Definitions
A Rate is...
A comparison of two quantities with different units
4 bananas cost $1. How much does on banana cost?
$0.25
What is the unit rate? (You MUST include the units).
$52/4 hours
$13 per hour
What is 12 x 12
144
Completely simplify:
8/18
4/9
A Unit Rate is...
A rate with a denominator of one
A comparison of one quantity to another quaintity with the value one
Steven earns extra money babysitting. Steven charges $31.25 for 5 hours and $50 for 8 hours. Is this a proportional relationship? How do you know?
Yes, there is a constant rate of change/unit rate
What is the unit rate? (You MUST include the units).
$52.16/16 gallons
$3.26 per gallon
What is 13 - (-10)
23
Which fraction is the smallest?
3/5, 10/17, 15/22, 30/54, 60/121
60/121
What are the two things this graph needs to be a proportional relationship?
1) It must be a straight line
2) It must go through the origin - (0,0)
A skydiver jumps out of an airplane. After 0.8 seconds, she has fallen 100 feet. After 3.1 seconds, she has fallen 500 feet. She says that she should have fallen about 187.5 feet in 1.5 seconds. Is this correct? Why?
No! This is not a proportional relationship, so we cannot make the claim that the skydiver fell 187.5 feet in 1.5 seconds.
Paige mows 1/6 of an acre in 1/4 of an hour. How many acres per hour does Paige mow?
2/3
4/6
0.6667 acres
(-7)(-10)(3)
210
What does pi represent?
The ratio of the circumference of a circel to the diameter of a circle the same circle
What does the k stand for in y=kx?
The constant of proportionality
The Constant Rate of Change
The constant Unit Rate
There is a proportional relationship between your distance from a thunderstorm and the time it takes from when you see lightning to when you hear the thunder. If there are 9 seconds between when you see the lightning and hear thunder then the storm is 3 kilometers away. If you double the amount of time between when you see lightning and hear thunder, does the distance in kilometers between you and the storm also double? Why?
Yes! because it is a proportional relationship, we must double the distance to maintain a constant rate of change/unit rate.
Terrance and Jesse are training for a long distance race. Terrance trains at a rate of 6 miles every half hour, and Jesse trains at a rate of 2 miles every 15 minutes. What is the unit rate in miles per hour for each runner?
Terrance: 12 miles an hour
Jesse: 8 miles an hour
Simplify: 12(3-5)+18
-6
Give an example of an irrational number
Mr. Williams knows
A complex fraction is...
A fraction where both the numerator and denominator are fractions as well.
Solve for x:
4/5 = x/9
x = 7.2
Eli takes a typing test and types all 300 words in 1/10 of an hour. He takes the test a second time and types all of the words in 1/12 of an hour. Was he faster or slower the second time? How do you know?
The second time.
The unit rate for the first was 3000 words per hour, while the second one was 3600 words per hour.
1/12 is less time than 1/10
Last week Bill earned $15 an hour. He worked for 35 hours. He was also paid a bonus a $50. Write and solve an equation to represent how much money Bill made last week...
15(35)+50
$575
What is the name of the MSU fight song?
Victory for MSU!