Unit 3 Semester 1 Review 3 of 4

Ratios & Proportions

Comparing Ratios and Solving Proportions

A ratio is simply a comparison between two numbers. We often write this as a fraction, but there are other ways.​

​

​The image shows the three main ways to express a ratio.

​Ratios

​

A proportion is a comparison between two ratios. Usually we put an equal sign between them.

​

​Proportions

Multiple Choice

$$\frac{5}{8}$$  is an example of

• A Ratio

• A Proportion

• Neither

• Both

Uses For Proportions

In order to solve proportions, we will use cross multiplication which is something you have already seen.

​

​Solving Proportions

​By cross multiplying, we get the question:

Does 1 * 10 = 2 * 5? If they are equal, than the fractions are equal.

In this ​case, 1 * 10 = 10, and 2 * 5 = 10. Therefore, the fractions are equal.

Multiple Choice

Is this proportion true:

$$\frac{6}{10}=\frac{2}{5}$$  

• Yes, they are equal

• No, they are not equal

• I cannot answer that question from the information given

Multiple Choice

Is this proportion true?

$$\frac{1}{6}=\frac{5}{30}$$  

• Yes, this is true

• No, this is not true

• I cannot answer the equation from the information given

We can still cross multiply to give us 8 * x = 4 * 6​ which gives us a nice, one step equation to solve

8x = 24 or x = 3.​

We can use a similar process to solve for one of the four numbers if they are missing.​

Solve For A Variable

Multiple Choice

Solve for X $$\frac{x}{8}=\frac{25}{40}$$  

• 5

• 12.8

• 200

• 480

Multiple Choice

Solve for X $$\frac{4}{7}=\frac{20}{x}$$  

• 35

• 11.43

• 140

• 80

Multiple Choice

Solve for X $$\frac{x+4}{10}=\frac{3}{5}$$  

Don't forget to distribute 5(x+4)

You will need to solve a two step equation this time

• 2

• 5.2

• 6

• 10

Multiple Choice

Solve for X $$\frac{x-2}{14}=\frac{4}{7}$$  

• 10

• 14

• 8.29

• 26.5

Multiple Choice

Word Problem

In the past two years, Chipotle has opened 232 stores. If the rate of growth remains constant, how many stores will the retailer open in the next 3 years?

Which proportion does not represent this situation?

Jot it down in your notebook

• $$\frac{2}{3}=\frac{232}{x}$$  

• $$\frac{3}{2}=\frac{x}{232}$$  

• $$\frac{2}{232}=\frac{3}{x}$$  

• $$\frac{2}{3}=\frac{x}{232}$$  

​See if you can figure out why that one didn't work.

Multiple Choice

Solve the proportion to see how many stores will be opening in the next 3 years.

$$\frac{2}{232}=\frac{3}{x}$$  

• 348

• 154.67

• 38.67

• 464

Begin working on your homework

Multiple Choice

Solve:

• 2

• 9

• 35

• 7

Multiple Choice

Solve:

• 4

• 32

• 2

• 9

Multiple Choice

Solve:

• 1

• 4

• 10

• 5

Multiple Choice

Solve:

• 3

• 4

• -7

• 15

Multiple Choice

Solve:

• 6

• 7

• -8

• -5

Multiple Choice

Solve:

• 4

• 6

• -2

• 5

Multiple Choice

Solve:

• -4

• 10

• 3

• -4

Multiple Choice

Solve:

• -2

• 4

• 15

• 9

Multiple Choice

Solve:

• 3

• 12

• 5

• 3

Multiple Choice

Solve:

• -9

• -28

• 9

• 4

Multiple Choice

Solve:

• 18

• 3

• 4

• 6

Multiple Choice

Solve:

• -8

• 1

• -8

• 36

Multiple Choice

If I need 5 cups of flour to make 3 pies, how many pies can I make with 25 cups of flour?

• 30

• 15

• 25

• 5

Multiple Choice

Gracie brought 24 cookies to give to her 3 classes. Tomorrow she has 4 classes, so how many cookies should she bring?

• 24

• 32

• 8

• 64

Multiple Choice

Hank made 4 pizzas and used 8 lbs of cheese. How much cheese does he need for 1 pizza?

