Pre-Algebra

8-5 Estimating with Percents

Pledge & Moment of Silence

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 Percents

Student Learning Goal Chart

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

Vocabulary

estimatecompatible numbers

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: