Transcript Ch 6-2 Estimating with Percents

6-2 Estimating with Percents
California
Standards
NS1.3 Convert fractions to decimals and
percents and use these representations in
estimations, computations, and applications.
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.
13
24
13 and 24 are not compatible numbers.
12
24
12 and 24 are compatible numbers because
12 is a common factor of 12 and 24.
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
Additional Example 1A: Estimating with Percents
Estimate.
21% of 66
21% ≈ 20%
≈
1
5

1
5
Use a benchmark close to 21%.
Write 20% as a fraction.
66 ≈ 65
Use compatible numbers.
65 = 13
Use mental math: 65 ÷ 5.
So 21% of 66 is about 13.
6-2 Estimating with Percents
Additional Example 1B: Estimating with Percents
Estimate.
36% of 120
36%  35%
Round.
 30% + 5%
3
35%


Break down the percent into
smaller parts.
10% + 5%
120 = (3

10% + 5%)

120
Set up an
equation.
6-2 Estimating with Percents
Additional Example 1B Continued
=3

10%
= 36 + 6

120 + 5%

120
Use the Distributive Property.
10% of 120 is 12, so 5% of 120 is 6.
= 42
So 36% of 120 is about 42.
6-2 Estimating with Percents
Check It Out! Example 1A
Estimate.
29% of 86
29% ≈ 30% Use a benchmark close to 29%.
≈
3
10
86 ≈ 90
3 
10 90 = 27
Write 30% as a fraction.
Use compatible numbers, 90 and 10.
Use mental math: 90 ÷ 10.
So 29% of 86 is about 27.
6-2 Estimating with Percents
Check It Out! Example 1B
Estimate.
44% of 130
44%  45%
Round.
 40% + 5%
4
45%


Break down the percent into
smaller parts.
10% + 5%
130 = (4

10% + 5%)

130
Set up an
equation.
6-2 Estimating with Percents
Check It Out! Example 1B Continued
=4

10%
= 52 + 6.5
= 58.5

130 + 5%

130
Set up an equation.
10% of 130 is 13,
so 5% of 130 is 6.5.
So, 44% of 130 is about 58.5.
6-2 Estimating with Percents
Check It Out! Example 2
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?
6-2 Estimating with Percents
Check It Out! Example 2 Continued
1
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
Check It Out! Example 2 Continued
2
Make a Plan
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
Check It Out! Example 2 Continued
3
Solve
First round $24.85 to $25.
15% = 10% + 5%
10% of $25 = $2.50
5% of $25 = 10%  2 = $1.25
15% = 10% + 5%
= $2.50 + $1.25 = $3.75
$24.85 + $3.75 = $28.60
They should pay about $28.60.
6-2 Estimating with Percents
Check It Out! Example 2 Continued
4
Look Back
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 Percents
Additional 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.
≈ 100
Multiply.
The manager’s number is not reasonable. Only
about 100 books have errors. 250 is much greater
than 100.
6-2 Estimating with Percents
Check 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.
≈ 400
Multiply.
Because 397 is close to 400, the manager’s number
is reasonable.