Connect Ratios and Rates
Write the ratio as a fraction:
8:10
4/5
Find the unit rate:
7 miles / 1/3 gallon
21 miles per gallon.
Are these ratios equivalent?
2/4, 4/8, 6/12, 8/16
Yes. They all equal 0.5.
What variable do we use to represent the constant of proportionality?
k
The graph of a proportional line is ______________ and goes through the ______________.
Straight and through the origin.
Write the ratio as a fraction:
80 to 60
4/3
Hadley paddled a canoe 3/4 of a mile in 1/8 hour. How fast did Hadley paddle, in miles per hour?
6 miles per hour.
64/4, 125/5, 216/6, 1000/10
No
You can represent a proportional relationship using what equation?
y=kx
A graph shows a proportional relationship between the cups of flour (x) a baker uses and the number of cookies made (y). What does the point (0,0) represent in this situation?
The baker uses 0 cups of flour to make 0 cookies.
A package of 5 pairs of insulated gloves costs $25.00. What is the cost of a single pair of gloves?
$5.00
Aiden walked 1/5 of a mile in 1/15 of an hour. What is his rate in miles per hour?
3 miles per hour.
Are these ratios equivalent?
21/6, 28/8, 35/10, 49/14
Yes. They each equal 3.5.
What is the constant of proportionality in the following equation:
y=45x
45
A graph shows a proportional relationship between the cups of flour (x) a baker uses and the number of cookies made (y). What does the point (1,18) represent in this situation?
The baker uses 1 cup of flour to make 18 cookies.
18/1 is the unit rate.
k=18.
An arts academy requires there to be 6 tutors for every 72 students. How many tutors does the academy need if it has 120 students?
10 Tudors
Leo reads 13 pages in 1/3 of an hour. How many pages does he read in one hour?
39 pages.
Solve the proportion:
2/5 = 12/n
30
3 eggs weigh 120 grams. Assuming the eggs are all the same weight, what is the constant of proportionality?
40
The points (2, 50) and (4, 100) are on the graph of a proportional relationship. What is the constant of proportionality?
25
Lena is making two dishes for an event. Each batch of her mac-n-cheese recipe calls for 6 ounces of cheese. For every two pizzas, she needs 16 ounces of cheese.
Lena buys a 32- ounce package of cheese. Does she have enough cheese to make 2 batches of mac-n-cheese and 3 pizzas? Explain.
No. Lena needs 36 ounces of cheese in total, so the 32-ounce package won't be enough.
2 batches of mac-n-cheese = 12 ounces cheese
3 pizzas = 24 ounces of cheese
A recipe calls for 3/4 cup of flour per 1/2 tsp of oil. How much flour is used per tsp of oil?
1 1/2 cups of flour.
Cross multiply to solve the proportion.
6/2 = 21/n
n=7
Anne's car can travel 228 miles on 6 gallons of gas.
Write an equation to represent the distance, y, in miles Ann's car can travel on x gallons of gas.
Anne's car used 7 gallons of gas during a trip. How far did Anne drive?
y=38x
266 miles
The points (3,15) and (9, 45) are on the graph of a proportional relationship. Write an equation that represents the proportional relationship.
y=5x