Pre-Algebra

8-5 Estimating with Percents

• Warm-up

Pre-Algebra

8-5 Estimating with Percents

Learn to estimate with percents.

Pre-Algebra

8-5 Estimating with Percents

• Going to get into groups of 3• Work together on wkbk pg. 68 #1-5• Come up with a strategy for

estimating• Each group will share their strategy

for the problem I choose for them.• You will have about 20 minutes.

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 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.

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%) 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.

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. 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%) 130 Set up an equation.

Try This: Example 1B

Pre-Algebra

8-5 Estimating with Percents

= 42 + 6.5 10% of 130 is 13, so 5% of 130 is 6.5.

= 48.5

So 44% of 130 is about 48.5.

= 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?

Pre-Algebra

8-5 Estimating with Percents

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.

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%

2 Make a Plan

Think: The numbers 2160 and 27% are difficult to work with.

Find an equivalent ratio for 25%.25% = = 25100

14

Pre-Algebra

8-5 Estimating with Percents

Solve3

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 Back4

25% of 8000 mi is , or 2000 mi. This is the

approximate diameter of the moon.

80004

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: