1. Percent

2. = = Writing Ratios Step 1 Step 2 Step 3 1 girls 20 girls 4∙5 girls
Write the ratio of girls to boys in simplest form
A class has 20 girls to 16 boys.
Identify the two quantities being compared
Step 1
Step 2
Write as a ratio
Step 3
Simplify
girls
20 girls
4∙5 girls
5 girls 1 = =
boys
16 boys
4∙4 boys
4 boys
5 girls:4 boys
5 girls to 4 boys
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
5.1 Ratios

3. Comparing Unit Rates Step 1 Step 2 Step 3 Derrick Louise
Derrick’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)?
Identify the two ratios being compared and the units of each ratio
Step 1
Step 2
Write each ratio
Divide each ratio (make each ratio into a unit rate) and compare!
Step 3
miles
Derrick
360 mi
= 24 miles per gallon
gallons
15 gal
Louise
miles
340 mi
= 34 miles per gallon
gallons
10 gal
Louise’s car gets 10 miles per gallon more than Derrick’s!
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
5.2 Rates and unit rates

4. Solving Proportions 1 Solve: Step 1: Cross multiply 3 x =12 5 3x = 60
Step 2: Solve for x
3x = 60 1
x = 20
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
5.3 Proportions

5. Solving Real-life Problems Using Proportions
Jason can read 12 pages of a book in
15 minutes. How many pages can he read
in 25 minutes?
Step 1: Write a ratio
using words
Pages
minutes 12 15 x 25 =
Step 2: Set-up
a proportion
= 15 x
300 = 15x
300 = 15x
Step 3: Cross multiply
Step 4: Solve for x
x = 20 pages
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
5.3 Proportions

6. 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?
Pages
Step 1: Write a ratio using words
Minutes
Step 2: Set-up a proportion
How many pages does Jared
have left to print? 60 4
180 x
240 ― 60 =
180
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

7. Solving Real-Life Problems Using Proportions (cont.)
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? 60 4
180 x
Step 3: Cross multiply
and solve for x 3
60x = 4•180
It will take 12 minutes to print the rest of the paper! 1 1
x = 4 • 3
x = 12
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

8. Solving Real-life Problems Using Proportions
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?
Step 1: Write as proportion using words
Square feet
Square feet =
Cans of paint
Cans of paint
Wall 1 + Wall 2
=1075
Step 2: Set-up
a proportion
75 sq. ft.
3 cans
1075 sq. ft.
p cans =
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
5.3 Proportions

9. Austin needs 43 cans of paint.
Solving Real-life Problems Using Proportions (Continued)
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?
Step 3: Cross multiply and solve 1 1 25 1 75 3 =
1075 p
Austin needs 43 cans of paint.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

10. Dimensional Analysis Convert 5.5 ft to inches
Step 1 Write 5.5 ft as a fraction
Step 2 Find the conversion factor
How many inches in 1 ft?
1 ft = 12 in
Step 3 Multiply 5.5 ft and the conversion factor
Step 4 Simplify
66 in
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
5.4 Dimensional Analysis

11. How many minutes in 1 hour?
Dimensional Analysis
Convert 480 minutes into hours
Step 1 Write 480 minutes as a fraction
Step 2 Find the conversion factor
How many minutes in 1 hour?
1 hour = 60 minutes
Step 3 Multiply 480 min. and the conversion factor
8 hours
Step 4 Simplify
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
5.4 Dimensional Analysis

12. Percents
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

13. 6-1 Fraction, Decimals, Percents
Let’s Find Percents
Per  Out of or Divide
Cent  100
Percent means out of a hundred
70% of 90
“of” means multiply
70% • 90
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
6-1 Fraction, Decimals, Percents

14. = = % 25 25 100 Fractions to Decimals to Percents! Fraction DECIMAL2 5
Fraction 4 1 8 1
DECIMAL 2 2 25 = = % 25
100
DECIMAL
Percent
Percent is defined as how many parts out of100.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
6-1 Fraction, Decimals, Percents

15. Let's Find 10% and 20% of a Number !75
X .10
7.50 75
X .20
15.00
7.5
X 2
15.0 75 OR 50
X .10
5.00 50
X .20
10.00 5
X 2 10 50 OR
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.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
6-2 Estimating with Percents

16. Proportions for Percent Problems
Part (is)
100
Whole (of)
The variable can be placed in the
Part, Whole, or Percent.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

17. Proportions for Percent Problems
Louis got 40 out of 50 correct on his test. What is his percent correct?
Part
Whole
100
Percent
50x = 40  100
50x = 4000 x 40 50
100 50
x = 80
Louis got 80% right.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
6-3 Finding Percents

