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7-9 Percent Problems
Warm UpWarm Up
Lesson Presentation
Problem of the Day
Lesson Quizzes
7-9 Percent Problems
Warm UpWrite each decimal as a percent and fraction.
1. 0.38
2. 0.06
3. 0.2
38%,
6%,
20%,
1950
__
350
__
1 5
__
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
7-9 Percent Problems
Learn to find the missing value in a percent problem.
7-9 Percent Problems
To find the percent one number is of another, use this proportion:
% 100
= is of
Because 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.
7-9 Percent Problems
Additional Example 1: Application
First estimate your answer. Think: 35% = ,
which is close to , and 560 is close to 600. So
about of the students participate in after-school sports.
35100
___
1 3
__
1 3
__
1 3
__ This is the estimate.• 600 = 200
Think: “35 out of 100 is how many out of 560?”
Helpful Hint
There are 560 students in Ella’s school. If 35% of the students participate in after-school sports, how many students participate in after-school sports?
7-9 Percent Problems
Additional Example 1 ContinuedNow solve:
s 560
___ 35 100
___ =
100 • s = 35 • 560
100s = 19,600
100s 100
____ 19,600 100
_____ =
s = 196
Let s represent the number of students who participate in after-school sports.
The cross products are equal.
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.
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?
First estimate your answer. Think: 70% = ,
which is close to , and 480 is close to 500. So
about of the students participate in after
school sports.
70100
___
3 4
__
3 4
__
This is the estimate. 3 4
__ • 500 = 375
7-9 Percent Problems
Check It Out: Example 1 ContinuedNow solve:
s 480
___ 70 100
___ =
100 • s = 70 • 480
100s = 33,600
100s 100
____ 33,600 100
_____ =
s = 336
Let s represent the number of students who participate in the fundraising program.
The cross products are equal.
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.
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?
is of
__ % 100
___ =
100 • 20 = 25 • m
25% of the exercises are completed, so 20 minutes is 25% of the total time needed.
The cross products are equal.
20 m
__ 25 100
___ = Set up a proportion. The “of” part is what you have been asked to find.
7-9 Percent Problems
Additional Example 2 Continued
2,000 = 25m
2,000 25
_____ 25m 25
____ =
80 = m
m is multiplied by 25.
Divide both sides by 25 to undo multiplication.
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.
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?
is of
__ % 100
___ =
100 • 15 = 30 • m
30% of the exercises are completed, so 15 minutes is 30% of the total time needed.
The cross products are equal.
15 m
__ 30 100
___ = Set up a proportion. The “of” part is what you have been asked to find.
7-9 Percent Problems
Check It Out: Example 2 Continued
1,500 = 30m
1,500 30
_____ 30m 30
____ =
50 = m
m is multiplied by 30.
Divide both sides by 30 to undo multiplication.
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.
7-9 Percent Problems
Instead of using proportions, you can also multiply to find a percent of a number.
7-9 Percent Problems
Additional Example 3: Multiplying to Find a Percent of a Number
36% = 0.36
0.36 • 50
Write the percent as a decimal.
Multiply using the decimal.
18So 18 is 36% of 50.
Find 36% of 50.
0 5 10 15 20 25 30 35 40 45 50
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
CheckUse a model to check the answer.
7-9 Percent Problems
Check It Out: Example 3
20% = 0.20
0.20 • 70
Write the percent as a decimal.
Multiply using the decimal.
14So 14 is 20% of 70.
Find 20% of 70.
0 7 14 21 28 35 42 49 56 63 70
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
CheckUse a model to check the answer.
7-9 Percent Problems
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
7-9 Percent Problems
Lesson Quiz
1. Find 28% of 310.
2. Find 70% of 542.
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?
4. Crystal has a collection of 72 pennies. If 25% of them are Canadian, how many Canadian pennies does she have?
379.4
86.8
30 min
18
7-9 Percent Problems
1. Identify 35% of 260.
A. 35 B. 91
C. 260 D. 295
Lesson Quiz for Student Response Systems
7-9 Percent Problems
2. Identify 60% of 422.
A. 253.2 B. 482
C. 362 D. 25320
Lesson Quiz for Student Response Systems
7-9 Percent Problems
3. Ella has to draw a flowchart as a part of an assignment. She has drawn 40% of the flowchart in 10 minutes. How much longer will it take her to complete the flowchart?
A. 10 min B. 25 min C. 15 min D. 35 min
Lesson Quiz for Student Response Systems
7-9 Percent Problems
4. Of 80 sheep in a field, 65% are ewes. How many ewes are there in the field?
A. 28 ewes B. 52 ewes
C. 65 ewes D. 108 ewes
Lesson Quiz for Student Response Systems