1. 7-9 Percent Problems Warm Up Problem of the Day Lesson Presentation
Course 1
Warm Up
Problem of the Day
Lesson Presentation

2. Write each decimal as a percent and fraction.
Warm Up
Write each decimal as a percent and fraction.
3. 0.2 19 50 __
38%, 3 50 __
6%, 1 5 __
20%,

3. 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

4. Learn to find the missing value in a percent problem.

5. To find the percent one number is of another, use this proportion:
% 100 =
is 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.

6. 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 after-school sports?
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. 35
100
___ 1 3 __ 1 3 __
• 600 = 200
This is the estimate.
Helpful Hint
Think: “35 out of 100 is how many out of 560?”

7. Additional Example 1 Continued
Now solve:
Let s represent the number of students who participate in after-school sports. 35
100
___ s
560
___ =
100 • s = 35 • 560
The cross products are equal.
100s = 19,600
s is multiplied by 100.
100s
100
____
19,600
100
_____
Divide both sides of the equation by 100 to undo multiplication. =
s = 196
Since 196 is close to your estimate of 200, 196 is a reasonable answer.
196 students participate in after-school sports.

8. 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. 70
100
___ 3 4 __ 3 4 __
• 500 = 375
This is the estimate.

9. Check It Out: Example 1 Continued
Now solve:
Let s represent the number of students who participate in the fundraising program. 70
100
___ s
480
___ =
100 • s = 70 • 480
The cross products are equal.
100s = 33,600
s is multiplied by 100.
100s
100
____
33,600
100
_____
Divide both sides of the equation by 100 to undo multiplication. =
s = 336
Since 336 is close to your estimate of 375, 336 is a reasonable answer.
336 students participate in the fundraising program.

10. 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 completed, so 20 minutes is 25% of the total time needed. %
100
___ is of __ =
Set up a proportion. The “of” part is what you have been asked to find. 25
100
___ 20 m __ =
100 • 20 = 25 • m
The cross products are equal.

11. Additional Example 2 Continued
m is multiplied by 25.
2,000 25
_____
25m 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 – 20 = 60, Johan will be finished in 60 min.

12. 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 completed, so 15 minutes is 30% of the total time needed. %
100
___ is of __ =
Set up a proportion. The “of” part is what you have been asked to find. 30
100
___ 15 m __ =
100 • 15 = 30 • m
The cross products are equal.

13. Check It Out: Example 2 Continued
m is multiplied by 30.
1,500 30
_____
30m 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 – 15 = 35, Phil will be finished in 35 min.

14. Instead of using proportions, you can also multiply to find a percent of a number.

15. 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%

16. Write the percent as a decimal.
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%

17. 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?
86.8
379.4
30 min 18