• 1 lb

• 2 lbs

• 16 lbs

• 4 lbs

Multiple Choice

2.2 lbs $$\approx$$  1 kg

If Mr. Wellner weighs 195 lbs, how much does he weigh in kilograms?

• 66.6 kg

• 88.6 kg

• 86.8 kg

• 68.8 kg

Multiple Choice

It takes Emma 18 minutes to type and spell check 14 pages of manuscript. How long will it take her to type and spell check 77 pages?

• 18 minutes

• 99 minutes

• 60 minutes

• 1,386 minutes

Multiple Choice

If 7 sandwich rolls cost $1.68, how much will 29 rolls cost?

• $11.76

• $6.96

• $13.76

• $7.96

Multiple Choice

The Mayflower started with 150 passengers. It lost 60% due to illness. How many people remained?

• 60

• 90

• 100

• 15

Multiple Choice

The waiting time to ride a roller coaster is 20 minutes when 150 people are in line. How long is the waiting time when 240 people are in line?

• 32 People
• 32 Min.
• 12.5 Min.
• 12.5 People

Multiple Choice

A car travels 420 miles in 8 hours.  If the car continues at the same rate, how far will it travel in 12 hours?

• 630 miles
• 630 hours
• 600 miles
• 540 hours

Multiple Choice

On a map, if one centimeter represents 25 kilometers, how many kilometers does 7 centimeters represent?

• 175
• 185
• 200
• 220

Multiple Choice

Hamburger sells for 3 pounds for $6. If Alicia buys 10 pounds of hamburger, how much will she pay?

• $30
• $20
• $60
• $10

Multiple Choice

A cake recipe calls for 1.5 cups of milk and 3 cups of flour. Seth made a mistake and used 5 cups of flour. How many cups of milk should he use to keep the proportions correct?

• 2.5 cups milk
• 1.75 cups milk
• 2 cups flour
• 2.25 cups milk

Multiple Choice

Josh bought a pizza with eight slices of pizza for $12. What is the cost of a slice of pizza?

• $12
• $1.50
• $3
• $1

Multiple Choice

Solve the equation for x:

• 17
• 16
• 15
• 14

Multiple Choice

Solve the proportion:

• 4
• 21
• 24
• 3

Multiple Choice

Solve for k

• 165
• 17
• 1/17
• 1/165

Multiple Choice

Solve for b 

• 8
• 17/12
• 4/3
• 1/8

Measurement Conversion

Magic Numbers

What are Magic Numbers?

• The "relationship" between two units of measurement

• The magic number is the number that specifies the difference between two measurements.

Horse = larger unit & fly = smaller unit

Convert the measurement

• 9 yards = ______ feet

• Which unit is larger?

• Are you converting a smaller unit into a larger unit, or a larger unit into a smaller unit?

Poll

9 yards = ____ feet

Is yards the smaller or larger unit?

• smaller

• larger

Convert the measurement

• 9 yards = ______ feet

• Yards is the larger unit, so...

• Convert a larger unit to a smaller unit means - Horse to fly, MULTIPLY!

• 3 feet = 1 yard, so the "magic number" is 3, this is the number you will multiply by.

Multiple Choice

Convert

9 yards = ______ feet

3 feet = 1 yard

• 12 feet

• 27 feet

• 9 feet

Let's try some more!

Horse to fly, MULTIPLY...Fly to horse, DIVIDE of course

Multiple Choice

Step 1: Horse to fly or Fly to Horse? (larger to smaller or smaller to larger)

84 inches = _____ feet

• Horse to fly

• Fly to horse

• I have no idea...

Fly to horse, DIVIDE of course!

Now for Step 2...

Multiple Choice

Step 2: What is the "magic number" between inches and feet?

Look at the conversion chart in the image.

• 12 inches = 1 foot

• 6 inches = 1 foot

• 12 inches = 1 yard

12 inches = 1 foot

The magic number is 12

Multiple Choice

Step 3: Divide

84 inches = _____ feet

84  $$\div$$  12 =?

• 7 feet

• 6 feet

• 9 feet

Practice Time...

Are you ready??

