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.


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


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 𝑥 ?

3 𝑥
4 6


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

  • Ano
  • Byes


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

  • A no
  • B yes


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?

  • Ano
  • Byes


The following table represents the number of sites dug by a group of archaeologists 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
  • Ayes
  • Bno


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
  • Ano
  • Byes


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

  • A no
  • B yes


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

  • Atrue
  • Bfalse


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?

  • A no
  • B yes


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

  • A yes
  • B no


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

  • Anot proportional
  • Bproportional


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

  • A 16 in by 20 in
  • B 18 in by 24 in
  • C 20 in by 24 in
  • D 24 in by 36 in
  • E 8 in by 10 in


Bassem built a model of his room using toy blocks. The table shows the dimensions of the room and Bassem’s model respectively. Is his model a proportional representation of his actual room?

Actual Room Arthur’s Model
Height 15 feet 5 blocks
Width 60 feet 10 blocks
Length 75 feet 25 blocks
  • Ano
  • Byes


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

  • A yes
  • B no


Rania 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 unit rate of this proportional relationship is $15/hour.
  • BThe point shows that Rania would earn $60 if she worked 4 hours.
  • CAny point of coordinates on this graph shows that Rania would earn if she worked hours.
  • DIf Rania worked for 4 hours, she would earn $15.
  • EIf Rania worked for 10 hours, she would earn $150.


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?

  • A yes
  • B no

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

  • A yes
  • B no


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?

  • A85 million
  • B70 million
  • C75 million
  • D80 million
  • E60 million


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

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