Model Ratios
Reciprocals
Are the ratios equivalent?
Proportional Equations
Constant of proportionality
100
Write a ratio of yellow to red circles as a fraction:
3/4, 3:4, 3 to 4
100
Write the reciprocal of 2/3
3/2
100
Are the Ratios Equivalent?
2/4 = 8/12
No!
100
y =
x = 4
100
The __________is the ratio of two quantities that are proportional to each other
constant of proportionality
200
Write a ratio of yellow to red circles as a fraction:
5/3, 5:3, 5 to 3
200
Write the reciprocal of 4
1/4
200
Are the Ratios Equivalent?
5/10 = 30/60
x6
Yes!
200
Solve for x to make the Ratios Equivalent:
3/9 = 9/x
x = 27
200
There are 2.54 centimeters in every inch. What is a constant of proportionality for the relationship between centimeters and inches?
1 in x 2.54 = 2.54 cm
2.54
300
Write a ratio of red to blue circles:
5/6, 5:6, 5 to 6
300
What do you get when you multiply a number by its reciprocal?
1
300
Are the Ratios Equivalent?
1/2 = 16/18
No!
300
Solve for x to make the Ratios Equivalent:
7/14 = x/42
x = 21
300
In a cake recipe, we use 1/2 cup of milk and 2 eggs. What is the constant of proportionality between cups of milk and eggs?
1/2 c milk x 4 = 2 eggs
2 eggs x 1/4 = 1/2 c milk
4 or 1/4
400
Write a ratio of squares to diamonds:
15:20, 15:20, 15 to 20
400
Write the reciprocal of 1.25 as a fraction
4/5 or 1/1.25
400
Are the Ratios Equivalent?
13/14 = 39/42
Yes!
400
Solve for x to make the Ratios Equivalent:
2/16 = x/80
x = 10
400
A car drives 90 miles in 3 hours. What is the constant of proportionality between distance and time?
Bonus 100 pts: What is another word for what this constant of proportionality represents?
3 hours x 30 = 90 miles
30 mph
Bonus: speed
500
Write a ratio of Blue Circles to all White Shapes:
4/8, 4:8, 4 to 8
500
!!!!DAILY DOUBLE!!!!
What is the reciprocal of 0?
There is none!
500
Are the Ratios Equivalent?
8/32 = 32/128
Yes!
500
!!!!DAILY DOUBLE!!!!
Solve for x to make the Ratios Equivalent:
X/30 = 54/90
x = 18
500
The ratio of blueberries to strawberries is 1:7. If there are210 strawberries, how many blueberries are there.
30 Blueberries