18. Proportions for Percent Problems
Susan answered 90% of the questions from an online survey. If she has answered 18 questions, how many questions were on the survey?
Part
Whole
100
Percent
90x = 18  100
90x = 1800 90 18 90
100 x
x = 20
The survey had 20 questions.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
6-4 finding a number when % is known

19. Proportions for Percent Problems
Five hundred students applied to Jordan’s IB magnet. How many will get accepted if Jordan IB only accepts 40% ?
Part
Whole
100
Percent
100x = 40  500
100x = 20000 1 40 x
100
100
100
500
x = 200
200 students will be accepted into Jordan’s IB magnet.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
6-4 finding a number when % is known

20. The percent of increase is 30%.
At Julio’s Computers they buy computers for $500 and sell them for $650. What is the percent of increase?
Find the amount of change between the old price and new price
650 — 500 =
Use
150
Original
Amount of Change
Change to decimal
The percent of increase is 30%.
Change to percent
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
6-5 Applying % increase and decrease

21. Percent of Increase (equation)
Find the amount of change between the old price and new price
400 – 250 = 150
Use an equation and solve
At Kat’s Computers they buy computers for $250 and sell them for $400. What is the percent of increase?
Original • Percent = Amount of
price change
250 • p = 150
The percent of increase is 60%.
p = 0.6
Change to percent
p = 60%
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

22. The percent of decrease is 40%.
Kat’s Computers is having a sale. They are advertising a $1000 computer for $600. What is the percent of decrease?
Find the amount of change between old price and new price
1000―600 = 400
Use an equation and solve
Original • Percent = Amount of
price change
1000 • p = 400
p = 0.4
The percent of decrease is 40%.
Change to percent
p = 40%
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

23. 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
Part
Whole
100
Percent
The discount is $45
$150 original price
discount
$105 sale price
Step 2: Subtract the
discount from the
original price
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
6-5 Applying % increase and decrease

24. Discounts (equation) 360 • 40% = ? 360 • 0.40 = 144
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
360 • 40% = ?
Whole • Percent = Part
360 • 0.40 = 144
The discount is $144
$360 original price
― 144 discount
$216 sale price
Step 2: Subtract the
discount from the
original price
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
6-5 Applying % increase and decrease

25. Sales Tax (proportion)
Steve bought a jacket that was priced
at $80. Find the sales tax and
price including tax if the sales tax is 6%.
Step 1: Calculate the sales tax
Part
Whole
100
Percent
The sales tax is $4.80
Step 2: Add the
sales tax to the
price
$ price
sales tax
$ price after tax
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
6-6 Sales Tax, Commission, and Profit

26. 6-5 Applying % increase and decrease
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
80 • 9% = ?
Whole • Percent = Part
80 • 0.09 = 7.2
The sales tax is $7.20
$80.00 original price
sales tax
$ Total price
Step 2: Add the
Sales tax to the
original price
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
6-5 Applying % increase and decrease

27. 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?
Price • Percent off = discount
Step 1:
Find the discount
220 • 15% = ?
220 • 0.15 = $33
Step 2:
Find the sales price
Original – discount = sales price
$220-$33 = $187
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

28. Total Price (cont.) The total price of the Wii is $203.83
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?
Sales price = $187
Step 3
Find the sales tax
Sale price • tax rate = Sales tax
187 • 9% = ?
187 • 0.09 = 16.83
Step 4
Find the total price
Sales price + tax = Total price =
The total price of the Wii is $203.83
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

29. Commission
Phillip makes 8% commission at AA Appliance store. His sales last month were $15,000. What was his commission last month?
Part
Whole
100
Percent
Phillip made $1200 in commission!
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
6-6 Sales Tax, Commission, and Profit

30. Profit
Marilee'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?
Whole • Percent = Part
s • 20% = 60,000
s • 0.20 = 60,000
0.20
0.20
s = 300,000
Marilee’s total sales were $300,000.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

31. Simple Interest Interest = Principal  rate  time I = P  r  t
Interest: the amount of money paid to you on savings, or paid by you on money borrowed
Principal: the initial amount of money
rate: the percent charged or paid (must be changed to a decimal or fraction)
time: measured in years
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
6-7 Applying Simple and Compound Interest

32. Simple Interest I = Prt I = 5000  0.03  2 I = 300 $300 interest
You have $5000 in a savings
account earning 3% interest.
How much interest will you earn in 2 years?
Write the formula
Step 1
I = Prt
Step 2
Substitute the values
I = 5000  0.03  2
Step 3
Simplify
I = 300
Step 4
Answer the question
$300 interest
Your savings account will have earned $300 in interest in 2 years.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7