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Percent of a number Lesson 1
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Slide1

Percent of a number

Lesson 1Slide2

Find the Percent of a Number

To find the percent of a number, choose one of the methods

1. Write percent as a fraction and then multiply.

OR

2. Write percent as a decimal and then multiply. Slide3

Example 1

Find 5% of 300 by writing the percent as a fraction.

5% =

of 300 =

x 300

x = = = 15So, 5% of 300 is 15.

 Slide4

Example 2

Find 25% of 180 by writing the percent as a decimal.

25% = 0.25

0.25 of 180 = 0.25 x 180

Solve this without a calculator.

So, 25% of 180 is 45.Slide5

Got it?

Find the percent of each number.

a. 40% of 70 b. 15% of 100

c. 55% of 160 d. 75% of 280

281588210Slide6

Use

Percents

Greater Than 100%

150% =

=

= 1 = 1.5 Slide7

Example 3

Find 120% of 75 by writing the percent as a fraction.

Write 120% as

of

.

of 75 = x x = x 6 x 15 = 90So, 120% of 75 is 90.

 Slide8

Example 4

Find 150% of 28 by writing the percent as a decimal.

Write 150% as

.

of 28

1.5 x 28= 42So, 150% of 28 is 45.  Slide9

Got it?

Find each number.

a. 150% of 20 b. 160% of 35

30

56Slide10

Example 5

Refer to the graph. If 275 students took the survey, how many can be expected to have 3 TV’s in each of their houses?

23% of 275

0.23 x 275

= 63.25

So, about 63 students can be expected to have a 3 TV’s in their house. Slide11

Percent and estimation

Lesson 2Slide12

Estimate the Percent of a Number

Sometimes an exact answer is not needed when using

percents

.

Take 70%.

70% = 70% = 7 x 10% Slide13

Example 1

Jodi has paid 62% of the $500 she owes for her loan. Estimate 62% of 500.

62% of 500

60% of 500

60% = 0.6

0.6 x 500 = 300So, 62% of $500 is about $300.  Slide14

Example 2

Marita

and four of her friends ordered a pizza that cost $14.72. She is responsible for 20% of the bill. About how much money will she need to pay?

$14.72 is close to $15.

Find 10% of 15, which is $1.5.

Multiply $1.5 by 2, since 20% is twice as much as 10%. $1.5 x 2 = $3.00Marita should pay about $3.00.Slide15

Got it?

Estimate 42% of 120.

Dante plans to put 80% of his paycheck into a savings account and spend the other 20%. His paycheck this week is $295. About how much will he put into his savings account?

48

About $240Slide16

Example 3

Estimate 122% of 50.

122% = 100% + 22%

100% of 50 + 22% of 50

(1 x 50) + (20% x 50)

50 + ( x 50)50 + 10 = 60So, 122% of 50 is about 60.  Slide17

Example 4

There are 789 seventh grader students at Washington Middle School. About

of the 7

th

grade students have traveled overseas. What is the approximate number of 7

th graders that have traveled overseas? Explain. % can be estimated to 1%.789 can be estimated to 800.1% x 800 = 0.01 x 800 = 88 x = 2So, about 2 seventh graders have traveled overseas. Slide18

Got it?

A country receives

of a sales tax. About how much money would a country receive from the sale of a computer that costs $1,020?

% can be estimated to 1%.

1,020 can be estimated to 1000.

1% x 1000 = 0.01 x 1000 = 1010 x = 7.5So, it would cost about $7.50 in tax.  Slide19

Example 5

Last year, 639 students attended summer camp. Of those who attended this year, 0.5% also attended camp last year. About how many students attended the summer camp two years in a row?

0.5% is half of 1%.

1% of 639

6

So, 0.5% of 639 is half of 6 or 3.About 3 students attended summer camp two years in a row.  Slide20

The Percent Proportion

Lesson 3Slide21

Use the Percent Proportion

Type

Example

Proportion

 

 Find the Percent  What percent of 5 is 4?  Find the Part

 

 

 

What

number is 80% of 5?

 

 

 

Find

the

Whole

 

 

 

4

is 80% of what number?

 

 

 

 

 

 

 

4

out of

5

is

80%

=

=

 Slide22

Example 1

What percent $15 is $9?

Ask: What type of percent proportion do you use?

Find the percent. Let n represent the percent.

In the table, the first number is the denominator and the second number in the numerator.

9(100) = 15n900 = 15nDivide 900 and 15. n = 60 Slide23

Got it?

a. What percent of 25 is 20?

80%

b. $12.75 is what percent of 4?

25.5%Slide24

Example 2

What number is 40% of 120?

p • 100 = 120 • 40

100p = 4800p = 48So, 48 is 40% of 120.  Slide25

Got it?

a. What number is 5% of 60?

3

b. 12% of 85 is what number?

112Slide26

Example 3

18 is 25% of what number?

w

25 = 18 • 10025w = 1800w = 72So, 18 is 25% of 72.  Slide27

Got it?

a. 40% of what number is 26?

65

b. 84 is 75% of what number?

112Slide28

Example 4

The average adult male Western Lowland gorilla eats about 33.5 pounds of fruit each day. How much food does the average adult male gorilla eat each day?

Western Lowland Gorilla Diet

FOOD

PERCENT

Fruit67%Seeds, leaves, stems, and pith17%Insects, insect larvae16%33.5 •100 = w • 673350 = 67w50 = w

 

So, an average male gorilla eats 50 pounds of food each day. Slide29

The Percent Equation

Lesson 4Slide30

Percent Equation

Part = percent • whole

whole = percent • _____________

____________ = percent • whole

 

percentwholepartSlide31

Use the Percent Equation

Type

Example

Proportion

Find the Percent

3 is what percent of 6?Find the PartWhat number is 50% of 6?Find the Whole3 is 50% of what number?3 = n • 6p = 0.5 • 63 = 0.5 • w3 is 50% of 63 = 0.5 x 6

part

percent

wholeSlide32

Example 1

What number is 12% of 150?

Do you need to find percent, part or whole? ________

part = 0.12 • 150

p = 18

So, 18 is 12% of 150. partSlide33

Got it? 1

a. What is 6% of 200?

p = 0.06 • 200

p = 12

c. What is 14% of 150

p = 0.14 • 150p = 21b. Find 72% of 50.p = 0.72 • 50p = 36d. Find 50% of 70.p = 0.5 • 70p = 35Write an equation and solve. Slide34

Example 2

21 is what percent of 40?

Do you need to find percent, part or whole? ________

21 = n • 40

= n

0.525 = nSo, 21 is 52.5% of 40.  percentSlide35

Got it? 2

a. What percent of 40 is 9?

9 = n • 40

22.5% = n

b. 27 is what percent of 150?

27 = n • 15018% = nWrite an equation and solve. Slide36

Example 3

13 is 26% of what number?

Do you need to find percent, part or whole? ________

13 = 0.26 • w

= w

50 = wSo, 13 is 26% of 50.  wholeSlide37

Got it? 3

a. 39 is 84% of what number?

39 = 0.84 • w

46.4= w

b.

26% of what number is 45?.26 = w • 45173.1 = wWrite an equation and solve. Slide38

Example 4

A survey found that 25% of people aged 18-24 gave up their home phone and only use a cell phone. If 3264 people only used a cell phone, how many people were surveyed?

Do you need to find percent, part or whole? ________

3,264 = 0.25w

13,056 = w

About 13,056 people were surveyed. wholeSlide39

Percent of Change

Lesson 5Slide40

Percent of Change

Words:

A

percent of change

is the ratio that compares the change in quantity to the original amount.

Equation: percent of change =  Slide41

Percent of Increase and Decrease

Increase:

percent of increase =

Decrease:

percent of

decrease =  Slide42

Example 1

Find the percent of change in the cost of gasoline from 1970 to 2010. Round to the nearest whole percent if necessary.

This is a percent increase. It increased $1.65.

percent of increase =

= ≈ 1.27 or 127%The cost of gasoline increase by about 127% from 1970 to 2010.  Slide43

Example 2

Yusuf bought a DVD recorder for $280. Now it is on sale for $220. Find percent of change in the price. Round to the nearest whole percent if necessary.

This is a percent decrease. It decreased by $60.

percent of

decrease

= = ≈ 0.21 or 21%The price of the DVD recorder decreased by about 21%. Slide44

Got it? 1 & 2

a. Find the percent of change from 10 yards to 13 yards.

30% increase

b.

The price of a radio was $20. It is on sale for $15. What is the percent of change in the price of a radio?

25% decreaseSlide45

Percent Error

Words:

A

percent error

is a ratio that compares the inaccuracy of an estimate, or amount of error, to the actual amount.

Equation: percent error = Suppose you guess there are 300 gum balls in the jar, and you guessed 400. =  Slide46

Example 3

Ahmed wants to practice free-throws. He estimates the distance from the free-throw line to the hoop and marks it with chalk. Ahmed’s estimate was 13.5 feet. The actual distance should be 15 feet. Find the percent error.

=

The percent error is 10%.

 Slide47

Sales Tax, Tips, and Markups

Lesson 6Slide48

Example 1 – Sales Tax

Drew wants to buy exercise equipment that cost $140 and the sales take is 5.75%. What is the total cost?

Add sales tax to the regular price.

First, find the sales tax. Let t represent sales tax.

t = 0.0575 x 140

t = 8.05Next, add the sales tax to the regular price.$8.05 + 140 = $148.05Slide49

Example 1 – Sales Tax

Drew wants to buy exercise equipment that cost $140 and the sales take is 5.75%. What is the total cost?

Add the percent of tax to 100%.

100% + 5.75% = 105.75% Let t represent sales tax.

t = 1.0575 x 140

t = $148.05The total cost of the exercise equipment is $148.05. Slide50

Got it? 1

What is the total cost of a sweatshirt if the regular price is $42 and the sales tax is 5

%?

$44.31

 Slide51

Tips and Markups

A

tip

or

gratuity

is a small amount of money in return for a service. The total price is the regular price of the service plus the tip. The store sells items for more than it pays for those items. The amount of increase is called the markup. The selling price is the amount the customer pays for an item. Slide52

Example 2

A customer wants to tip 15% on a restaurant bill that is $35. What will be the total bill with the tip?

Add sales tax to the regular price.

First, find the tip. Let t represent the tip.

t = 0.15 x 35

t = 5.25Next, add the tip to the bill.$5.25 + $35 = $40.25Slide53

Example 2

A customer wants to tip 15% on a restaurant bill that is $35. What will be the total bill with the tip?

Add the percent of tip to 100%.

100% + 15% = 115% Let t represent the total.

t = 1.15 x 35

t = $40.25Using either method, the total cost of the bill with tip is $40.25.Slide54

Example 3

A haircut costs $20. Sales tax is 4.75%. Is $25 sufficient to cover the haircut with tax and a 15% tip?

Sales tax and tip together is 19.75%.

Let t represent the tax and tip.

t = 0.1975 x 20

t = $3.95$20 + $3.95 = 23.95Since $25 is more than $23.95, $25 would be enough. Slide55

Got it? 2 & 3

a. Scott wants to tip his taxicab driver 20%. If his commute costs $15, what is the total cost?

$18

b. Find the total cost of a spa treatment of $42 including a 6% tax and 20% tip.

$52.92Slide56

Example 4

A store pays $56 for a GPS navigation system. The markup is 25%. Find the selling price.

First, find the markup.

Let

m

represent the markup. m = 0.25 x 56m = $14$14 + $56 = $70The selling price of the GPS is $70. Slide57

Discount

Lesson 7Slide58

Vocabulary

Discount

or

markdown

is the amount by which the regular price of an item is reduced. The sales price is the regular price minus the discount. Slide59

Example 1

A DVD normally costs $22. This week it is on sale for 25% off the original price. What is the sale price of the DVD?

Subtract the discount from the regular price.

First, find the amount of the discount.

Let d represent the discount.

d = 0.25 x 22d = 5.50

Next, subtract the discount from the regular price.

$22 - $5.50 = $16.50Slide60

Example 1

A DVD normally costs $22. This week it is on sale for 25% off the original price. What is the sale price of the DVD?

Subtract the percent of discount from 100%.

100% - 25% = 75%

The sales price is 75% of the regular price.

Let s represent sales price. s = 0.75 x 22s = 16.50 Slide61

Got it? 1

A shirt is regularly priced at $42. It is on sale for 15% off of the regular price. What is the sale price of the shirt?

$35.70Slide62

Example 2

A boogie board that has a regular price of $69 is on sale at a 35% discount. What is the price with 7% tax?

Find the amount of

the discount.

Let d represent the discount.

d = 0.35 x 69d = 24.15Subtract the discount from the regular price.

$

69 - $24.15 = $44.85Slide63

Example 2

A boogie board that has a regular price of $69 is on sale at a 35% discount. What is the price with 7% tax?

The percent of tax is applied after the discount is taken.

7% of $44.85 = 0.07 • 44.85

= 3.14$44.85 + $3.14 = $47.99The sales price of the boogie board including tax is $47.99Slide64

Got it? 2

A CD that has a regular price of $15.50 is on sale at a 25% discount. What is the sales price with 6.5% tax?

$12.38Slide65

Example 3

A cell phone is on sale for 30% off. If the sale price is $239.89, what is the original price?

The sales price is 100% - 30% or 70% of the original price.

Let p represent the original price.

239.89 = 0.7 x p

= 342.70 = p The original price is $342.70. Slide66

Example 4

Clothes Are Us and

Ratcliffe’s

are having sales. At Clothes Are Us, a pair of sneakers is on sale for $40 off the regular price of $50. At

Rattcliffe’s

, the same brand of sneakers is discounted by 30% off of the regular price of $40. Which store has the better sale price? Clothes Are Us60% of $50 = 0.6 x $50= $30The sales price is $30. Ratcliffe’s70% of $40 = 0.7 x $40= $28The sales price is $28. The sales price at Ratcliffe’s is a better buy. Slide67

Got it? 4

If the sales at Clothes Are Us was 50% off, which store would have the better buy?

Clothes Are Us is cheaper

$25 < $28Slide68

Financial Literacy: Simple Interest

Lesson 8Slide69

Simple Interest Formula

Words:

Simple interest I is the product of the principal p, the annual interest rate, r, and the time t, expressed in years.

Symbols: I =

p

rtSlide70

Example 1

Arnold puts $540 into a savings account. The account pays 3% simple interest. How much will he earn in each amount of time?

a. 5 years

I =

p

rtI = 580 • 0.03 • 5I = 87He will earn $87 in interest in 5 years. Slide71

Example 1

Arnold puts $540 into a savings account. The account pays 3% simple interest. How much will he earn in each amount of time?

b. 6 months

I =

p

rtI = 580 • 0.03 • 0.5I = 8.7He will earn $8.7 in interest in 6 months. Slide72

Got it? 1

a. Jenny puts $1,560 into a savings account. The account pays 2.5% simple interest How much interest will she earn in 3 years?

$117

b. Marcos invests $760 into a savings account. The account pays 4% simple interest. How much interest will he earn after 5 years?

$152Slide73

Example 2

Rondell’s

parents borrow $6,300 from the bank for a new car. The interest rate is 6% per year. How much simple interest will they pay if they take 2 years to repay the loan?

I =

p

rtI = 6,300 • 0.06 • 2I = 756Rondell’s parents will pay $756 in interest in 2 years. Slide74

Example 3

Derrick’s dad bought new tires for $900 using a credit card. His card has an interest rate of 19%. If he has no other charges on his card and does not make a payment, how much money will he owe after one month?

I =

p

r

tI = 900 • 0.19 • I = 14.25$900 + $14.25 = $914.25The total amount owed is $914.25. Slide75

Got it? 2

a. Mrs. Hanover borrows $1,400 at a rate of 5.5% per year. How much simple interest will she pay if it takes 8 months to repay the loan?

$51.33

b. An office manager charged $425 worth of office supplies on a credit card. The credit card has an interest rate of 9.9%. How much money will he owe at the end of one month if he makes no other charges on the card and does not make a payment?

$428.51Slide76

Example 4

Luis is taking out a car loan for $5,000. He plans on paying off the car loan in 2 years. At the end of 2 years, Luis will have paid $300 in interest. What is the simple interest rate on the car loan?

I =

p

r

t300 = 5000 • r • 2300 = 10,000r = r = 0.03 or 3% Slide77

Got it? 4

Maggie is taking out a student loan for $2,600. She plans on paying off the loan in 3 years. At the end of 3 years, Maggie will have paid $390 in interest. What is the simple interest rate on the student loan?

5%

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Percent of a number Lesson 1 - Description


Find the Percent of a Number To find the percent of a number choose one of the methods 1 Write percent as a fraction and then multiply OR 2 Write percent as a decimal and then multiply ID: 672740 Download Presentation

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