Transcript 6-2 Estimate With Percents

6-2
6-2 Estimate
Estimatewith
withPercents
Percents
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
33
6-2 Estimate with Percents
Warm Up
Write each percent as a fraction.
1. 33%
1
3
3. 20%
1
5
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2. 75%
3
4
4. 60%
3
5
6-2 Estimate 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%
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6-2 Estimate with Percents
Learn to estimate with percents.
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6-2 Estimate with Percents
Vocabulary
estimate
compatible numbers
benchmark
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6-2 Estimate 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.
not compatible 13  12 compatible
24 24
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6-2 Estimate 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.
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Percent
Decimal
Fraction
5%
0.05
10%
0.1
25%
0.25
50%
0.5
66.6%
0.6
1
20
1
10
1
4
1
2
2
3
100%
1
1
6-2 Estimate 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 and 5.
65 = 13
Use mental math: 65 ÷ 5.
So 21% of 66 is about 13.
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6-2 Estimate with Percents
Additional Example 1B: Estimating with Percents
Estimate.
36% of 120
Instead of computing the exact answer of
36%  120, estimate.
36%  35%
Round.
 30% + 5%
3
35%
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

Break down the percent into
smaller parts.
10% + 5%
120 = (3

10% + 5%)

120
Set up an
equation.
6-2 Estimate with Percents
Additional Example 1B Continued
= 3  10%
Property.
= 36 + 6

120 + 5%

120
Use Distributive
10% of 120 is 12, so 5% of 120 is 6.
= 42
So 36% of 120 is about 42.
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6-2 Estimate with Percents
Check It Out: Example 1A
Estimate.
29% of 86
29% ≈ 30%
≈ 3
10
86 ≈ 90
3 
10 90 = 27
Use a benchmark close to 29%.
Write 30% as a fraction.
Use compatible numbers, 90 and 10.
Use mental math: 90 ÷ 10.
So 29% of 86 is about 27.
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6-2 Estimate with Percents
Check It Out: Example 1B
Estimate.
44% of 130
Instead of computing the exact answer of
44%  130, estimate.
44%  45%
Round.
 40% + 5%
4
45%
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

Break down the percent into
smaller parts.
10% + 5%
130 = (4

10% + 5%)

130
Set up an
equation.
6-2 Estimate with Percents
Check It Out: Example 1B Continued
=4

10%
= 52 + 6.5
= 58.5

130 + 5%

130
10% of 130 is 13,
so 5% of 130 is 6.5.
So, 44% of 130 is about 58.5.
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Set up an equation.
6-2 Estimate with Percents
Additional Example 2: Problem Solving Application
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?
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6-2 Estimate with Percents
Additional Example 2 Continued
1
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.
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•
The sales tax is 7%.
•
Maria wants to leave a 15% tip.
6-2 Estimate with Percents
Additional Example 2 Continued
2
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%.
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6-2 Estimate with Percents
Additional Example 2 Continued
3
Solve
$20.00

20% = $20.00

= $4.00
$20.15 + $4.00 = $24.15.
Maria should pay $24.15.
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0.20
6-2 Estimate with Percents
Additional Example 2 Continued
4
Look Back
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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6-2 Estimate with Percents
Check It Out: Example 2
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?
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6-2 Estimate with Percents
Check It Out: Example 2 Continued
1
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.
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•
The sales tax is 8.5%.
•
They wants to leave a 16% tip.
6-2 Estimate with Percents
Check It Out: Example 2 Continued
2
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%.
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6-2 Estimate with Percents
Check It Out: Example 2 Continued
3
Solve
$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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6-2 Estimate with Percents
Check It Out: Example 2 Continued
4
Look Back
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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6-2 Estimate 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
≈ 100

2000 Write 5% as a decimal.
Multiply.
The manager’s number is not reasonable. Only
about 100 books have errors. 250 is much greater
that 100.
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6-2 Estimate 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.
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6-2 Estimate with Percents
Lesson Quiz: Part 1
Estimate. Possible answers:
1. 34% of 12
4
2. 113% of 80
90
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?
$13.23
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6-2 Estimate with Percents
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.
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