1. Chapter 5 Ratios, Proportions, and Percents
Section 2: Proportions

2. Warm Up: What are the three ways of writing a ratio?
I drove 489 miles from San Diego to San Jose, California. I had a full tank of 16 gallons of gas in my tank when I left San Diego. I now have ¼ of a tank left. How many miles to 1 gallon did drive?

3. Proportion An Equality of TWO Ratios. For Example: 6/9 = 8/12
The ratios are equivalent.
Which means they reduce to the same fraction in it’s simplest form!

4. Try This On For Size…a/b = c/d
Multiplication Property of Equality (Method 1) (get the denominators to be the same  what is done to the bottom is done to the top)
b/b = 1 and d/d = 1 (cancel out stuff on the top and bottom that are the same)
ad and bc are called the Cross Products of the proportion a/b = c/d.

5. Get Common Denominators and Multiply TOP and BOTTOM.
PROOF OF PROPORTIONS:
Multiplication Property of Equality!
If a/b = c/d
Simplify
Get Common Denominators and Multiply TOP and BOTTOM.
Then Cancel!

6. Cross Product: The Easy Way (Method 2)
In a proportion, the cross products of the two ratios are equal!
Arithmetic: 6/9 = 8/12 if, 6•12 = 9•8
72 = 72
Algebra: a/b = c/d if, a•d = c•b
ad = cb
You can use Cross Product to find variables in proportions to make the proportions true.

7. Try the Two Ways to Find Variables in Proportions: X/9 = 4/6
Method 1: Multiplication Property of Equality. (Common Denominator)
Method 2: Cross Product. (Cross Multiply)

8. Solve Using Your Favorite Method

9. Do the two Ratios form a Proportion?
Two ratios form a proportion if the cross product are equal.
Tell me whether each pair of ratios form a proportion by your Favorite Method.
15/20 and 5/7 Yes or No?
7/12 and 17.5/30 Yes or No?

10. You Can Use Proportions to Solve Word/World Problems
One hundred nautical miles equals about 115 standard, or statue, miles. To the nearest mile, how far in statue miles is 156 nautical miles?
Let d = distance in statue miles.
100/115 = 156/d
100d = 115(156)
d = 179
Proportion  two ratios that are equal.
Written as Cross Product
Divide Each Side by 100.
156 nautical miles is about 179 statue miles.