Multiple Choice

7 yards = _____ feet

3 feet = 1 yard

• 10 feet

• 21 feet

• 2.5 feet

Multiple Choice

96 feet = _____ yards

3 feet = 1 yard

• 99 yards

• 64 yards

• 32 yards

Multiple Choice

2 yards = ____ inches

12 inches = 1 foot

3 feet = 1 yard

• 6 inches

• 72 inches

• 24 inches

Multiple Choice

The Burke family is taking a 3-week vacation to Alaska. How many days will their vacation last?

• 7 days

• 14 days

• 21 days

• 30 days

Multiple Choice

The table shows a pattern for two units of time. Which are the best labels?

• Years, Months

• Years, Weeks

• Weeks, days

• Months, days

Multiple Choice

The tour of the art museum started at 9:35 am. It lasted 1 hour 20 minutes. What time did the tour end?

• 9:55 am

• 10:35 am

• 10:45 am

• 10:55 am

Multiple Choice

An author signed copies of her newest book for 57 minutes until the bookstore closed at 5:00 pm. What time did the author signing books?

• 4:03 pm

• 4:57 pm

• 5:03 pm

• 5:57 pm

Multiple Choice

Fred has been taking guitar lessons for 100 weeks. Nancy has been taking guitar lessons for 3 years. Which statement is TRUE about Fred and Nancy?

• Fred has been taking lessons for less time than Nancy has.

• Fred has been taking lessons for twice as long as Nancy has.

• Fred has been taking lessons for longer than Nancy has

• Fred and Nancy have been taking lessons for the same length of time.

Multiple Choice

The plumber began to fix the leaky sink at 1:45 He worked on it for 1 hour 45 minutes. What time did the plumber finish the job?

• 2:45 pm

• 3:00 pm

• 3:20 pm

• 3:30 pm

Multiple Choice

Mark spent 3 hours hiking one afternoon. How many minutes did he spend hiking?

• 60 minutes

• 120 minutes

• 180 minutes

• 240 minutes

Multiple Choice

Jonas starting reading books to kindergarten students at 3:20 pm. He finished reading at 4:30 pm. How long did he spend reading to the kindergarten students?

• 60 minutes

• 70 minutes

• 80 minutes

• 90 minutes

Multiple Choice

Jordan and his mother are going to start baking cookies at 6:00 pm. It is 4:55. How long will Jordan have to wait to start making cookies?

• 1 hour 5 minutes

• 1 hour

• 2 hours 5 minutes

• 45 minutes

Multiple Choice

Dylan and his family left their house at 9:00 am and arrived at the park at 10:10 am. How long did it take them to reach the park?

• 50 minutes

• 60 minutes

• 10 minutes

• 70 minutes

Multiple Choice

The product of two numbers is 640. Their difference is 12. What are the two numbers?

• 16 and 40

• 42 and 30

• 32 and 20

• 12 and 24

Multiple Choice

Jewel buys 3 yards of fabric to make a cat bed. She starts the project by cutting 4 feet of fabric off the end. How many feet long is the remaining piece of fabric?

• 5 feet
• 12 feet
• 9 feet
• 17 feet

Multiple Choice

John's mom is making lemonade. Her recipe calls for 3 1/2 cups of lemon juice per pitcher. How many gallons of lemon juice would she need to make 10 pitchers? 

• 35 gallons 
• 35 cups
• 2 3/16 gallons
• 2 3/16 cups

Multiple Choice

At field day students were competing in a relay race with a total distance of 750 meters.  There were 3 students on each relay team. How many meters did each student run? 

• 2250 meters 
• 750 meters
• 250 meters
• 2150 meters

Multiple Choice

If a swimmer swam 500 meters in a race, how many kilometers did they swim? 

• 1 km
• 100 km
• 1/2 km
• 1/3 km 

Multiple Choice

During a science unit on weather,  the students were comparing the average annual rainfalls. The average in Charlotte is 2 1/3 feet. The average in New York is 45 inches. Which city has the greatest annual rainfall, and by how much? 

• Charlotte, by 17 inches
• New York, by 21 inches
• Charlotte, by 21 inches
• New  York, by 17 inches 

Multiple Choice

Ms. Lang purchased two bottles of soda for her birthday party.  Each bottle contained 2-liters of soda. She poured exactly 200 mL of soda in each glass.  How many glasses was she able to fill if she used all 2 soda bottles?

