Ratios and Proportions EOG Lesson Review

​MGSE7.RP.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour.​

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​LEARNING TARGETS

I can compute unit rates associated with ratios of fractions.

I can include ratios of lengths.

I can include area ratios.

I can include quantities measured in like units.

I can include quantities measured in unlike units. (inches to feet…)​

​Vocabulary

Rate

Unit Rate

Ratio

Fraction

Multiplicative Inverse​

​Essential Question

How do I interpret a unit rate mathematically using words?

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What is a unit rate?

• used to compare quantities in which the second quantity is one

• The denominator in the fraction is ONE

• miles per hour

• earnings per hour

• cost per gallon

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When finding the unit rate:

Calculating Unit Rate

• miles per hour

• words per minute

• miles per hour

• EXAMPLE:

• $40 for 5 pizzas. Find the price per pizza!

• $87 for 3 video games. Find the price per video game.

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Multiple Choice

It takes a turtle 3 ¼ hours to walk 1 ½ miles. How many hours does it take to walk one mile?

• 6/13 hours

• 39/8 hours

• 13/6 hours

• 8/39 hours

Multiple Choice

A recipe calls for 2/3 cup white sugar for every ¾ cup brown sugar. If I want to use 1 cup of white sugar, how much brown sugar should I use?

• 9/8 cups

• 1/2 cups

• 8/9 cups

• 2 cups

Multiple Choice

Lauren bikes 4/3 miles in 1/10 hour. How long does it take her to bike one mile?

• 15/2 hours

• 2/15 hours

• 40/3 hours

• 3/40 hours

Multiple Choice

Joe can run 3 2/5 miles in 7/8 of an hour. What is his speed in miles per hour?

• 3  9/13 mph

• 119/40 mph

• 3  31/35 mph

• 35/136 mph 

Multiple Choice

What is a unit rate?

• Two unlike things compared to each otehr 

• How often something occurs 

• A rate expressed as something per two

• A rate expressed as something per one

Multiple Choice

Paige mows 1/6 of an acre in 1/4 hour. How many acres does Paige mow per hour? 

• 6/4

• 2/3

• 2

• 3

Multiple Choice

A recipe calls for 2/3 cup white sugar for every ¾ cup brown sugar. If I want to use 1 cup of white sugar, how much brown sugar should I use?

• 9/8 cups

• 1/2 cups

• 8/9 cups

• 2 cups

Proportional Relationships

Characteristics of Proportional Graphs.

• They are in the shape of a straight line.

• They start or cross at the point of origin.

Multiple Choice

Which graph is non-proportional?

• A
• B
• C
• D

Multiple Choice

Does this graph represent a proportional relationship?

• Yes
• No

Multiple Choice

Is the graph proportional or non proportional?

• proportional
• non proportional

Multiple Choice

The origin is located where in the coordinate plane?

• (0, 0)

• (10,10)

• (100, 100)

• (50, 50)

Constant of Proportionality

Multiple Choice

Does the table represent a proportional relationship?

• Yes.
• No.

Multiple Choice

What is the constant of proportionality?

• 15
• 5
• 75
• 25

Multiple Choice

In the equation y = 14x, what is the constant of proportionality?

• y
• x
• 14
• y=14

Multiple Choice

Write an equation for this relationship.

• y=1/5x
• y=1/2x
• y=2x
• y=5x

Multiple Choice

Write the equation for the table given.

• y = 16/2x
• y=8x
• y=12x

Multiple Choice

Write the equation for the table given

• y = 1/3x
• y = 3x
• y = 1/2x

Multiple Choice

What is the constant of proportionality?

• $3

• $4

• $2

• $9

7.RP.3 Reteach - Percents, Tax, Tip, Discount

Percent

A percent literally means "per 100" or "out of 100".

Given a ratio, we can convert it into a percentage be converting the denominator to 100.

How does a proportion change to a percent?

• find out how much to multiply the denominator by to reach 100.

• In this example the original denominator is 10, so we just need to multiply by 10 to get to 100.

How does a proportion change to a percent?

• Then we multiply the numerator by the same amount to get the final percentage!

• In this case the percentage is 60.

Multiple Choice

45/50 is what percent?

• 45%

• 95%

• 9%

• 90%

Multiple Choice

2/5 is what percent?

• 40%

• 25%

• 52%

• 2.5%

Percent Equation Set-up

• We use this equation to find out what percentage a ratio is.

• We use percents to find out the proportional amount of something.

Percent Equation Set-up

• To be able to use this equation we need to have 2 of the unknown pieces:

• The Whole: what is the total we are looking at?

