6 2 estimate with percents

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6-2 Estimate with Percents6-2 Estimate with Percents

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Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

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6-2 Estimate with Percents

Warm UpWrite each percent as a fraction.

1. 33% 2. 75%

3. 20% 4. 60%

13

34

15

35

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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%

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Learn to estimate with percents.

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Vocabularyestimatecompatible numbersbenchmark

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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

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When estimating with percents, it helps to know some benchmarks. Benchmarks are common numbers that serve as points of reference. Some common benchmarks for percents are shown in the table.

Percent Decimal Fraction

5% 0.05

10% 0.1

25% 0.25

50% 0.5

66.6% 0.6

100% 1 1

1 201 101 41 22 3

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Estimate.

21% of 66

Additional Example 1A: Estimating with Percents

21% ≈ 20% Use a benchmark close to 21%.

≈ 15 Write 20% as a fraction.

66 ≈ 65 Use compatible numbers, 65 and 5.

15

65 = 13 Use mental math: 65 ÷ 5.

So 21% of 66 is about 13.

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Estimate.

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.

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Additional Example 1B Continued

= 36 + 6 10% of 120 is 12, so 5% of 120 is 6.

= 42


= 3 10% 120 + 5% 120 Use Distributive Property.

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Estimate.

29% of 86

Check It Out: Example 1A

29% ≈ 30% Use a benchmark close to 29%.

≈ 310 Write 30% as a fraction.

86 ≈ 90 Use compatible numbers, 90 and 10.

310

90 = 27 Use mental math: 90 ÷ 10.


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Estimate.

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.

Check It Out: Example 1B

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= 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 Set up an equation.

Check It Out: Example 1B Continued

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Maria took her mother out to lunch for her birthday. The total cost of their food, drinks, and dessert was $20.15. if the sales tax was 7% and Maria wants to leave a 15% tip, about how much should she pay?

Additional Example 2: Problem Solving Application

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Additional Example 2 Continued11 Understand the Problem

The answer is the total amount Maria should pay for their lunch.

List the important information:

• The total cost of food, drinks, and dessert was $20.15.

• The sales tax is 7%.

• Maria wants to leave a 15% tip.

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22 Make a Plan

Think: Sales tax and tip together are 22% of Maria and her mother’s lunch total (7% + 15% = 22%). The numbers $20.15 and 22% are difficult to work with. Use compatible numbers: $20.12 is close to $20.00; 22% is close to 20%.

Additional Example 2 Continued

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Solve33

$20.00 20% = $20.00 0.20

= $4.00

$20.15 + $4.00 = $24.15.


Maria should pay $24.15.

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Look Back44


To determine whether $24.15 is a reasonable estimate of what Maria should pay; use a calculator to find the tax and the tip for $20.15.

$20.15 1.22 = $24.58, so $24.15 is a reasonable estimate.

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Fred and Claudia went out to lunch. The total cost of their food and drinks, was $24.85. if the sales tax was 8.5% and they want to leave a 16% tip, about how much should they pay?

Check It Out: Example 2

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Check It Out: Example 2 Continued11 Understand the Problem

The answer is the total amount Fred and Claudia should pay for their lunch.

List the important information:

• The total cost of food, drinks, and dessert was $24.85.

• The sales tax is 8.5%.

• They wants to leave a 16% tip.

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22 Make a Plan

Think: Sales tax and tip together are 24.5% of Fred and Claudia’s lunch total (8.5% + 16% = 24.5%). The numbers $24.85 and 24.5% are difficult to work with. Use compatible numbers: $24.85 is close to $25.00; 24.5% is close to 25%.

Check It Out: Example 2 Continued

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Solve33

$25.00 25% = $25.00 0.25

= $6.25

$24.85 + $6.25 = $31.10.


Fred and Claudia should pay $31.10.

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Look Back44

To determine whether $31.10 is a reasonable estimate of what Fred and Claudia should pay; use a calculator to find the tax and the tip for $24.85.

$24.85 1.245 = $30.94, so $31.10 is a reasonable estimate.


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Additional Example 3: Printing ApplicationA printing company has determined that approximately 6% of the books it prints have errors. Out of a printing run of 2050 books, the production manager estimates that 250 books have errors. Estimate to see if the manager’s number is reasonable. Explain.6% 2050 ≈ 5% 2000 Use compatible numbers.

≈ 0.05 2000 Write 5% as a decimal.

Multiply. ≈ 100

The manager’s number is not reasonable. Only about 100 books have errors. 250 is much greater that 100.

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Check it Out: Example 3A clothing company has determined that approximately 9% of the sheets it makes are irregular. Out of a shipment of 4073, the company manager estimates that 397 sheets are irregular. Estimate to see if the manager’s number is reasonable. Explain.

9% 4073 ≈ 10% 4000 Use compatible numbers.

≈ 0.10 4000 Write 10% as a decimal.

Multiply. ≈ 400

Because 397 is close to 400, the manager’s number is reasonable.

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Lesson Quiz: Part 1Estimate.

1. 34% of 12

2. 113% of 80

3. Ian had dinner with some friends at a restaurant. His food and drink cost $10.25. If the sales tax is 8.25% and he wants to leave a 20% tip, about how much should Ian pay?

4

90

$13.23

Possible answers:

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Lesson Quiz: Part 2

4. Approximately 8% of each batch of jeans produced at one factory is defective. Ms. Fleming said that in a batch of 400 jeans, about 35 jeans would be defective. Estimate to determine if her number is reasonable. Explain.

Yes, it is reasonable because 8% of 400 is a little less than 10% of 400. 10% of 400 is 40, and 35 is a little less than 40.

6 2 estimate with percents

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