• 2000 mL
• 10 mL
• 100 mL
• 1000 mL

Multiple Choice

Mrs. Jones has enough money to buy 2  pounds of candy. She put 48 ounces  of candy in her bag. Does she have enough money to pay for the 48 ounces or does she need to remove some candy from the bag?

• Yes, she has enough money.
• No, she does not have enough money. 

Multiple Choice

How many centimeters are in 1 meter?

• 10
• 100
• 1,000
• 10,000

Multiple Choice

How many pounds are in 1 ton?

• 1000
• 2000
• 100
• 200

Multiple Choice

How many liters are in 250 milliliters?

• 1
• 1/2
• 1/3
• 1/4

Multiple Choice

How many pints are in 4 gallons?

• 8
• 16
• 32
• 48

Multiple Choice

Olivia knew it was very cold out. Her father said it was -7 degrees Celsius outside, but it was going to be 11 degrees Celsius by the afternoon. How many degrees would the temperature have to rise to reach eleven degrees Celsius?

• 4 degrees

• 7 degrees

• 11 degrees

• 18 degrees

Multiple Choice

You are traveling to the moon. Which changes?

• mass

• weight

• both

• neither

Multiple Choice

Twin brothers wanted to know who was taller. Michael measured 1.78 meters. Mitchell was 164 centimeters. Which twin is taller?

• Michael

• Mitchell

Multiple Choice

At 5pm, the temperature was 5 degrees Celsius. A blizzard was approaching. What it began snowing at 11pm, the temperature dropped to -11 degrees Celsius. How many degrees did the temperature drop from 5pm to 11pm?

• 5 degrees

• 6 degrees

• 11 degrees

• 16 degrees

Multiple Choice

It was unusual for Cinnamon to wander so far from home. She was a good dog and usually stayed very close to home. After looking for her for almost 3 hours, Dylan found her 3 km from home. How many decimeters was she from home?

• 0.003

• 0.0003

• 3000

• 30000

Multiple Choice

Which is equal to 750 ms?

• 7500 cs

• 7.5 ds

• 750000 s

• 0.0075 ks

Multiple Select

Check ALL metric measurements.

• inch

• centimeter

• gallon

• pint

• Liter

Multiple Choice

Which measurement would be best for measuring the distance from your house to school?

• millimeters

• centimeters

• meters

• kilometers

Poll

Are you ready for a quiz on Conversions tomorrow?

• yes!

• no!

• possibly

Multiple Choice

How do you find the area of a rectangle?

• Length + Length + Length + Length
• Length + Width
• Length x Width
• Width x Width

Multiple Choice

• Area of a square
• Area of a rectangle
• Area of a triangle
• Area of a parallelogram

Multiple Choice

Find the Area of this triangle

• 19.8 km²
• 37.8 km²
• 18.9 km²
• 35 km²

Multiple Choice

Find the area of the triangle.

• 39 sq feet
• 30.8 sq feet
• 78 sq feet
• 101.4 sq feet

Multiple Choice

What is the area of this figure?

• 40 square units
• 45 units
• 13

Multiple Choice

Find the PERIMETER of this figure.

• 20 square feet
• 20 cm
• 25 square feet
• 20 cm sq.

Multiple Choice

If I wanted to place a fence around my backyard to keep my dog from running away, I would be looking at?

• Perimeter
• Area

Multiple Choice

Adam was painting a wall in his room. The wall was 4 feet wide and 4 feet tall. What is the area of the wall he has to paint?

• 16ft
• 8ft
• 12ft
• 4ft

Multiple Choice

A lawn had an area of 35 square feet. If it was 7 feet width, how long was it? 

• 84 ft.
• 245 ft.
• 5 ft.
• 14 ft.

Multiple Choice

The woods behind Tom's house were 8 miles wide and has a perimeter of 28 miles. What is the area of the woods?

• 28 miles

• 48 miles

• 86 miles

• 42 miles

Multiple Choice

Ashley wants to use ribbon to put a border around her picture. The picture is 6 inches long and 4 inches wide. How much border will she need?

• 24 inches

• 20 inches

• 10 inches

Multiple Choice

Faye was cutting out some fabric for a friend. She cut a piece that was 3 centimeters wide and had an area of 24 cm. How long was the piece? 

