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6-2 Estimating with Percents

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Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


Warm UpWrite each percent as a fraction and as a decimal.

1. 75%

2. 10%

3. 32%

4. 17%

34

, 0.75

, 0.1 10 1

, 0.32 25 8

, 0.17 10017


Problem of the Day

You are biking to the library. When you are 75% of the way there, you realize you forgot a book. So you turn around

and head back. When you are of the way back you realize you don’t need the book, so you turn around again and bike 3.2 miles back to the library. How far do you live from the library?

6.4 miles

13


Learn to estimate percents.


The table shows common percents and their fraction equivalents. You can use fractions to estimate the percent of a number by choosing a fraction that is close to a given percent.

Fraction

Percent 10% 20% 25% 50%33 %13 66 %2

3

15

14

13

12

23

110


Use a fraction to estimate 27% of 63.

Additional Example 1: Using Fractions to Estimate Percents

27% of 63 14

· 63

14

· 60

1527% of 63 is about 15.

Compatible numbers are close to the numbers in the problem and help you use mental math to find a solution.

Remember!

Think: 27% is about 25% and

25% is equivalent to .14

Change 63 to a compatible number.

Multiply.


Use a fraction to estimate 48% of 91.

Check It Out: Example 1

48% of 91 12

· 91

12

· 90

45

48% of 91 is about 45.

Think: 48% is about 50% and

50% is equivalent to .12

Change 91 to a compatible number.

Multiply.


Tara’s T’s is offering 2 T-shirts for $16, while Good-T’s is running their buy one for $9.99, get one for half price sale. Which store offers the better deal?

Additional Example 2: Consumer Math Application

First find the discount price for 2 t-shirts at Good T’s.

50% of $9.99 = 12

· $9.99

12

· $10

$5The second shirt cost approximately $5. Since $10 + $5 = $15, the 2 T-shirts for $15 at Good-T’s is the better deal.

Think: 50% is equivalent to .12

Change $9.99 to a compatible number.

Multiply.



First find the discount on the notebook at Billy’s Office Supply.

25% of $9.75 = 14

· $9.75

14

· $10

$2.50The discount is approximately $2.50. Since $10 - $2.50 = $7.50, the notebook from K’s Office Supply Store is the better deal.

Think: 25% is equivalent to .14

Change $9.75 to a compatiblenumber.

Multiply.

Billy’s Office Supply Store is offering 25% off a leather notebook, originally priced at $9.75. K’s Office Supply Store offers the same notebook, not on sale, at $7.00. Which store offers the better deal?


Another way to estimate percents is to find1% or 10% of a number. You can do thisby moving the decimal point in the number.

1% of 45 = 10% of 45 =

To find 1% of a number, move the decimal point two places to the left.

To find 10% of a number, move the decimal point one place to the left.

. .45. 45.


Use 1% or 10% to estimate the percent of each number.

Additional Example 3A: Estimating with Simple Percents

4% of 18

18 is about 20, so find 4% of 20.

1% of 20 = 20.

4% of 20 = 4 · 0.2 = 0.8

4% of 18 is about 0.8.

4% equals 4 · 1%.

.



Additional Example 3B: Estimating with Simple Percents

29% of 80

29% is about 30, so find 30% of 80.

10% of 80 = 80.

30% of 80 = 3 · 8.0 = 24.0


30% equals 3 · 10%.

.



Check It Out: Example 3A

5% of 14

14 is about 15, so find 5% of 15.

1% of 15 = 15.

5% of 15 = 5 · 0.15 = 0.75

5% of 14 is about 0.75.

5% equals 5 · 1%.

.



Check It Out: Example 3B

21% of 60

21% is about 20, so find 20% of 60.

10% of 60 = 60.

20% of 60 = 2 · 6.0 = 12.0


20% equals 2 · 10%.

.


Tim spent $58 on dinner for his family. About how much money should he leave for a 15% tip?

Additional Example 4: Consumer Math Application

Since $58 is about $60, find 15% of $60.

15% = 10% + 5%

10% of $60 = $6

5% of $60 = $6 ÷ 2 = $3

$6 + $3 = $9

Tim should leave about $9 for a 15% tip.

Think: 15% is 10% + 5%.

5% is of 10% so divide $6 by 2.

12

Add the 10% and 5% estimates.


Amanda spent $12 on a hair cut. About how much money should she leave for a 15% tip?


Since $12 is about $10, find 15% of $10.

15% = 10% + 5%

10% of $10 = $1

5% of $10 = $1 ÷ 2 = $0.50

$1 + $0.50 = $1.50

Amanda should leave about $1.50 for a 15% tip.

Think: 15% is 10% + 5%.

5% is of 10% so divide $1 by 2.

12

Add the 10% and 5% estimates.


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz1. Use a fraction to estimate 48% of 72.

2. A café is offering 10% off the $4.99 lunch. If a diner is offering the same lunch for $4.59, which is offering the better deal?

Use 1% or 10% to estimate the percent of each number.3. 4% of 220

4. 19% of 75

5. Mr. and Mrs. Dargen spend $46.25 on a meal. About how much should they leave for a 15% tip?

The café

36

8.8

15

$7

Possible answers:


1. Use a fraction to estimate 52% of 84.

A. 30

B. 40

C. 50

D. 60



2. During the annual sale, Brand A offers 20% off on a $6.55 shirt. Which of the following will make Brand B a better deal?

A. Brand B sells the same shirt for $4.89.

B. Brand B sells the same shirt for $5.59.

C. Brand B sells the same shirt for $5.89.

D. Brand B sells the same shirt for $6.29.



3. Use 1% or 10% to estimate 6% of 239.

A. 2.4

B. 14.4

C. 16.6

D. 24



4. Use 1% or 10% to estimate 18% of 88.

A. 8.8

B. 14

C. 18

D. 22



5. Patricia bought accessories worth $52.75 in an online store. About how much would she spend for a 13% shipping charge?

A. $5

B. $7

C. $9

D. $13


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