Unit Rate
Find the unit rate:
84 miles in 12 days
7 miles/day
The Unit Rate MUST include the units.
Find the slope of the line between these two points:
(2, 10) and (4,20)
slope = 5
Define slope
The difference in y divided by the difference in X
or
Slope = rise/run
or
Slope = the change in y divided by the change in X
or
Slope is the steepness of a line
Are these Proportional?
56/20 and 24/10
why or why not?
No.
cross products aren't equal.
Equiv. Fractions: 24/10 * 2/2 = 48/20 not 56/20
Solve for x:
x/8 = 9/4
x = 18
Find the Unit Rate:
2.25 km in 3.75 minutes
0.6 km / minute
The Unit Rate MUST include the units.
Find the slope of the line between these two points:
(1, 3) and (5, 11)
slope = 2
If you were to plot distance in miles versus time in hours, what would go on the y-axis?
distance in miles goes on the y-axis.
(the time in hours goes on the x-axis)
Are these Proportional?
5/8 and 42.5/68
why or why not? Explain.
Yes.
Unit rates are the same:
5/8 = 0.625 and 42.5/68 = 0.625
Cross products are equal: 5(68) = 8(42.5)
340 = 340
5 movie tickets cost $36.25 .
What is the cost of 8 tickets?
$58
Joey runs 3 laps around the track in 9 minutes. At this rate, how long will it take him to complete 25 laps?
It will take 75 minutes to complete 25 laps.
Find the slope of the line between these two points:
(5, 150) and (3, 90)
slope = 30
Your baseball team won 6 games and lost 4 games.
If you don't lose any more games, how many games must the team win to have a win:loss ratio of 2:1?
The team must win 2 more games.
Then the team will have won 8 games and lost 4 games.
8:4 is equivalent to 2:1
Is this a proportional relationship?
x 5 10 15 20
y 1 3 5 7
Why or why not? Explain
No.
Ratios of x/y are not equal
5/1 not equal to 10/3 not equal to 15/5
15/5 not equal to 20/7
Solve the proportion for x:
5/x = 4/(9.2)
x = 11.5
The bakery sells croissants in a baker's dozen (13) for $29.25.
What is the constant of proportionality?
$2.25 per croissant
Find the slope of the line between these two points:
(15, 9) and (-5, -3)
slope = 3/5 or 0.6
Jay rides 18 miles per hour on his bike.
How far will he ride in 1 hour and 20 minutes?
24 miles
The table shows the different rates to ship books through the mail. Are the rates proportional?
Explain:
pounds Cost
4 $3.80
6 $5.70
8 $7.60
Yes. the unit rate per pound is the same for all.
$0.95 per pound
You can buy 5 pounds of grapes for $9.95.
What is the cost of 4 pounds of grapes?
$7.96 for 4 pounds of grapes.
(The unit rate is $1.99 per pound)
You earn $102 for 12 hours of yardwork.
Your friend earns $120 for working 15 hours at the store.
What is the difference in your hourly rates of pay, and who earns more per hour?
You earn: $102/12 hrs = $8.50/hr
Friend earns: $120/15 hrs = $8 /hr
You earn $0.50/hour more than your friend.
Which is harder to climb? A hill with slope 1/3 or a hill with slope 1/4?
The hill with slope 1/3.
Paul travelled from France to the U.S.
The exchange rate is 7 Euros to $7.91.
How many dollars will he receive if he exchanges 125 Euros?
$141.25
A photo is 3.6 inches by 8.4 inches.
Someone wants to enlarge it to a dimension of 5.4 inches by 12.6 inches.
Are the photos proportional?
yes.
3.6 * 1.5 = 5.4
8.4 * 1.5 = 12.6
3.6/8.4 = 5.4/12.6
A specific shade of green is 5 parts blue to 3 parts yellow.
Someone mixed 25 quarts of blue and 9 quarts of yellow.
How can you fix the mixture to make the specific shade of green?
Add 6 quarts of yellow.