6-2 Estimating with Percents

NS1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.

California Standards

6-2 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

12 and 24 are compatible numbers because 12 is a common factor of 12 and 24.

13 24

13 and 24 are not compatible numbers.

6-2 Estimating with Percents

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.

6-2 Estimating with Percents

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.

15

65 = 13 Use mental math: 65 ÷ 5.

So 21% of 66 is about 13.

6-2 Estimating with Percents

Estimate.

36% of 120

Additional Example 1B: Estimating with Percents

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.

6-2 Estimating with PercentsAdditional 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 the Distributive Property.

6-2 Estimating with Percents

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.

So 29% of 86 is about 27.

6-2 Estimating with Percents

Estimate.

44% of 130

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

6-2 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 Set up an equation.

Check It Out! Example 1B Continued

6-2 Estimating with Percents

Fred and Claudia went out to lunch. The total cost of their food was $24.85. If they want to leave a 15% tip, about how much should they pay?

Check It Out! Example 2

6-2 Estimating with PercentsCheck It Out! Example 2 Continued

11 Understand the Problem

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

List the important information:

• The total cost of lunch was $24.85.

• They want to leave a 15% tip.

6-2 Estimating with Percents

22 Make a Plan

Check It Out! Example 2 Continued

Use estimation and mental math to find the tip. Then add the tip to the check amount to find the total amount they should pay.

6-2 Estimating with Percents

Solve33

Check It Out! Example 2 Continued

First round $24.85 to $25.

15% = 10% + 5%

10% of $25 = $2.50

5% of $25 = 10% 2 = $1.25

15% = 10% + 5%

$24.85 + $3.75 = $28.60

They should pay about $28.60.

= $2.50 + $1.25 = $3.75

6-2 Estimating with Percents

Look Back44

Check It Out! Example 2 Continued

Use a calculator to determine whether $3.75 is a reasonable estimate of a 15% tip.

24.85 0.15 3.73, so $3.75 is a reasonable estimate.

6-2 Estimating with PercentsAdditional Example 3: Printing Application

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

6-2 Estimating with PercentsCheck It Out! Example 3

A 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.