Definitions
A comparison of two quantities by division.
What is a ratio?
What is the unit rate for $12 for 3 burgers?
4 dollars per burger.
How do you find a unit rate?
Divide the numerator by the denominator.
Solve 2:5 = x:15
x=6
Write a proportion to show 2 cups of flour is needed for 3 loaves of bread and 6 cups of flour is needed for x loaves.
2:3 = 6:x or 3:2=x:6
A ratio compares two quantities, while a rate compares two quantities with different units.
What is the difference between a ratio and a rate?
Which is the better deal: 5 apples for $3 or 7 apples for $5?
5 apples for $3 = $0.60 each; 7 apples for $5 = $0.71 each, so 5 apples for $3 is better.
How do you test if two ratios form a proportion?
Cross multiply; if the cross products are equal, they form a proportion OR simplify + mental math + show work
solve 8:10 = 12:x
x=15
Write a proportion for the statement: "12 is to 16 as 3 is to 4.
12:16=3:4
An equation stating that two ratios are equivalent
What is a proportion?
A train travels 300 miles in 5 hours. What is the train's speed?
60 miles per hour
What does "simplify a ratio" mean?
Rewrite it in its simplest form by dividing both terms by their greatest common factor
Is 4:9 proportional to 12:27
Yes
Write a proportion for the following: A car travels 120 miles in 3 hours. How far can it travel in 5 hours?
120:3 = x:5
True or False: Ratios can only be written using fractions.
False—ratios can also be written with colons or the word "to."
You earn $45 in 6 hours babysitting. What is your hourly rate?
7.50 per hour
When solving proportions, why is it important to set up the equation correctly?
So the ratios represent the correct relationship and the solution makes sense.
A recipe calls for 3 cups of sugar for 4 cakes. How much sugar is needed for 10 cakes?
7.5 cups of sugar
Write a proportion for this problem: 4 apples cost $2. How much do 10 apples cost?
4:2=10:x
Give an example of a real-world situation where you’d use a rate.
Answers may vary, e.g., "driving 60 miles per hour."
If you jog 8.4 miles in 70 minutes, what is your speed in miles per hour?
7.2 miles per hour.
Why do we use equivalent ratios when solving real-world problems?
To scale up or down while maintaining the same relationship between quantities
Solve: If 5 pencils cost $1.25, how much do 12 pencils cost?
$3
I would like to know how much one song costs. I know that 3 songs cost $2.99. How would I set up a proportion to help me figure this out?
2.99:3=x:1