Ratios and Proportions
We see ratios used every day in measurements, sports, and business. Look at the headlines of any news story, such as. "One out of ten teenagers Drinks Coffee" or "More than 8 out of 10 teenagers say they enjoy school."
Vocabulary
- ratio
- proportion
- extremes
- means
- Cross Product Property
- Reciprocal Property
- extended ratio
Ratio
A ratio is a comparison of two numbers in the same unit. Ratios can be expressed
- As a fraction 3/2
- Using words three dogs and two cats
- With a colon 3:2
Roll over each phrase above to see an example of the ratio of dogs to cats.
Proportion
A proportion is an equation that equates two ratios.
The a and d in the proportion 
are called extremes.
The b and c in the proportion are called means.
The proportion is read a is to b as c is to d.
Your Turn #1
The relationship below is called a ___.
Answer: proportion
In the proportion above, one extreme is 3, what is the other?
Answer: 12
In the proportion above, one mean is 9, what is the other?
Answer: 4
Proportion Properties
Cross Product Property
In a proportion, the product of the extremes = the product of the means.
If , then ad = bc
You've used this property before in Algebra I. The cross product property allows you to eliminate fractions from problems through cross-multiplying.
Reciprocal Property:
If two ratios are equal, then their reciprocals are also equal.
If 
then 
Example #1
Now, let's use the properties of proportions to solve the proportion.
- Let's start by getting rid of the denominators on both sides by using the cross products property
If a/b = c/d, then ad = bc
3(x - 4) = 4x - Next, let's simplify the right side of the equation using the distributive property.
3x - 12 = 4x
- 12 = x - Finally, get all of the x-terms on the right by subtracting 3x from each side to find the answer.
Your Turn #2
Solve the proportion
Start by using the cross products property If a/b = c/d, then ad = bc to eliminate the fractions.
___ = (9)( ___ )
Answer: 10x, 25
Nice job. Now that you have the equation, simplify the right side by finding the product of the numbers in parentheses.
10x = ___
Answer: 225
Nice job. Just divide both sides by 10 to isolate the x and solve the proportion!
x = ___
Answer: 22.5
