Pre-Algebra
8-5 Estimating with Percents
Pre-Algebra HOMEWORK
Page 423
#31-38 &Spiral Review (#39-45)
Pre-Algebra
8-5 Estimating with Percents
Our Learning GoalStudents will be able to determine and construct fractions, decimals, and percents by understanding their relationships, solving for the unknown, solving increase and decrease, solving sales tax/total cost contextual problems and compute simple interest.
Our Learning Goal Assignments
• Learn to relate decimals, fractions, & percents (8-1)
• Learn to find percents (8-2)
• Learn to find a number when the percent is known (8-3)
• Learn to find percent increase and decrease (8-4)
• Learn to estimate with percents (8-5)
• Learn to find commission, sales tax, and withholding tax (8-6)
• Learn to compute simple interest (8-7)
Pre-Algebra
8-5 Estimating with PercentsLearning Goal Scale
Students are able to determine & construct fractions, decimals, & percents:
4 3 2 1 0
• Clear understanding their relationships
• Able to solve for the unknown
• Understands how to solve for increase & decrease
• Calculating solving sales tax/total cost contextual problems
• Computing simple interest
• Understands their relationships
• Some solving for the unknown
• Difficulty solving for increase & decrease
• Understands their relationships
• Difficulty solving for the unknown
• Some understanding their relationships
• Even with help, no understanding or skill demonstrated
Pre-Algebra
8-5 Estimating with Percents8-5 Estimating with Percents
Pre-Algebra
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Pre-Algebra
8-5 Estimating with Percents
Warm UpFind 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
Pre-Algebra
8-5 Estimating with Percents
58
34
17% decrease
Pre-Algebra
8-5 Estimating with Percents
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%
Pre-Algebra
8-5 Estimating with Percents
Today’s Learning Goal Assignment
Learn to estimate with percents.
Pre-Algebra
8-5 Estimating with Percents
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.
12 24
compatible13 24
not compatible
Pre-Algebra
8-5 Estimating with Percents
Estimate.
A. 21% of 66
Additional Example 1A: Estimating with Percents
Instead of computing the exact answer of 21% 66, estimate.
21% = 21100
20100
Use compatible numbers, 20 and 100.
15 Simplify.
66 65 Use compatible numbers, 65 and 5.15
65 = 13 Use mental math: 65 ÷ 5.
So 21% of 66 is about 13.
Pre-Algebra
8-5 Estimating with Percents
Estimate.
A. 29% of 86
Try This: Example 1A
Instead of computing the exact answer of 29% 86, estimate.
29% = 29100
30100
Use compatible numbers, 30 and 100.
310 Simplify.
86 90 Use compatible numbers, 90 and 10.310
90 = 27 Use mental math: 90 ÷ 10.
So 29% of 86 is about 27.
Pre-Algebra
8-5 Estimating with Percents
Estimate.
B. 36% of 120
Additional Example 1B: Estimating with Percents
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%) 120 Set up an equation.
Pre-Algebra
8-5 Estimating with Percents
Additional Example 1B Continued
= 36 + 6 10% of 120 is 12, so 5% of 120 is 6.
= 42
So 36% of 120 is about 42.
= 3 10% 120 + 5% 120 Use Distributive Property.
Pre-Algebra
8-5 Estimating with Percents
Estimate.
B. 44% of 130Instead 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%) 130 Set up an equation.
Try This: Example 1B
Pre-Algebra
8-5 Estimating with Percents
= 52 + 6.5 10% of 130 is 13, so 5% of 130 is 6.5.
= 58.5
So 44% of 130 is about 58.5.
= 4 10% 130 + 5% 130 Setup an equation.
Try This: Example 1B Continued
Pre-Algebra
8-5 Estimating with Percents
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?
Additional Example 2: Problem Solving Application
Pre-Algebra
8-5 Estimating with Percents
Additional Example 2 Continued
11 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.
2160 27% e
Diameter of the Moon 27% Diameter of Earth
Pre-Algebra
8-5 Estimating with Percents
Use compatible numbers: 2160 is close to 2000; 27% is close to 25%
22 Make a Plan
Think: The numbers 2160 and 27% are difficult to work with.
Additional Example 2 Continued
Find an equivalent ratio for 25%.25% = = 25100
14
Pre-Algebra
8-5 Estimating with Percents
Solve33
Think: 2000 is of what number?14
4 2000 = e
8000 = e
The diameter of Earth is approximately 8000 miles.
Additional Example 2 Continued
Pre-Algebra
8-5 Estimating with Percents
Look Back44
25% of 8000 mi is , or 2000 mi. This is the
approximate diameter of the moon.
80004
Additional Example 2 Continued
Pre-Algebra
8-5 Estimating with Percents
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?
Try This: Example 2
Pre-Algebra
8-5 Estimating with Percents
11 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.
Try This: Example 2 Continued
Let l represent the length of a soccer field.
100 83% l
Length of football field 83% Length of soccer field
Pre-Algebra
8-5 Estimating with Percents
Use compatible numbers: 83% is close to 80%
22 Make a Plan
Think: The number 83% is difficult to work with.
Try This: Example 2 Continued
Find an equivalent ratio for 80%.80% = = 80100
45
Pre-Algebra
8-5 Estimating with Percents
Solve33
Think: 100 is of what number?45
125 = l
The length of a soccer field is approximately 125 yards.
100 = l54
Try This: Example 2 Continued
Pre-Algebra
8-5 Estimating with Percents
Look Back44
Try This: Example 2 Continued
80% of 125 yards is 125 , or 100 yards. This is
the length of a soccer field.
4 5
Pre-Algebra
8-5 Estimating with Percents
Lesson QuizEstimate.
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.
20%
4
90
40%
10%
Possible answers: