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: 673270
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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
Can you 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 280Slide6
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 42. Slide9
Got it?
Find each number.
a. 150% of 20 b. 160% of 35
Slide10
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?
Slide16
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?
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 of $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?
b. $12.75 is what percent of 4?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?
b. 12% of 85 is what number?Slide26
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?
b. 84 is 75% of what number?Slide28
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?
c. What is 14% of 150
b. Find
72% of 50
.d. Find 50% of 70.Write 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?
b. 27 is what percent of 150?
Write 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?
b.
26% of what number is 45?
Write 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.
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?Slide45
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 tax 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
%?
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?
b. Find the total cost of a spa treatment of $42 including a 6% tax and 20% tip. Slide56
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? Slide62
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?Slide65
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? Slide68
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 = 540 • 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 = 540 • 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?
b. Marcos invests $760 into a savings account. The account pays 4% simple interest. How much interest will he earn after 5 years? Slide73
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?
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? Slide76
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?