• 72 cm
• 6 cm
• 8 cm
• 12 cm

Multiple Choice

What is the area of the shaded region?

• 4 cm²
• 16 cm²
• 8 cm²
• 12 cm²

Multiple Choice

What is the area of the shaded region?

• 14 m²
• 120 m²
• 106 m²
• 134 m²

Multiple Choice

What is the area of the shaded region?

• 20 sq cm
• 4 sq cm
• 30 sq cm
• 24 sq cm

Fill in the Blanks

Multiple Choice

What is the formula for finding area of a rectangle?

• A = l•w
• A = s•df
• A = b•c
• A and C

Multiple Choice

Before soccer practice, Laura warms up by jogging around the outside of the entire soccer field. The field measures 80 meters by 120 meters.

If Laura wants to know how many meters she jogged in all, which measurement should she find?

• Area

• Perimeter

• Length

• Width

Multiple Choice

The diameter of a circle is 3 centimeters. What is the circumference?

• 11.5cm2
• 9.42 cm2
• unicorns are awsome
• 45.3 cm2

Multiple Choice

what is the area of this semicircle ?
d = 8 cm 

• 100.48 cm²
• 80 cm²
• 200.96 cm²
• 25.12 cm²

Multiple Choice

A circular swimming pool is 21 feet in diameter.
How many feet around is the pool?

• 10.5 ft
• 42 ft
• 65.94 ft
• 131.95 ft

Multiple Choice

Dan is framing a picture of his baseball team. What would be the BEST measurement for Dan to find in order to know the length of the molding he will need to frame the picture?

• the area of the picture

• the weight of the picture

• the volume of the picture

• the perimeter of the picture

Multiple Choice

Mrs. Lozano is choosing carpet for her family room. Which of the following must Mrs. Lozano know to find out how much carpet she needs?

• the cost of one square yard of carpeting

• the perimeter of the family room floor

• the area of the family room floor

• the height of the family room

Multiple Choice

What is the perimeter of this figure?
(click to show image)

• 12 m
• 20 m
• 12 cm
• 20 cm

Multiple Choice

Find the perimeter of the rectangle

• 2x - 2 
• 6x - 15 
• 4x - 4 
• 6x - 15

Multiple Choice

The radius of a cookie is 5 inches. What is the cookie’s

circumference?

• 10 in

• 2.5 in

• 15.7 in

• 31.4 in

Multiple Choice

What is the formula for finding the area of a circle?

Multiple Choice

Find the area. Round your answer to the nearest tenth.

• 62.9 in

• 31.4 in

• 1256.6 in²

• 314.2 in²

Multiple Choice

Find the area of the circle

• 43.96
• 153.86
• 87.82
• 307.72

Multiple Choice

What is the area of this square if one side is equal to 6 inches?

• $$36\ in^2$$  

• $$12\ in^2$$  

• $$24\ in^2$$  

• $$1,296in^2$$  

Multiple Choice

Read or Listen Carefully!! The perimeter of a square piece of confetti is 24 millimeters. How long is each side?

• $$6mm^{ }$$  

• $$6mm^2$$  

• $$48mm^2$$  

• $$96mm^{ }$$  

Multiple Choice

Which of the following expressions is equivalent to 5x + 1?

• 3x + 3x + 1

• 5(x + 1)

• 3x + 2x + 1

• 10x - 6x + 1

Multiple Choice

Which of the following expressions is equivalent to x - 3?

• x + 3

• 5x - 3 + 4x

• 5x - 3 - 4x

• x + x - 3

Multiple Choice

Which expression is equivalent to 5(x + 3) + 2(3x + 4)

• 11x + 23

• 11x + 7

• 10x + 23

• 11x + 14

Multiple Choice

Find the area of the rectangle.

• 2x + 4
• x + 2 
• 8x - 16 
• 4x - 8 

Multiple Choice

Find the area of the rectangle.

• 6x - 15
• 4x - 4 
• 2x - 2 
• 5x - 2

Multiple Choice

Find the perimeter of the rectangle.

• 3x² + 6x
• 4x + 6
• 8x + 12
• 6x + 12

Multiple Choice

Find the perimeter of the rectangle.

• 3x + 7
• 6x + 14
• 18x + 6
• 18x + 6