2.1
Maura runs 5 miles in 1.25 hours. Ava runs 3 miles in 50 minutes,
or 0.83 hour. Who runs faster?
Maura
or a–d, choose Yes or No to tell whether each rate is a unit rate.
a. 1/(1/3)
b. 2/3
c. 3/1
d.(2/3)/1
A and B no
C and D yes
How do you know whether two quantities x and y are proportional?
Every ratio y/x for related
pairs of x and y is equivalent.
Write the equation that relates two proportional quantities x and y.
Which variable represents the constant of proportionality?
y = kx; k represents the
constant of proportionality.
Luis rides his bicycle 3/4 mile in 5 minutes, or 1/12 hour,
along the bike trail. Assuming he rides at a constant
rate, what is his speed, in miles per hour?
9mph
It costs $36.75 for 3 tickets to visit the science center. It costs $51
for 4 tickets to visit the zoo. Which attraction will cost more money
for a group of 12 students to visit? How much more?
The zoo; $6 for the group
Josef typed a 36-word paragraph in 23 minute. What is his typing
speed, in words per minute?
54 words per minute
Is there a proportional relationship between x and y? Explain.
x 8 10 12 14
y 5 7 9 11
No; Sample answer: Every ratio yx is not
equivalent.
For a–d, choose Yes or No to tell whether each equation represents
a proportional relationship.
a. y = 7x - 3
b. y = 150x
c. y = x
d. y = x + 3.75
A and D no
B and C yes
There are 120 Calories in a 3/4-cup serving of cereal. How many Calories are
in 6 cups of cereal?
960 Calories
Clara and Toby are telemarketers. Yesterday, Clara reached 4 people
in 10 phone calls, while Toby reached 3 people in 8 phone calls. If
each telemarketer continues at the same rate, who will reach more
people in 40 calls? How many more?
Clara; 1 person
Kelly is knitting a scarf for her brother. It took her 1/3 hour to knit 3/8 foot of the scarf. How fast is Kelly’s knitting speed, in feet per hour?
1 1/8 ft per hour
The equation y = 0.25x describes a proportional relationship
between x and y. What is the constant of proportionality?
0.25
Does this table show a proportional relationship? If so, what is the constant
of proportionality?
X 3 6 9 12
Y 12 24 45 60
Not Proportional
Which of the following statements about unit rates is NOT true?
𝖠 A unit rate relates a quantity to 1.
𝖡 Unit rates can be used to compare two rates.
𝖢 Any rate is equivalent to its unit rate.
𝖣 A unit rate always relates quantities with the same units
D is not true
Stacy and Neil painted 280 ft2 of their living room wall with 4/5 gallon of paint. How many square feet can they paint with 3 gallons of paint?
1,050 ft2
The relationship between x and y is proportional. When x is 3, y is 51.
What is x when y is 204?
12
The equation y =1/9*x relates proportional quantities x and y.
What is the value of x when y is 4?
36
At the local dairy farm, Kareem buys a 32-oz container of yogurt for
$2.56. Jonah buys a 6-oz container of yogurt for $0.48. Are the cost, y,
in dollars and the amount of yogurt, x, proportional? Explain. Write an
equation to represent this relationship.
Yes; The ratios 2.56/32 and 0.48/6
are equivalent, y = 0.08x.
Machine A pops 12.75 ounces of popcorn in 3 minutes. Machine B
pops 18 ounces of popcorn in 4 minutes. If each machine pops
popcorn for 10 minutes, will there be enough popcorn for eight
9-ounce bags? Explain.
Yes; Machine A and Machine B
combine to pop 87.5 ounces in 10 minutes.
87.5 + 72, so there will be enough popcorn.
Harper knows he is 50 yards from school. The map on his phone shows that the school is 3/4 inch from his current location. If Harper’s current location is 3 inches from home on the same map, how far is Harper from home?
200 yards
A recipe calls for 1 1/2 teaspoons of cinnamon to make 2 dozen
oatmeal cookies. How many teaspoons of cinnamon are needed to
make 60 oatmeal cookies?
3 3/4 teaspoons
Danielle earns $36.80 for 4 hours of yardwork. MacKenzie earns $50.40
for 6 hours of yardwork. Who earns more per hour? How much more?
Danielle; $0.80 more per hour