• The Part: what portion of the whole are we dealing with?

• The Percent: what is the equivalent ratio over 100?

Percent Equation Example:

• The Part: In this case the number of strikes

• The Whole: the number of frames bowled

• The Percent: this is what we must figure out.

Percent Equation Example:

• You can use the same model we used before. This means we would multiply the numerator and denominator by 10/3 to get our solution.

• The answer is 40 percent

Percent Equation Example:

• Or we could rewrite the equation as shown here:

Multiple Choice

What is 30% of 50?

• 16

• 16.3

• 17.4

• 15

Multiple Choice

Bob wants to buy a computer. He needs to raise 10% to be able to put it on layaway. If the computer costs $700, how much will he need to save?

• $140

• $100

• $70

• $700

Multiple Choice

Josie makes 20% commission on every car that she sells. If she sells a car for $50,000, how much commission did she make?

• $40,000

• $10,000

• $1,000

• $4,000

Multiple Choice

Harris ran a total of 15 miles last week. She ran 4.2 of those miles on Monday. What percent of her total distance did she run on Monday?

• 28%

• 42%

• 72%

• 58%

Sales Tax

• Sales tax is a percentage of the cost of things you are buying.

• It is then added to the end of your bill.

Sales Tax

• In this example the sales tax percent is 7%

• The purchase amount is $9.99

• The total sales tax you will pay will be $0.70

Sales Tax

• The total cost you will pay then becomes the purchase amount plus the sales tax

• The purchase amount is $9.99

• The total sales tax you pay is $0.70

• The total cost is $10.69

Multiple Choice

Carrie's car is valued at $11,250. If the property tax rate is 1.5%, how much tax does she owe?

• $1687.50

• $168.75

• $16.88

• $1.69

Multiple Choice

You bought several Christmas presents that cost $58.50. The sales tax was 6.5%. How much money did you spend in taxes?

• 3.80

• 8.30

• 62.30

• 54.70

Multiple Choice

You bought several Christmas presents that cost $58.50. The sales tax was 6.5%. How much money did you spend on your family's Christmas presents?

• 3.80

• 8.30

• 62.30

• 54.70

Multiple Choice

At McDonald’s a McChicken cost $1.49. Meals tax is 5%. What is the total cost?

• $1.54

• $1.65

• $1.56

• $1.42

Multiple Choice

A water bottle costs $9.45. Sales tax is 7%. What is the total cost?

• $9.52

• $0.66

• $10.11

• $8.79

Tip

(Also Called Gratuity)

• Tip is calculated based off of the purchase amount BEFORE you add the tax.

• The Tip amount is also calculated using a percent. (Like Tax)

• A Tip is then added on at the end.

Tip

(Also Called Gratuity)

• In this case the purchase amount is $24.99

• The percent you wish to tip is 18%

• The tip amount you will pay is $4.50

Multiple Choice

Johan's bill for food was $32.64. He left a tip of 16%. How much did he leave for a tip?

• $7.73

• $16.00

• $5.22

• $37.86

Multiple Choice

You get a new haircut that costs $15. You give a tip of 20%. What is the total cost?

• $35.00

• $3.00

• $18.00

• $12.00

Multiple Choice

Breakfast at Denny’s cost $8.63. You give a 15% tip. What is the total cost?

• $8.78

• $1.29

• $9.92

• $7.34

Multiple Choice

Dinner at the Olive Garden cost $52.37. You leave a 20% tip. What is the total cost?

• $72.37

• $10.47

• $62.84

• $41.90

Finding Tax and Tip for the same purchase

• Here our purchase amount is $43.28

• We must find our tax

• We must find out Tip

• Then we take the total to find out how much we spend

Multiple Choice

You go to a restaurant and your total cost (before tax and tip) is $34.00. How much will the 6% sales tax cost you?

• $20.40

• $2.04

• $0.24

• $2.40

Multiple Choice

You go to a restaurant and your total cost (before tax and tip) is $34.00. How much will a 20% tip cost you?

• $6.96

• $0.68

• $68.00

• $6.80

Multiple Choice

You go to a restaurant and your total cost (before tax and tip) is $34.00. How much will your total bill be if the tax is 6% and you decide to leave a 20%?

• $52.96

• $36.68

• $68.04

• $42.80

Multiple Choice

You restaurant bill is $50.00. How much is your total cost after a 6% tax and a 20% tip? (Tip is calculated BEFORE tax)

• $63.00

• $53.00

• $50.00

• $1000

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