15,625
Course 1
7-9 Percent Problems
Learn to find the missing value in a
percent problem.
Course 1
7-9 Percent Problems
To find the percent one number is of
another, use this proportion:
%
is
=
100
of
If you are looking for 45% of 420, 45
replaces the percent sign and 420
replaces “of.” The first denominator, 100,
always stays the same. The “is” part is
what you have been asked to find.
Course 1
7-9 Percent Problems
Additional Example 1: Application
There are 560 students in Ella’s school. If 35%
of the students participate in after-school
sports, how many students participate in afterschool sports?
35
___
First estimate your answer. Think: 35% = 100 ,
1
__
which is close to
, and 560 is close to 600. So
3
1
__
about
of the students participate in after-school
3
sports.
1 • 600 = 200
__
3
This is the estimate.
Helpful Hint
Think: “35 out of 100 is how many out of 560?”
Course 1
7-9 Percent Problems
Additional Example 1 Continued
Now solve:
Let s represent the number of
35
s
___
= ___
students who participate in after100
560
school sports.
100 • s = 35 • 560 The cross products are equal.
100s = 19,600
100s = 19,600
____
_____
100
100
s = 196
s is multiplied by 100.
Divide both sides of the equation
by 100 to undo multiplication.
Since 196 is close to your estimate of 200, 196 is a
reasonable answer.
196 students participate in after-school sports.
Course 1
7-9 Percent Problems
Check It Out: Example 1
There are 480 students in Tisha’s school. If
70% of the students participate in the
fundraising program, how many students
participate in the fundraising program?
70
First estimate your answer. Think: 70% = ___ ,
100
3
which is close to __ , and 480 is close to 500. So
4
3 of the students participate in after
about __
4
school sports.
3 • 500 = 375
__
This is the estimate.
4
Course 1
7-9 Percent Problems
Check It Out: Example 1 Continued
Now solve:
Let s represent the number of
70
s
___
= ___
students who participate in the
100
480
fundraising program.
100 • s = 70 • 480 The cross products are equal.
100s = 33,600
100s = 33,600
____
_____
100
100
s = 336
s is multiplied by 100.
Divide both sides of the equation
by 100 to undo multiplication.
Since 336 is close to your estimate of 375, 336 is a
reasonable answer.
336 students participate in the fundraising program.
Course 1
7-9 Percent Problems
Additional Example 2: Application
Johan is 25% of the way through his
exercises. If he has exercised for 20 minutes
so far, how much longer does he have to work
out?
25% of the exercises are
%
is
___
__
completed, so 20 minutes is 25%
=
100
of
of the total time needed.
25
20
___
= __
100
m
100 • 20 = 25 • m
Course 1
Set up a proportion. The “of” part
is what you have been asked to
find.
The cross products are equal.
7-9 Percent Problems
Additional Example 2 Continued
2,000 = 25m
m is multiplied by 25.
2,000 = ____
25m
_____
25
25
Divide both sides by 25 to undo
multiplication.
80 = m
The time needed for the exercises is 80 min. So
far, the exercises have taken 20 min. Because
80 – 20 = 60, Johan will be finished in 60 min.
Course 1
7-9 Percent Problems
Check It Out: Example 2
Phil is 30% of the way through his
homework. If he has worked for 15 minutes
so far, how much longer does he have to
work?
30% of the exercises are
%
is
___
__
completed, so 15 minutes is 30%
=
100
of
of the total time needed.
30
15
___
= __
100
m
100 • 15 = 30 • m
Course 1
Set up a proportion. The “of” part
is what you have been asked to
find.
The cross products are equal.
7-9 Percent Problems
Check It Out: Example 2 Continued
1,500 = 30m
m is multiplied by 30.
1,500 = ____
30m
_____
30
30
Divide both sides by 30 to undo
multiplication.
50 = m
The time needed for the homework is 50 min. So
far, the homework has taken 15 min. Because
50 – 15 = 35, Phil will be finished in 35 min.
Course 1
7-9 Percent Problems
Instead of using proportions, you can
also multiply to find a percent of a
number.
Course 1
7-9 Percent Problems
Additional Example 3: Multiplying to Find a
Percent of a Number
Find 36% of 50.
36% = 0.36 Write the percent as a decimal.
0.36 • 50
Multiply using the decimal.
18
So 18 is 36% of 50.
Check
Use a model to check the answer.
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
0
Course 1
5
10
15
20
25
30
35
40
45
50
7-9 Percent Problems
Check It Out: Example 3
Find 20% of 70.
20% = 0.20 Write the percent as a decimal.
0.20 • 70
Multiply using the decimal.
14
So 14 is 20% of 70.
Check
Use a model to check the answer.
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
0
Course 1
7
14
21
28
35
42
49
56
63
70
7-9 Percent Problems
Lesson Quiz
1. Find 28% of 310. 86.8
2. Find 70% of 542. 379.4
3. Martha is taking a 100-question test. She has
completed 60% of the test in 45 minutes. How
much longer will it take her to finish the test?
30 min
4. Crystal has a collection of 72 pennies. If 25% of
them are Canadian, how many Canadian pennies
does she have?
18
Course 1