1. Estimating with Percents
8-5
Estimating with Percents
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra

2. Estimating with Percents
Pre-Algebra
8-5
Estimating with Percents
Warm Up
Find each percent increase or decrease to the nearest percent.
1. from 1 to 0.62
2. from 162 to 177
3. from 16 to 22
4. from to
38% decrease
9% increase
38% increase 3 4 5 8
17% decrease

3. Problem of the Day
If you enlarge a picture by 25%, by what percent do you need to reduce it to return it to its original size? (Hint: Try using a simple number for the original area of the picture.)
20%

4. Learn to estimate with percents.

5. Vocabulary
estimate
compatible numbers

6. Some problems require only an estimate
Some problems require only an estimate. Estimates involving percents and fractions can be found by using compatible numbers, numbers that go well together because they have common factors.
13 24
not compatible
12 24 
compatible

7. Additional Example 1A: Estimating with Percents
Estimate.
A. 21% of 66
Instead of computing the exact answer of
21%  66, estimate. 21
100 20
100
Use compatible numbers, 20 and 100.
21% =   1 5
Simplify.
66  65 Use compatible numbers, 65 and 5. 1 5
 65 = Use mental math: 65 ÷ 5.
So 21% of 66 is about 13.

8. Additional Example 1B: Estimating with Percents
Estimate.
B. 36% of 120
Instead of computing the exact answer of
36%  120, estimate.
36%  35% Round.
 30% + 5% Break down the percent into smaller parts.
 3  10% + 5%
35%  120 = (3  10% + 5%)  Set up an equation.

9. Additional Example 1B Continued
= 3  10%  %  Use Distributive Property.
= % of 120 is 12, so 5% of 120 is 6.
= 42
So 36% of 120 is about 42.

10. Instead of computing the exact answer of 29%  86, estimate.
Try This: Example 1A
Estimate.
A. 29% of 86
Instead of computing the exact answer of
29%  86, estimate. 29
100 30
100
Use compatible numbers, 30 and 100.
29% =   3 10
Simplify.
86  90 Use compatible numbers, 90 and 10. 3 10
 90 = 27 Use mental math: 90 ÷ 10.
So 29% of 86 is about 27.

11. Try This: Example 1B
Estimate.
B. 44% of 130
Instead of computing the exact answer of 44%  130, estimate.
44%  45% Round.
 40% + 5% Break down the percent into smaller parts.
 4  10% + 5%
45%  130 = (4  10% + 5%)  Set up an equation.

12. Try This: Example 1B Continued
= 4  10%  %  Setup an equation.
= % of 130 is 13,
so 5% of 130 is 6.5.
= 58.5
So 44% of 130 is about 58.5.

13. Additional Example 2: Problem Solving Application
The diameter of the Moon is about 2160 miles. If the diameter of the Moon is about 27% of the diameter of Earth, what is the approximate diameter of Earth?

14. Understand the Problem
Additional Example 2 Continued 1
Understand the Problem
The answer is the approximate diameter of Earth.
List the important information:
The diameter of the Moon is about 2160 miles.
The diameter of the Moon is about 27% of the diameter of the Earth.
Let e represent the diameter of the Earth.
Diameter of the Moon  27%  Diameter of Earth
 27%  e

15. Additional Example 2 Continued
Make a Plan
Think: The numbers 2160 and 27% are difficult to work with.
Use compatible numbers: 2160 is close to 2000; 27% is close to 25%
25% = = 25
100 1 4
Find an equivalent ratio for 25%.

16. Additional Example 2 Continued
Solve 3
Think: 2000 is of what number? 1 4
4  2000 = e
8000 = e
The diameter of Earth is approximately 8000 miles.

17. Additional Example 2 Continued
Look Back 4
25% of 8000 mi is , or 2000 mi. This is the approximate diameter of the moon.
8000 4

18. Try This: Example 2
The length of a football field is 83% of the length of a soccer field. If a football field is 100 yards, what is the approximate length of a soccer field?

19. Understand the Problem
Try This: Example 2 Continued 1
Understand the Problem
The answer is the approximate length of a soccer field.
List the important information:
The length of a football is about 100 yards.
The length of a football field is 83% of a soccer field.
Let l represent the length of a soccer field.
Length of football field  83%  Length of soccer field
 83%  l

20. Try This: Example 2 Continued
Make a Plan
Think: The number 83% is difficult to work with.
Use compatible numbers: 83% is close to 80%
Find an equivalent ratio for 80%.
80% = = 80
100 4 5

21. Try This: Example 2 Continued
Solve 3
Think: 100 is of what number? 4 5
 100 = l 5 4
125 = l
The length of a soccer field is approximately 125 yards.

22. Try This: Example 2 Continued
Look Back 4
80% of 125 yards is  125 , or 100 yards. This is the length of a football field.
4 5

23. Lesson Quiz
Estimate.
1. 34% of 12
2. 47 out of 236
3. 113% of 80
4. 22 out of 51
5. According to the last census, 33,871,648 people live in California, and 3,694,820 of those people live in Los Angeles. Estimate the percent of Californians who live in Los Angeles.
Possible answers: 4
20% 90
40%
10%