Name ______________________________________________ Class ___________
Lessons 1 – 15 Ratio and Proportional Relationships Study Guide
Lesson 1: Ratios
1. There are 16 girls and 12 boys in Mrs. Eshelman’s class.
a. What is the ratio of girls to students in her class?
b. What fractional portion of the students in Mrs. Eshelman’s are boys?
c. Suppose Mrs. Eshelman’s had a huge class of 63 students at the same ratio as above.
How many students would you expect to be boys and girls?
Lesson 2: Comparing Ratios
2. You want to sell lemonade by the park. Different brands of lemonade have different
formulas.
Mix A: 2 cups concentrate, 3 cups water
Mix C: 3 cups concentrate, 5 cups water
Mix B: 4 cups water mixes with 1 cup concentrate
a. Suppose you make a single batch of each mix. What fraction of each batch is
concentrate?
Mix A _____
Mix B _____
Mix C _____
b. You want to sell the lemonade that tastes the most “lemony.” Which recipe would you
choose? Explain your reasoning.
Lesson 3: Rates and Unit Rates
3. John walks at a constant rate of 8 miles every 3 hours.
a. What is the unit rate?
b. How far can John walk in 5 hours?
4. Mauricio sometimes swims laps at his local recreation center for exercise. He wants to
check whether he is swimming laps faster over time. When he first starts swimming, he
can swim a 100 meter lap in 90 seconds. Fill in his unit rates for seconds per lap.
Which set of laps had the fastest pace?
Lesson 4: Unit Rate with Decimals
5. An 11 ounce can of condensed soup, costs $1.45. A 20 ounce can of ready to serve soup
costs $1.29. Which can of soup has the best price per ounce?
Lesson 5: Unit Rates with Fractions
1
6. At the 4th of July Fun Run, Ivory ran 3 2 miles in
per hour?
3
4
of an hour. How fast is that in miles
Lesson 6: Determining if Two Ratios are Proportional
7. Dylan makes $336 for 32 hours of work, and Angela makes $420 for 42 hours of work. Is
this relationship proportional? Explain.
Lesson 7: Proportional Relationship in a Table
8. The following table shows the relationship between the amount of cherries (in pounds) and
cost ($).
a. Is this a proportional relationship? How do you know?
b. What is the cost for 13 pounds of cherries?
c. If the cost is $10.50, how many pounds of cherries are in the bag?
Lesson 8: Comparing and Contrasting Proportional Relationships
9. Jayanna is filling a bathtub that is 18 inches deep. She notices that it takes two
minutes to fill the tub with three inches of water. She estimates it will take ten more
minutes for the water to reach the top of the tub if it continues at the same rate. Is
she correct? Explain.
Lesson 9: Graphing Proportional Relationships
 In the table the column on the left is the 𝒙 and column on the right is the 𝒚.
 Write ordered pairs from the table as (𝒙, 𝒚).
 When making the graph the 𝒙-axis is the horizontal line and the 𝒚-axis is the vertical line.
Remember to label each axis with words and numbers (consistently counted).
Using the table create a graph.
10.
Lesson 10: Qualitative Comparisons and Proportionality Using a Graph

For a graph to have proportional relationship it must be a straight line going through the
origin (0, 0).
11. Decide if the following graphs show a proportionality. Explain.
a.
b.
Lesson 11: Ratio Table to Graph Proportional Relationships
 To graph a table place the first row (horizontal table) or left column (vertical table) on
the 𝒙-axis. Next place the second row (horizontal table) or right column (vertical table)
on the y -axis.
Graph the following table.
12a.
b. Is the graph proportional? How do you know?
Lesson 12: Proportionality in Table, Graph, and Equation
𝑦

To find the constant (unit rate) in the table divide to find the unit rate


Use the table to make ordered pairs (𝒙, 𝒚) and graph the ordered pairs.
To make an equation for a proportional relationship: 𝒚 = 𝒌𝒙, substitute the value of the
𝑥
.
constant (unit rate) in place of 𝒌. The 𝒙 and 𝒚 values are always left as variables.
13. Complete the table.
14. Sketch the graph.
15. Write an equation that represents the table and graph.
Lesson 13: Deciding Whether Two Quantities are in a Proportional Relationship

One quantity is proportional to a second if a constant (number) exists such that each
measure in the first quantity multiplied by this constant gives the corresponding
measure in the second quantity.

Steps to determine if two quantities in a table are proportional to each other:
For each given measure of Quantity 𝑨 and Quantity 𝑩, find the value of
value of
𝑩
𝑨
𝑩
𝑨
. If the
is the same for each pair of numbers, then the quantities are proportional
to each other.
The tables below show the cost of rides at the Heart of Illinois Fair and Steamboat Days Fair.
At the Heart of Illinois Fair it cost $4 to get into the fair and $2 per ride. Rides at the
Steamboat Days Fair are $3 each.
16. Complete the tables.
a. Heart of Illinois Fair Costs
b.
Steamboat Days Fair Costs
c. Is the table for Heart of Illinois Fair Costs proportional? Explain.
d. Is the table for Steamboat Days Fair Costs proportional? Explain.
Lesson 14: Comparing Proportional and Non Proportional Relationships



Proportional Table: a relationship exists between the 𝑥 and 𝑦 quantities. Each part of
the table has a constant unit rate.
Proportional Graph: The line is straight and goes through the origin.
Proportional Equation: The equation is in the form of 𝒚 = 𝒌𝒙. Nothing is added or
subtracted with the constant (𝒌𝒙).
17. Circle the equations that are non proportional relationships.
𝒚 = 2𝒙
𝒚 = 10 + 2𝒙
𝒚 = 2/3𝒙
𝒚 = 7𝒙 + 4
Lesson 15: Proportional Relationship Graphs with Unit Rate

The points (0, 0) and (1, 𝒓), where 𝒓 is the unit rate, will always fall on the line
representing two quantities that are proportional to each other.

Unit rate: The unit rate on the graph is (1, 𝒓) where the 𝒙 coordinate is 1 and 𝒚
coordinate is the unit rate

𝒚
𝒙
.
A proportional graph is a straight line that goes through the origin.
The graph shows the total amount of dog food that Sophia’s dog Nipper eats.
18a. Describe the relationship that the graph depicts.
b. Identify two points on the line and explain what they mean in the context of the
problem.
c. What is the unit rate?
d. What point represents the unit rate?
e. How many pounds of food will Nipper eat in 10 days?
f. How long will it take Nipper to eat 20 pounds of food?