Unit Rates involving ratios of fractions
Russel runs 9/10 mile in 5 minutes. At this rate, how many miles can he run in one minute?
9/50 mile in 1 minute
The recipe for homemade class cleaner indicates to use a ratio of 1 part vinegar to 4 parts water. Elyse used 3 tablespoons of vinegar and 12 tablespoons of water to make the cleaner. Is the relationship proportional? Why?
Proportional because the ratio was maintained/kept the same
The table shows the amount of dietary fiber in bananas. Use the table to find the constant of proportionality.
Dietary fiber Bananas
9.3 3
18.6 6
27.9 9
37.2 12
3.1
Name the coordinate that is called the origin.
0, 0
True or false: A relationship is proportional if it is a straight line and passes through the origin.
True
Tia is painting one side of her shed. She paints 36 square feet in 45 minutes. At this rate how many square feet can she paint in 1 hour?
48 square feet
No because 1 ratio is 2:3 and the other is 3:4
Carrie earns $8.50 per hour babysitting. Is the amount of money she earns proportional to the number of hours she babysits? How/what is the constant number? Here is the table:
Number of hours Amount Earned
1 $8.50
2 $17
3 $25.50
4 $34
Yes proportional because each has a unit rate of $8.50
A rabbit challenges a tortoise to a race. The table shows the distance the tortoise moved after 0, 1, 2, and 3 minutes. Determine whether the number of feet the tortoise moves is proportional to the number of minutes by graphing the relationship on the coordinate plane.
See graph on board
Yes proportional because it is a straight line and passes through the origin 0, 0
A mechanic charges $270 for 5 hours of work on a car. Write an equation that compares the total cost to the number of hours he works on a car if it is a proportional relationship.
y=54x
A garden hose was left on a yard and spilled 7/8 gallon every 2/3 minute. Find the average number of gallons spilled per minute.
21/16 or 5/16 gallons per minute
A saltwater solution for an aquarium calls for 35 parts salt to 1000 parts water. Tareq used 7 tablespoons of salt and 200 tablespoons of water. Is the relationship proportional?
Yes because both have a ratio of 7:200
The cost of the school lunch is $2.50. Complete the table and explain whether this is a proportional relationship/explain.
Lunches bought Total cost (you complete)
1
2
3
4
Lunches bought Total cost
1 $2.50
2 $5
3 $7.50
4 $10
Yes proportional because all quantities have a unit rate of $2.50
The table shows the account balance in a savings account at the end of each week. Determine if the account is proportional by graphing.
Part A see graph
Part B non-proportional because points form a straight line but it does NOT pass through the origin
Tell me what EACH part of the equation in y=mx+b represents. (You MUST get all 3 parts correct to get the full points)
y=total/proportionality
x=how many/# of items
k=unit rate/constant proportionality
Thunder bolt from a bolt of lightning travels 1/10 mile in 1/2 second. At this rate, how many miles can it travel in 1 second?
1/5 mile in 1 second
Half of an orange juice mixture is orange concentrate. Explain why the ratio of the orange concentrate to water is 1:1.
Both are 1/2 OJ to half water so ratio is 1:1
Fun Center rents popcorn machines for $20 per hour. In addition to the hourly charge, there is a rental fee of $35. Complete the table and tell whether this is a proportional relationship and why?
Hours Cost (you complete)
1
2
3
4
Hours Cost
1 $55
2 $75
3 $95
4 $115
No because the ratios between the quantities are not equal.
Briana decides to save money each week for her family vacation. Use the graph on the board to find the constant of proportionality. Then describe what it means.
Part A constant of proportionality is 20
Part B Briana saves $20 each week
The wait time for two different rides are shown in the table. If there are 120 people in line for the swings, how long can you expect to wait to ride the ride?
Ride Wait times
Carousel 6 min for 48 people
Swings 12 min for 75 people
19.2 minutes
A walk a thon was held at a local middle school. The table gives the average distances and times for 4 walkers for certain periods of the walk a thon. If the total distance of the route was 2 miles, who completed the route first? Here is the table:
Lakeisha 7/8 mile 18 minutes
Baydan 9/10 mile 22 minutes
Madison 4/5 mile 17 minutes
Lakeisha 41.4 minutes
One blend of garden soil is 1 part minerals, 1 part peat moss, and 2 parts compost. Select all of the mixtures below that are in a proportional relationship with this blend. For this one number your boards 1-6 and write Yes if you would choose it and No if you would not.
1. 5 ft3 minerals, 5 ft3moss, 10 feet 3 compost
2. 10 ft 3 minerals, 15 ft 3 moss, 15 ft 3 compost
3. 12 ft 3 minerals, 12 ft 3 moss, 24 ft 3 compost
4. 20 ft 3 minerals, 20 ft 3 moss, 40 ft 3 compost
5. 100 ft 3 minerals, 100 ft 3 moss, 200 ft 3 compost
6. 50 ft 3 minerals, 50 ft 3 moss, 50 ft 3 compost
1. Yes
2. No
3. Yes
4. Yes
5. Yes
6. No
The table shows the cost to mail various letters based on different weights. Is the cost of mailing a letter proportional to the weight? If yes, what would be the cost of mailing a letter? If not explain.
Weight oz Cost
1 0.47
2 0.68
3 0.89
4 1.10
No ratios between quantities are not equal
The cost of a smoothie is proportional to the number of ounces shown on the graph on the board. Select all statements by numbering your boards 1-7 and putting yes if you would select it no if you would not
1. No
2. Yes
3. No
4. No
5. No
6. Yes
7. Yes
The ratio of kids to adults at a school festival is 11:7. Suppose there are a total of 810 kids and adults at the festival. How many adults are at the festival?
315 adults