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.
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?
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?
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|
Determine whether the following statement is true or false: A proportion is an equation in which two or more ratios are equal.
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?
Determine whether the quantities in the following rates are proportional: 39 computers for 95 students and 69 computers for 80 students.
- Bnot proportional
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
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|
Is the length of one side of this shape proportional to its perimeter?
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 statements is not true?
- AThe point shows that Hannah would earn $60 if she worked 4 hours.
- BAny point of coordinates on this graph shows that Hannah would earn if she worked 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.
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)|
Is the relationship between the number of cakes and the amount of flour proportional?
Is the relationship between the number of cakes and the number of eggs proportional?
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
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?
For the following square, are the perimeter and side length proportional?
The graph below shows the relation between distance and time for a moving car. Is there a proportional relationship between the two quantities?
The table shows how many pages of a book William has read at different times.
Is William reading at a constant speed? Why?
|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 for the number of pages read in minutes.
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?