percent. copyright ©, long beach unified school district. all rights reserved. - grade 7 writing...
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Percent
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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Writing RatiosWrite the ratio of girls to boys in
simplest formA class has 20 girls to 16 boys.
Identify the two quantities being comparedStep 1
Step 2 Write as a ratio
girls
boys
Step 3 Simplify20 girls
16 boys
4∙5 girls
4∙4 boys
5 girls4 boys= =
5.1 Ratios
5 girls:4 boys 5 girls to 4 boys
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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Comparing Unit RatesDerrick’s car travels 360 miles and uses 15 gallons of
gas. Louise’s car travels 340 miles and uses 10 gallons of gas. Whose car gets better gas mileage (in miles per
gallon)?
milesgallons
Identify the two ratios being compared and the units of each ratioStep 1
Step 2 Write each ratio
Step 3 Divide each ratio (make each ratio into a unit rate) and compare!
360 mi15 gal
= 24 miles per gallon
5.2 Rates and unit rates
milesgallons
340 mi10 gal
= 34 miles per gallon
Louise’s car gets 10 miles per gallon more than Derrick’s!
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35
12=
xSolving Proportions
Solve:
Step 1: Cross multiply
Step 2: Solve for x
3 x =12 5
3x = 603x = 603 3
x = 205.3 Proportions
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Solving Real-life Problems Using Proportions
Step 1: Write a ratiousing words
Step 3: Cross multiply
12 25 = 15 x 300 = 15x
300 = 15x 15 15
x = 20 pages
Step 4: Solve for x
Pagesminutes
1215
x 25
=
Jason can read 12 pages of a book in15 minutes. How many pages can he read
in 25 minutes?
Step 2: Set-upa proportion
5.3 Proportions
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Step 1: Write a ratio using words
Solving Real-life Problems Using Proportions
Jared is printing a 240 page research paper for his college class. The printer prints the first 60 pages in 4 minutes. How long will it
take to print the rest of the paper?
Step 2: Set-up a proportion
PagesMinutes
604
180x
How many pages does Jaredhave left to print?240 ― 60 = 180
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Solving Real-Life Problems Using Proportions (cont.)
Step 3: Cross multiply and solve for x
Jared is printing a 240 page research paper for his college class. The printer prints the
first 60 pages in 4 minutes. How long will it take
to print the rest of the paper?
60x = 4•18060 60
x = 4 • 3x = 12
It will take 12 minutes to print the rest of the
paper!
604
180x
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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
75 sq. ft.3 cans
1075 sq. ft.p cans
Solving Real-life Problems Using ProportionsAustin needs to paint two walls. One wall is 450 square feet and the other is 625 square
feet. If 3 cans of paint covers 75 square feet, how many cans will Austin need?
Step 1: Write as proportion using words
Step 2: Set-upa proportion
5.3 Proportions
Square feetCans of paint
Square feetCans of paint
Wall 1 + Wall 2450 + 625
=1075
=
=
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43p
75751075375 p
Step 3: Cross multiply and solve
Austin needs 43 cans of paint.
Austin needs to paint two walls. One wall is 450 square feet and the other is 625 square
feet. If 3 cans of paint covers 75 square feet, how many cans will Austin need?
753
1075p
=
Solving Real-life Problems Using Proportions (Continued)
254325
p
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Dimensional AnalysisConvert 5.5 ft to inchesStep 1 Write 5.5 ft as
a fraction
Step 2 Find the conversion factor
How many inches in 1 ft?
How many inches in 1 ft?
Step 3 Multiply 5.5 ft and the conversion
factorStep 4 Simplify
1
ft5.5
1 ft = 12 in1 ft = 12 in
ft1in12
1
ft5.5
ft1in12
66 in66 in5.4 Dimensional Analysis
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1min. 480
min. 60hour1
Dimensional AnalysisConvert 480 minutes into hours
Step 1 Write 480 minutes as a fraction
Step 2 Find the conversion factor
How many minutes in 1 hour?
How many minutes in 1 hour?
Step 3 Multiply 480 min. and the conversion factorStep 4 Simplify
1min. 480
1 hour = 60 minutes1 hour = 60 minutesmin. 60
hour1
8 hours8 hours5.4 Dimensional Analysis
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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Percents
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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Let’s Find Percents
70% of 90Percent means out of a hundred
“of” means multiply
Per Out of or Divide
Cent 100
6-1 Fraction, Decimals, Percents
70% • 90
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25.0
25.0
41
Percent is defined as how many parts out of100.
Percent is defined as how many parts out of100.
6-1 Fraction, Decimals, Percents
4 10
02
82
0
0
5
2 00
%25== 10025
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75
50
75X .10 7.50
50X .10 5.00
75 X .20 15.00
7.5 X 2 15.0
5 X 2 10
50 X .20 10.00
Notice that to find 10% of a number move the decimal one spot to the left
Notice that 20% of a number is 2 times 10% of a number.
6-2 Estimating with Percents
10% 20%number
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Proportions for Percent Problems
Part (is)
Whole (of)100Percent
The variable can be placed in the Part, Whole, or Percent.
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Proportions for Percent Problems
PartWhole100
Percent
Louis got 40 out of 50 correct on his test. What is his percent
correct?
4050100
x
50x = 40 100
50x = 400050 50
x = 80Louis got 80% right.
6-3 Finding Percents
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Proportions for Percent ProblemsSusan answered 90% of the
questions from an online survey. If she has answered 18 questions, how many questions were on the survey?
