Proportional Relationships
Example 1:
A new self-serve frozen yogurt store opened this summer that sells its yogurt at
a price based upon the total weight of the yogurt and its toppings in a dish. Each
member of Isabelle’s family weighed his/her dish and this is what they found.
Weight
(ounces)
12.5
10
5
8
Cost ($)
5
4
2
3.2
a. Does everyone pay the same cost per ounce? How do you know?
Find the cost per
ounce (unit rate)
for each yogurt
dish.
Yes, everyone pays the
same cost per ounce.
Each yogurt dish had
the same unit rate.
b. Isabelle’s brother takes an extra-long time to create his dish. When
he puts it on the scale, it weighs 15 ounces. If everyone pays the
same rate in this store, how much will his dish cost? How did you
calculate this cost?
Cost per ounce(number of ounces)
If one ounce costs $0.40, what
0.40(15)
can you do mathematically to
$6
find out how much 15 ounces
would cost?
The dish will cost $6. To find the cost you multiply the
number of ounces by the cost per ounce.
Example 2: A recipe for frosting calls for ½ cup of powdered sugar
and 2 tablespoons of milk. The chart below is what you used
when you made larger batches of frosting than what the recipe
listed. Is the amount of sugar used proportional to the amount of
milk used? Explain.
Cups of
Powdered Sugar
Tablespoons of
Milk
cups sugar
tablespoon s milk
Find the unit rate of
powdered sugar to milk
for each pair of values.
1
2
4
6
1
2
2
1

4
1
1
4
1

1
4
12
1
6
1

4
1
There is a proportional relationship between cups of powdered sugar
and tablespoons of milk since all of the simplified ratios are equal.
Example 3:
In the back of a recipe book, a diagram provides easy conversions to use while cooking.
a. What does the diagram tell us?
The number of ounces in a given number of cups.
b. Is the number of ounces proportional to the number of cups? How do you know?
Find the unit rate
of each cup
(ounces to cups).
There are 8 ounces for every cup. They all have the same unit rate.
c. How many ounces are in 4 cups? How do you know?
If there are 8 ounces in 1 cup.
What can you do to find out how
many ounces are in 4 cups?
4(8) = 32 ounces
There are 32 ounces in 4 cups. You
multiply the number of cups by 8.
Example 4:
Alex spent his summer helping out his family’s business. He was hoping to earn
enough money to buy a new $220 gaming system by the end of the summer. Halfway
through the summer, after working 4 weeks, he had earned $112. Alex wonders, “If I
continue to work and earn money at this rate, will I have enough money to buy the
gaming system by the end of the summer?” Alex made the table below with his total
money earned at the end of week 1 and his total money earned at the end of week 4.
Week
0
1
2
3
4
5
6
7
8
Total
Earnings
$0
$28
$56
$84
$112
$140
$168
$196
$224
a. Complete the table to answer Alex’s question.
Yes, if Alex continues to work and earn money at this rate he will have enough
money to buy the gaming system.
b. Are Alex’s total earning proportional to the number of weeks he worked? How do
you know?
Alex’s total earnings are proportional to the number of weeks he worked.
You can multiply each week by 28 to check.