Definitions and Formulas
What is a ratio?
Write the ratio as a fraction in simplest form.
25 to 45
5/9
Tell whether the ratios form a proportion.
6/4, 8/12
You must have work shown to prove your answer!
No, they do not form a proportion.
Solve the proportion.
2/7 = x/28
x=8
Find the slope that passes through the points (-2, -2), (4, 1)
The slope is 3/6=1/2
What is a unit rate?
A rate with a denominator of 1
Find the unit rate.
180 miles in 3 hours.
60 mi/h
Tell whether the ratios form a proportion.
25:20, 15:12
Yes, they do form a proportion.
test worth 50 points; test score of 40%
1) x/50 = 40/100
2) 20 points
Based on the equations below, determine which line would be steeper.
y=15x
y=20x
Since the slope of 20 is greater than 15, y=20x would be steeper.
What is a proportion?
An equation stating that two ratios are equal
Find the unit rate.
4 1/4 pages in 2 1/2 minutes
1.7 pages per minute OR 1 7/10 pages per minute
Tell whether the ratios form a proportion.
2 to 4, 11 to 11/2
No, they do not form a proportion.
Solve the proportion.
30/x+1 = 15/6
x=11
Tell whether x and y show direct variation. If so, find k and write an equation that relates x and y.
(1,2), (2,4), (3,6), (4,8)
Yes, they do show direct variation; k=2; y=2x
What is slope? What does it measure?
A constant rate of change. It is a measure of the steepness of the line.
A painter can paint 350 square feet in 1.25 hours. What is the painting rate in square feet per hour?
280 square feet per hour
You can do 90 sit-ups in 2 minutes. Your friend can do 135 sit-ups in 3 minutes. Do these rates form a proportion?
Yes; you can both do 45 sit-ups per minute.
A chef uses 1 tomato and 1.5 cups of black beans for a recipe. The chef increases the amounts of ingredients in the recipe to make a proportional recipe. The new recipe had 6 cups of black beans.
1) Write a proportion that gives the number x of tomatoes in the new recipe.
2) Solve to find the number of tomatoes in the new recipe.
1) Sample answer: 1.5 cups beans /1 tomato = 6 cups beans/x tomatoes
2) There are 4 tomatoes in the new recipe
1 inch is 2.54 centimeters. Write a direct variation equation that relates x inches to y centimeters.
y=2.54x
What is the general form of the equation for direct variation?
y=kx
You mix 1/2 cup of juice concentrate for every 2 cups of water to make juice. How much juice concentrate and water do you use to make 10 cups of juice?
You use 2 cups of juice concentrate and 8 cups of water.
Tell whether the ratios form a proportion.
2 to 4/5, 3/4 to 3/10
Yes, they do form a proportion.
There are 40 people in an audience. The ratio of adults to children is 5 to 3. How many are adults?
There are 25 adults.
Tell whether x and y show direct variation. If so, find k.
1) y-5=2x
2) 2x-y=0
1) No; the equation cannot be written as y=kx
2) Yes; the equation can be written as y=kx; k=2