Worksheet: Proportional and Nonproportional Relationships

In this worksheet, we will practice recognizing ratios that are in proportion, finding an unknown term in a proportion, and identifying proportionality in real-world problems.

Q1:

Determine whether the quantities in the following rates are proportional: 63 points scored in 7 games and 76 points scored in 10 games.

  • Anot proportional
  • Bproportional

Q2:

In the table below, the numbers in the first row are proportional to the corresponding numbers in the second row. What is the value of π‘₯?

3 π‘₯
4 6

Q3:

At a school book sale, Noah bought 8 books for $88, and Charlotte bought 9 books for $27. Are these rates proportional?

  • Ayes
  • Bno

Q4:

This year, Hannah celebrated her 10th birthday and her brother Daniel celebrated his 5th birthday. Hannah noticed that she is now twice as old as her brother. Is the relationship between their ages proportional?

  • AYes
  • BNo

Q5:

A survey showed that 5 out of 7 people wear a watch. Another survey showed that 11 out of 12 people wear a watch. Are these results proportional?

  • Ayes
  • Bno

Q6:

The following table represents the number of sites dug by a group of archeologists and the number of weeks they took. Does the table show a proportional relationship?

Number of Sites 2 3 4
Number of Weeks 12 18 24
  • ANo
  • BYes

Q7:

The table below shows the price to mail a first-class letter for various weights. Is the cost to mail a letter proportional to its weight?

Cost ($) 0.39 0.59 0.79 1.36
Weight (oz) 1 2 3 4
  • Ayes
  • Bno

Q8:

Is the length of one side of the given figure proportional to its area?

  • Ano
  • Byes

Q9:

Determine whether the following statement is true or false: A proportion is an equation in which two or more ratios are equal.

  • Atrue
  • Bfalse

Q10:

A shipping company charges $5.25 to deliver a package. In addition, they charge $0.45 for each pound over 1 lb that the package weighs. Is the cost of shipping a package proportional to the weight of the package?

  • Ano
  • Byes

Q11:

An elevator ascends or goes up at a rate of 750 feet per minute. Is the height to which the elevator ascends proportional to the number of minutes it takes to get there?

  • Ano
  • Byes

Q12:

Determine whether the quantities in the following rates are proportional: 39 computers for 95 students and 69 computers for 80 students.

  • Aproportional
  • Bnot proportional

Q13:

Sophia wants to enlarge a photo that is 4 inches by 6 inches. Which of the following is proportional to the original photo?

  • A18 in by 24 in
  • B8 in by 10 in
  • C20 in by 24 in
  • D24 in by 36 in
  • E16 in by 20 in

Q14:

Jacob built a model of his room using toy blocks. The table shows the dimensions of the room and Jacob’s model respectively. Is Jacob’s model to scale?

Actual Room Jacob’s Model
Height 15 feet 5 blocks
Width 60 feet 10 blocks
Length 75 feet 25 blocks
  • AYes
  • BNo

Q15:

Is the length of one side of this shape proportional to its perimeter?

  • Ayes
  • Bno

Q16:

Hannah works as a babysitter. The proportional relationship between the number of hours she works and the total amount of money she earns is shown in the graph.

Which of the following statement is NOT true?

  • AThe point 𝑄 shows that Hannah would earn $60 if she worked 4 hours.
  • BAny point of coordinates (π‘₯,𝑦) on this graph shows that Hannah would earn $𝑦 if she worked π‘₯ hours.
  • CThe unit rate of this proportional relationship is $15/hour.
  • DIf Hannah worked for 10 hours, she would earn $150.
  • EIf Hannah worked for 4 hours, she would earn $15.

Q17:

The following table shows the number of eggs and the amount of flour used to bake cakes at a bakery.

Number of Cakes Number of Egg Flour (in Ounces)
2 10 4.5
3 15 6.75
4 20 9
6 30 13.5

Is the relationship between the number of cakes and the amount of flour proportional?

  • Ano
  • Byes

Is the relationship between the number of cakes and the number of eggs proportional?

  • Ano
  • Byes

Q18:

Consider the relationship between the company’s profit and the time elapsed since the year 2008. How much profit would they need in the year 2016 to make that relationship proportional between the years 2008 and 2016?

  • A60 million
  • B75 million
  • C80 million
  • D85 million
  • E70 million

Q19:

Jennifer walks to school every day. Her school lies at the point shown on the graph and she walks in a line which represents a proportional relationship. Which of the following could represent another ordered pair that satisfies this relationship?

  • A ( 0 , 6 0 )
  • B ( 6 0 , 0 )
  • C ( 7 5 , 5 0 )
  • D ( 5 0 , 7 5 )
  • E ( 2 0 , 3 0 )

Q20:

Write the function that is represented by the graph.

  • A 𝑓 ( π‘₯ ) = βˆ’ 3 2 π‘₯ + 1 1 2
  • B 𝑓 ( π‘₯ ) = βˆ’ 2 3 π‘₯ βˆ’ 3
  • C 𝑓 ( π‘₯ ) = βˆ’ 2 3 π‘₯ + 3
  • D 𝑓 ( π‘₯ ) = βˆ’ 3 2 π‘₯ + 3
  • E 𝑓 ( π‘₯ ) = 2 3 π‘₯ + 3

Q21:

For the following square, are the perimeter and side length proportional?

  • Ayes
  • Bno

Q22:

The graph below shows the relation between distance and time for a moving car. Is there a proportional relationship between the two quantities?

  • Ayes
  • Bno

Q23:

The table shows how many pages of a book William has read at different times.

Is William reading at a constant speed? Why?

Time (Minutes) 12 28 36 48 60
Number of Pages 9 21 27 36 45
  • AYes, because the number of pages read is proportional to the reading time
  • BNo, because the number of pages read is not proportional to the reading time

What is the constant of proportionality (or unit rate)? What does it represent?

  • A60 pages per minute,the total reading time
  • B0.75 pages per minute,the time needed to read a page
  • C0.75 pages per minute,the reading speed
  • D9 pages,the first number of pages
  • E45 pages,the last number of pages

Write an equation in the form 𝑝=π‘šπ‘‘ for the number of pages read 𝑝 in 𝑑 minutes.

  • A 𝑝 = 4 3 𝑑
  • B 𝑝 = 0 . 7 5 𝑑
  • C 𝑝 = 0 . 7 5 + 𝑑
  • D 𝑝 = 9 + 𝑑
  • E 𝑝 = 4 3 + 𝑑

Q24:

Uptown Pizzeria sells medium pizzas for $7 each and charges a $3 delivery fee per order. Is the cost of an order proportional to the number of pizzas ordered?

  • Ano
  • Byes

Q25:

It is recommended to bake ham for 3 hours for every 10 pounds of meat. If Gordon baked a 7-pound ham for 2.1 hours, did he follow the recommendation?

  • Ano
  • Byes

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