6-3 estimating with percents warm up warm up lesson presentation lesson presentation problem of the...

6-3 Estimating with Percents

Warm UpWarm Up

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


Prep for MA.7.A.1.2 Solve percent problems, including problems involving discounts, … taxes,…[and] tips…

Sunshine State Standards


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 the percent of each number.

Check It Out: Example 1A

48% of 81 12

· 81

12

· 80

40

48% of 81



Check It Out: Example 1B

89% of 101 9 10

· 101

9 10

· 100

90

89% of 101



Check It Out: Example 1C

33% of 57 13

· 60

13

· 60

20

33% of 57



Check It Out: Example 1D

12% of 5,005 1 10

· 5,000

1 10

· 5,000

500

12% of 5,005


Tara’s T’s is offering 2 T-shirts for $18, while Good-T’s is having a sale in which you buy one T-shirt for $9.99 and get 30% off a second T-shirt. 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.

30% of $9.99 = 310

· $9.99

13

· $9.99

$3.33The second shirt costs approximately $3.33. Since $10 + $3 = $13, the 2 T-shirts at Good-T’s is the better deal.

Think: 30% is equivalent to . 310

Change 3/10 to a compatible number.

Multiply.


Check It Out: Example 2

25% of $9.75 25% of 10

14

· 10

2.509.75 - 2.50 = 7.50Price at Billy’s office supply; $7.50Price at K’s office supply; $77.50 > $7 so K’s Office Supply Store offers a better deal.

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, for $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

29% of 80 is about 24.

30% equals 3 · 10%.

.



Check It Out: Example 3A

21% of 60

21% is close to 20%

10% of 60 = 6

20% of 60 = 2 · 6 = 12

about 12



Check It Out: Example 3B

3% of 29

29 is close to 30

1% of 30 = 0.3

3% of 30 = 3 · 0.3 = 0.9

about 0.9


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 $28.80 on a hair cut. About how much money should she leave for a 15% tip?

Check It Out: Example 4

Since $28.80 ≈ $30, find 15% of 30.

15% = 10% + 5%

10% of 30 = 3.00

5% of 30 = 3.00 ÷ 2 = 1.50

3.00 + 1.50 = $4.50 tip

about $4.50


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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