Proportional Tables and Equations
Rates and Unit Rates
Proportional Real-World Problems
Converting Measurements
Graphs and Constants of Proportionality
100
The following table shows a proportional relationship. What number belongs in the missing place?
12
100
A runner travels 12 miles in 3 hours. What is the runner's speed in miles per hour?
4 miles per hour
100
A recipe uses 2 cups of flour to make 8 muffins. How many cups of flour are needed to make 16 muffins?
4 cups
100
Convert 8 inches to centimeters. Round to the nearest tenth. Use 2.54 centimeters = 1 inch
20.3 cm
100
A proportional relationship is represented by the equation, y=6x. What is the constant of proportionality?
6
200
A proportional relationship has a constant of proportionality of 7. What is an equation relating y to x?
y=7x
200
A printer prints 45 pages in 5 minutes. What is the printer's rate in pages per minute?
9 pages per minute
200
A car travels 180 miles on 6 gallons of gas. How many miles can the car travel on 10 gallons at the same rate?
300 miles
200
Convert 80 pounds to kilograms. Round to the nearest tenth. Use 2.2 pounds = 1 kilogram.
36.4 kilograms.
200
A proportional relationship has the equation
y=x/5 . What is the constant of proportionality?
1/5
300
The table shows a proportional relationship between the number of notebooks purchased and the total cost. What is the missing cost?
$24
300
Maya types 240 words in 4 minutes. Jordan types 315 words in 5 minutes. Who types faster? How much faster per minute?
Jordan; 3 words per minute faster
300
A printer uses 3 ink cartridges to print 900 pages. At the same rate, how many pages can be printed using 5 ink cartridges?
1500 pages
300
Convert 8 cups to milliliters. Round to the nearest tenth. Use 1 cup = 8 fluid ounces. Use 30 milliliters = 1 fluid ounce.
1920.0 milliliters.
300
Analyze the following table:
Is this a proportional relationship? If so, what is the constant of proportionality. If not, how do you know?
No; 10:2 and 20:4 are equivalent to 5:1, but 36:6 is equivalent to 6:1. Since the ratio is not consistent across all data points, the relationship is not proportional.
400
A proportional relationship is represented by the equation y=4.5x. What is y when x=12?
y=54
400
A cyclist travels 18 miles in 45 minutes. What is the cyclist's speed in miles per hour?
24 miles per hour
400
A tank contains 7.5 gallons of water after being filled for 3 minutes at a constant rate. How much water will be in the tank after 8 minutes?
20 gallons
400
Convert 3 meters to inches. Round to the nearest tenth. Use 1 meter = 100 centimeters. Use 2.54 centimeters = 1 inch.
118.1 inches.
400
A graph has a line which passes through the points (0,0), (3,12), and (5,20). What is the constant of proportionality, and what does it mean for this graph?
k=4. For every increase on 1 unit of x, y increases by 4 units.
500
A school purchases pencils at a constant rate as shown in the following table. What is the missing cost, and what is the constant of proportionality?
$10.50; constant of proportionality = 0.7
500
Machine A fills 84 bottles in 7 minutes. Machine B fills 150 bottles in 12 minutes. Which machine fills bottles at the greater rate, and by how many bottles per minute?
Machine B; 0.5 bottles per minute faster
500
A theater sells 12 tickets for every 5 minutes of online sales. If the theater continues selling tickets at this rate for 1 hour and 15 minutes, how many tickets will be sold?
180 tickets
500
Convert 0.5 yard to meters. Round to the nearest hundredth. Use 1 yard = 3 feet. Use 12 inches = 1 foot. Use 2.54 cm = 1 inch. Use 1 meter = 100 cm.
0.46 meters
500
A graph represents the number of fidget toys printed by a 3-D printer over time. The line on the graph passes through the points (2,30), (4,60), and (8,120), where x represents hours, and y represents fidget toys printed.
1. What is the constant of proportionality?
2. What does the constant mean in this situation?
3. What does the ordered pair (4,60) represent?
1. k=15
2. The machine prints 15 fidget toys per hour.
3. In 4 hours, the 3-D printer prints 60 fidget toys.