Rates
Unit Rates With Fractions
Find the Unit Price
Proportional Relationships
Constant of Proportionality
Graphs of Proportional Relationships
Proportional Reasoning
100
Maura runs 5 miles in 1.25 hours. Ava runs 3 miles in 50 minutes, or 0.83 hour. Who runs faster?
Maura
100
What is a complex fraction?
A fraction with a fraction in the numerator, the denominator or both.
100
20 ounces of grapes for $5.00. Find the unit price for 1 ounce
$0.25 per ounce
100
How do you solve a proportion for a missing value?
Cross Multiply
100
What is 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
100
when viewing a graph, how do you know a relationship is proportional?
straight line through the origin (0,0)
100
At the nearest wholesale store, 3 bags of cereal cost $21.75. At this rate, how much would 5 bags of cereal cost?
$36.25
200
Nora and Eli are making homemade spring rolls for a party. Nora can make 8 spring rolls in 10 minutes. Eli can make 10 spring rolls in 12 minutes. If they each make 40 spring rolls, how long will it take each of them?
Nora 32 Minutes
Eli 33.3 Minutes
200
Claire boarded an airplane in Richmond, VA, and flew 414 miles directly to Charleston, SC. The total flight time was 3/4 hour. How fast did Claire’s airplane fly, in miles per hour?
552 mph
200
$8.95 for 5 liters of soda.
Find the Price Per Liter
$1.79 per liter
200
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.
200
Find the Constant of proportionality and write the equation of the line.
k = .75
y = .75x
200
A graph is a straight line through the point (0, 5). Can the graph represent a proportional relationship? Explain
No, it doesn't pass through the origin.
200
Molly is making peanut butter cookies. To make a batch of cookies she needs 34 cups of peanut butter, 1.5 cups of sugar, and 1 egg. If Molly has 3 cups of peanut butter, 9 cups of sugar, and 5 eggs, how many batches of cookies can she make?
4
300
lara 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, One
300
Josef typed a 36-word paragraph in 2/3 minute. What is his typing speed, in words per minute?
54 words per minute
300
$1.99 for 0.5 liters of dish soap
Find the price per 1 liter
$3.98
300
Is this Proportional
No the ratio of y/x are not equal
300
Does this equation represents a proportional relationship? y = 150x
If yes, what is the constant of proportionality
Yes, 150
300
What does the point (2, 6) represent in this situation?
6 tennis balls in 2 cans
300
Sandra signed up for Workout Jazz during the spring special. Her credit card was charged $220.87. Is this the correct amount? Explain
No they charged her for 13 months
400
A group of 12 students is deciding whether to go to the science center or the zoo. Science center tickets are 3 for $36.75 and zoo tickets are 4 for $51.How much will a group of 12 students save by choosing the science center?
$6
400
Stacy and Neil painted 280 square feet of their living room wall with 4/5 gallon of paint. How many square feet can they paint with 3 gallons of paint?
1050 square feet
400
$5.60 for 0.8 ounces of ground cinnamon
$7.00 per ounce
400
Yes
400
Shipping rates for Company A and Company B are shown in the tables below. Which company has shipping rates that represent a proportional relationship?
Company B
400
The graph shows a proportional relationship between the number of miles Marco bikes and the number of hours. What equation relates the distance, y, and the time, x?
y=15x
400
In a florist shop, the ratio of roses to tulips is 5 : 3. The shop has 72 tulips on Friday morning. How many roses do they have?
120
500
Krystal is comparing two Internet service plans. Plan 1 costs $34.99 per month. Plan 2 costs $134.97 every 3 months. If Krystal plans to stay with one service plan for 1 year, which should she choose? How much will she save?
plan 1
500
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 feet per hour
500
1.3 pounds of ground beef for $9.23
Find the price for 1 pound
$7.10 per pound
500
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 of cinnamon
500
The equation y = 19x relates proportional quantities x and y. What is the value of x when y is 4?
36
500
Is there a proportional relationship between the cost and the number of shells? If so, what is the constant of proportionality?
yes, .40
500
When can you use proportional reasoning to solve a problem?
When one quantity is a constant multiple of the other