Math Terms
_________ are comparisons of two quantities. They can be written as a Fraction, with a Colon, or with the Word "To."
Ratios
How can you tell if a Graph is Proportional?
Straight Line that passes through the origin
For one sandwich it cost $5.75. For 3 sandwiches it cost $17.25. For 6 sandwiches it cost $34.50. Is the ratio of sandwiches to cost proportional?
Yes the ratio of sandwiches to cost is proportional. Each sandwich cost $5.75
What is the equation format to describe a proportional relationship look like?
y=kx
Mrs. Wilson gives 88 jolly ranchers to 4 people. How many jolly ranchers does each person get?
22 jolly ranchers per person
Give an example of an equivalent ratio for 15:6
Answer may vary: 5:2, 30 to 12, 45/18
How can we tell if a Table is Proportional?
The table will show a relationship between two quantities that maintains a constant ratio. Having a constant of proportionality.
The amount of money earned for 2 hours is $15.00 and for 3 hors is $22.50. What is the constant of proportionality?
$7.50 per hour
Assuming the pattern continues, write an equation for the problem below:
(x) (y)
5 10
4 8
6 12
y=2x
Xavia spends $99 for 6 hoodies. How much does each hoodie cost?
$16.50 per hoodie
A comparison of two quantities of unlike units is called a _____. We find this by dividing the numerator by the denominator.
Rate
Am I proportional?
No.
True or false? In the graph of a proportional relationship, the slope of the line is the same as the constant of proportionality.
True
Nazir is selling boxes of candy bars to raise money for the basketball team. He makes $6.00 for each box of candy bars he sells. Write an equation to represent the situation and define your variables.
y=6x where x is boxes of candy bars and y is total amount of money
Mr. Wright gives out 120 live school points to 8 scholars. How many live school points does each scholar get?
15 live school points per scholar
A rate/ratio expressed as a quantity of one (per).
Unit Rate
Am I proportional?
Yes.
Ms. Lawrance has $120 in her checking account and she makes $50.00 deposit in it each week. Is the relationship proportional? Explain.
No the relationship is not proportional because she starts with $120 in her checking account. Every week after she makes a constant $50.00 deposit, but since she started with $120 and $50, it is not a constant.
Ms. Prieto's family of 4 went to the Philadelphia Zoo and it cost them $52.00 for admissions. What is the constant of proportionality in this situation? Write an equation to represent the situation.
k = 13
y=13x where y represents the total cost and x represents the number of people who went to the zoo.
Destin spends $6.75 for 9 small Kit Kats. How much did each Kit Kat cost?
$0.75 per Kit Kat
What does Constant of Proportionality mean?
The Constant of Proportionality is the value of y divided by the value of x in a proportional relationship. k = y/x.
It is the number we multiply x by in order to get y. y=kx
It is the value of y when x=1 in a proportional relationship.
Which one is proportional? What is the constant of proportionality?
B is proportional.
k = 1.2 or k = 1-1/5
It cost $8.97 for 3 pack of turkey, $17.93 for 6 pack of turkey, and $26.91 for 9 package of turkey. Is the relationship of turkey pack to cost proportional? If so, what is the constant of proportionality?
The turkey packs to cost is proportional. The constant of proportionality is $2.99 per pack
Zoe and Azaria rode the bus and it cost them $11.78. Write an equation to represent this situations. How much would it cost for 5 people to ride the bus?
y= 5.89x
It will cost $29.40 for 5 people to ride the bus.
Find the Unit Rate:
272 Steps in 4 Hours
68 steps per hour