1. Proportions

2. S.W.B.A.T
Write a proportion when given a word problem and solve for the variable

3. What are Proportions?
A proportion is a name we give to a statement that two ratios are equal
It can be written two ways
To equal fractions
Using a colon
a:b = c:d

4. Cross Products
When two ratios are equal, the cross products of the ratios are equal
For the proportion
a:b = c:d
a (d) = b (c)

5. Reading Proportions
The following proportion is read as “twenty is to twenty-five as four is to five.”

6. Cross Proportions
In problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion
To find the cross products of a proportion, we multiply the other terms, called the extremes, and the middle terms, called the means

7. Cross Proportions
In this proportion 20 and 5 are the extremes, and 20 and 4 are the means
Cross Products: 20 (5) = 25 (4)
100 = 100
Since the cross products are both equal to 100, we know that these ratios are equal and that this is a true proportion

8. Word Problem
In a horror movie featuring a giant beetle, the beetle appeared to be 50 feet long. However, a model was used for the beetle that was really only 20 inches long. A 30-inch tall model building was also used in the movie. How tall did the building seem in the movie?

9. Word Problem Solution Step 1: Write the proportion
Step 2: Multiply to find the cross products
20 inches (x) = 50 feet (30 inches)
Step 3: Divide to find x
20x = 50 (30)
20x = 1500
Divide by 20
X = 75