Warm Up

1
Preview
Warm Up
California Standards
Lesson Presentation
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Warm Up Write each percent as a fraction. 1.
33 2. 75 3. 20 4. 60
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NS1.3 Convert fractions to decimals and percents
and use these representations in estimations,
computations, and applications.
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Vocabulary
estimate compatible numbers
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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.
13 and 24 are not compatible numbers.
12 and 24 are compatible numbers because 12 is a
common factor of 12 and 24.
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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.
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Additional Example 1A Estimating with Percents
Estimate. 21 of 66
21 20
Use a benchmark close to 21.
Write 20 as a fraction.
66 65 Use compatible numbers.
So 21 of 66 is about 13.
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Additional Example 1B Estimating with Percents
Estimate. 36 of 120
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
3 ? 10 ? 120 5 ? 120 Use the Distributive
Property.
36 6 10 of 120 is 12, so 5 of 120 is 6.
42
So 36 of 120 is about 42.
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Check It Out! Example 1A
Estimate. 29 of 86
29 30
Use a benchmark close to 29.
Write 30 as a fraction.
86 90 Use compatible numbers, 90 and 10.
So 29 of 86 is about 27.
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Check It Out! Example 1B
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.
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Check It Out! Example 1B Continued
4 ? 10 ? 130 5 ? 130 Set up an equation.
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.
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Additional Example 2 Problem Solving Application
Maria took her mother out to lunch for her
birthday. The check for lunch was 20.15. If
Maria wants to leave about a 15 tip, about how
much should she pay?
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Additional Example 2 Continued
The answer is the total amount Maria should pay
for their lunch.
List the important information

• The total cost of lunch was 20.15.

• Maria wants to leave a 15 tip.

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Additional 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 Maria should pay.
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Additional Example 2 Continued
First round 20.15 to 20.
15 10 5
10 of 20 2.00
5 of 20 10 ? 2 1.00
15 10 5
2.00 1.00 3.00
20.15 3.00 23.15
Maria should pay about 23.15.
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Additional Example 2 Continued
Use a calculator to determine whether 3.00 is a
reasonable estimate of a 15 tip. 20.15 ? 0.15 ?
3.02, so 3.00 is a reasonable estimate.
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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?
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Check It Out! Example 2 Continued
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.

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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.
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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
2.50 1.25 3.75
24.85 3.75 28.60
They should pay about 28.60.
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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.
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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 managers number
is reasonable. Explain.
6 ? 2050 5 ? 2000
Use compatible numbers.
0.05 ? 2000
Write 5 as a decimal.
Multiply.
100
The managers number is not reasonable. Only
about 100 books have errors. 250 is much greater
than 100.
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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 managers 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 managers number
is reasonable.
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Lesson Quiz Part I
Possible answers
Estimate. 1. 34 of 12 2. 113 of 80 3. Ian
had dinner with some friends at a restaurant. The
check for his dinner was 10.25. If he wants to
leave a 20 tip, what is the total amount Ian
should pay?
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90
Possible answer 12.25
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Lesson Quiz Part II
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, 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.