18x100
90
90x = 18 100
90x = 180090 90
x = 20The survey had 20
questions.6-4 finding a number when % is known
PartWhole100
Percent
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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Proportions for Percent ProblemsFive hundred students applied to
Jordan’s IB magnet. How many will get accepted if Jordan IB only
accepts 40% ?
x500100
40
100x = 40 500100x =
20000100 100x = 200
200 students will be accepted into Jordan’s IB magnet.
6-4 finding a number when % is known
PartWhole100
Percent
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Percent of Increase
0.15505015
At Julio’s Computers they buy computers
for $500 and sell them for $650.
What is the percent of increase?
1. Find the amount of change between the old price and new price
650 — 500 =
2. Use
500150
3.0
%30
The percent of increase is
30%.
The percent of increase is
30%. 6-5 Applying % increase and decrease
OriginalAmount of Change
Change to percent
Change to decimal
3.0
0
150
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Percent of Increase (equation)
At Kat’s Computers they buy
computers for $250 and sell
them for $400. What is the percent of increase?
1. Find the amount of change between the old price and new price
400 – 250 = 1502. Use an equation and solveOriginal • Percent = Amount of price change250 • p = 150
250 250
p = 0.6Change to percentChange to percent
p = 60%
The percent of increase is
60%.
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Percent of DecreaseKat’s Computers is having a sale.
They are advertising a
$1000 computer for $600. What is the percent of
decrease?
1. Find the amount of change between old price and new price
1000―600 = 4002. Use an equation and solveOriginal • Percent = Amount of price change1000 • p = 400
1000 1000p = 0.4
Change to percentChange to percent
p = 40%
The percent of decrease is
40%.
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Discounts (proportions)Sheila bought a dress that is 30% off.
The original price of the dress is $150. • What is the discount?• What is the sale price?
Step 1: Calculate the discount
Step 2: Subtract the discount from theoriginal price
The discount is $45$150 original price- 45 discount$105 sale price
6-5 Applying % increase and decrease
15010030 discount
=
30150100 discount100100
PartWhole100
Percent
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$360 original price― 144 discount $216 sale price
Discounts (equation)
Caleb bought a suit that is 40% off.
The original price of the suit is $360.
• What is the discount?• What is the sale price?Step 1: Calculate the discount
Step 2: Subtract the discount from theoriginal price
The discount is $144
6-5 Applying % increase and decrease
Whole • Percent = Part
360 • 40% = ?
360 • 0.40 = 144
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Sales Tax (proportion)Steve bought a jacket that was priced
at $80. Find the sales tax andprice including tax if the sales tax is 6%.
Step 1: Calculate the sales tax
Step 2: Add the sales tax to theprice
The sales tax is $4.80$80.00 price+ 4.80 sales tax$84.80 price after tax
801006 taxsales=
680100 taxsales100100
6-6 Sales Tax, Commission, and Profit
PartWhole100
Percent
8.4taxsales
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Sales Tax (equation)
Felicia is buying a pair of steel toe work boots for $80. Find the sales tax and price including tax
if the sales tax is 9%.
Step 1: Calculate sales tax
Step 2: Add the Sales tax to theoriginal price
The sales tax is $7.20
$80.00 original price+ 7.20 sales tax $87.20 Total price
6-5 Applying % increase and decrease
Whole • Percent = Part
80 • 9% = ?
80 • 0.09 = 7.2
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Total Price (multi- step problem)Lupe is buying a Wii console that regularly sells for $220. It is on sale for 15% off and the tax rate is 9%. How much will she pay for the Wii?
Step 1: Find the discount
Price • Percent off = discount
220 • 15% = ?
220 • 0.15 = $33
Step 2:Find the sales price
$220-$33 = $187
Original – discount = sales price
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Total Price (cont.)Lupe is buying a Wii console that regularly sells for $220. It is on sale for 15% off and the tax rate is 9%. How much will she pay for the Wii?
Step 3Find the sales tax 187 • 9%
= ?187 • 0.09 = 16.83Step 4 Find the total price
187 + 16.83 = 203.83
Sale price • tax rate = Sales tax
Sales price = $187
The total price of the Wii is $203.83
Sales price + tax = Total price
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CommissionPhillip makes 8% commission at AA
Appliance store. His sales last month were $15,000. What was his commission
last month?
000151008
,=
c
800015100 ,c100100
1200$c
Phillip made $1200 in commission!6-6 Sales Tax, Commission, and Profit
PartWhole100
Percent
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ProfitMarilee's Travel Agency makes 20% profit on all tickets sold. Last month Marilee’s Travel Agency made $60,000 in profit, what were the total sales last month?
Marilee’s total sales were $300,000.
Whole • Percent = Part s • 20% = 60,000
s • 0.20 = 60,0000.20 0.20
s = 300,000
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Simple InterestInterest = Principal rate time
I = P r tInterest: the amount of money
paid to you on savings, or paid by you on money borrowed
rate: the percent charged or paid (must be changed to a decimal or fraction)
Principal: the initial amount of money
time: measured in years6-7 Applying Simple and Compound
Interest
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Simple InterestYou have $5000 in a savings account earning 3% interest.
How much interest will you earn in 2 years?
I = Prt Write the formula
Step 1
Step 2 Substitute the values
I = 5000 0.03 2
Step 3 SimplifyI = 300Step 4 Answer the
question$300 interest
Your savings account will have earned $300 in interest in 2 years.