Equivalent Ratios
Are the ratios 2 : 3 and 4 : 6 equivalent?
What is Yes they are equivalent or proportional ?
A car travels 120 miles in 3 hours.
Find the Constant of Proportionality (C.O.P.) between distance and time.
What is 40 or y = 40x?
Find the unit rates for the following problems: 27 calls in 9 hours
What is 3 calls per 1 hour ?
A car travels ¾ mile in ¼ hour.
What is the unit rate in miles per hour?
What is 3?
On a graph, the line has to go through what to be proportional?
What is the origin or point 0,0
Do the ratios 5 : 8 and 15 : 20 form a proportional relationship?
What is No, because 5/8=0.625 and 15/20=0.75; they are not equal?
A printer produces 360 pages in 6 minutes.
Find the C.O.P. (pages per minute).
What is 60 or y=60x?
21 yards of yarn costs $42. What is the price per yard? What is the cost if you purchase 34 yards of yarn?
What is $2 per yard? What is $68?
A baker uses 2½ cups of flour to make 5/6 of a cake.
How many cups of flour are used for 1 whole cake?
What is 3?
Another name for constant of proportionality is..
What is unit rate ?
A recipe uses 3 cups of sugar for 5 cups of flour.
Another recipe uses 6 cups of sugar for 10 cups of flour.Are the two recipes proportional?
What is Yes, because 3/5=6/10?
A worker earns $168 for 12 hours of work.
Find the C.O.P., then write an equation to represent the relationship between hours worked (x) and money earned (y).
What is 14, y=14x?
Spenser bought 5 chocolate bars for $3.70. What is the unit price for 1 chocolate bar? What is the cost if purchase 4 chocolate bars?
What is $0.74 per 1 chocolate bar? What is $ 2.96?
A cyclist rides 5/8 of a mile in 1/10 of an hour.
What is the unit rate in miles per hour?
What is 50/8 or 6 1/4 or 6.25?
A printing company charges a fixed rate per booklet for a large order.
120 booklets cost $180.
200 booklets cost $300.
Assume the cost is directly proportional to the number of booklets printed.
Question:
Find the Constant of Proportionality (C.O.P.).
Write an equation to represent this relationship.
List four coordinate pairs (x, y) that would appear on the graph.
Identify the slope of the line and what it represents.
What is k=1.5 , y =1.5x , (0,0) (1,1.5), (2, 3), (3, 4.5)? m= 1.5 or m =3/2
A car travels 126 miles in 3 hours, while another travels 200 miles in 5 hours.
Do the distances and times represent a proportional relationship?
What is no they do not have proportional relationship?
A car uses 9 gallons of gas to travel 324 miles.
Find the C.O.P., representing miles per gallon.
What is 36 & y=36x?
"Quarterback" took a trip to the mountains and traveled 486 miles. It took you 9 hours to get there. What is his miles per hour? If he have traveled for 3 hr how many miles have they gone?
What is 54 miles per hour? What is 162 miles?
A tank fills 7/9 of its volume in 3/4 of an hour.
At this rate, how much of the tank fills in 1 hour?
What is 28/27 or 1 1/27 or 1.037 repeating?
A drone delivery company tracks how far its drones can travel based on battery usage.
The data shows that the distance traveled is directly proportional to the amount of battery power used.
A drone uses 25% of its battery to travel 7.5 miles.
When the drone uses 60% of its battery, how far can it travel?
Find the Constant of Proportionality (C.O.P.).
Write the equation that represents this relationship.
Predict the distance traveled for 60% battery use.
List four coordinate pairs (x, y) to plot on a coordinate plane.
Explain the meaning of the slope in context.
What is k= 0.3 , y= 0.3x , 18 miles , m = 0.3 or 3/10, (0,0) , (1, 0.3) , (2,0.6), (3, 0.9) , (4 , 1.2)?
In a science experiment, the ratio of red marbles to blue marbles is 9 : 12 in one trial and 15 : 20 in another trial. Are these ratios equivalent?
What is Yes they are proportional relationship?
A machine makes 7.5 parts in ⅝ of an hour.
Find the C.O.P. in parts per hour.
What is 12 & y = 12x
A bakery sells muffins in two different-sized boxes.
Box A: 8 muffins cost $12.
Box B: 15 muffins cost $21.
At a different bakery, Bakery C, the cost of muffins is shown by the equation:y=1.45xy where y represents the cost (in dollars) and x represents the number of muffins.Which bakery offers the lowest cost per muffin, and do any of these relationships appear proportional to each other?
What is Lowest cost $1.40 per muffin: Box B? What is All three are proportional relationships, but not equivalent?
A factory produces 12 ½ meters of fabric in 2 ⅔ hours.
What is the unit rate in meters per hour?
What is 4.6875 or 75/16 or 4 11/16 ?
A high-speed train travels a distance that is directly proportional to the time traveled.
During one test run, the train covers 162 miles in 1.8 hours.
Questions:
Find the Constant of Proportionality (C.O.P.).
Write the equation that represents this relationship.
Predict how far the train will travel in 3.5 hours.
List four coordinate pairs (x, y) to plot on a coordinate plane.
Interpret what the slope represents in this context.
What is k= 90, y=90x , 315, m= 90, (0,0) , (1,90), (2,180), ( 3, 270), (4,360)?