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?

Chapter 6: Ratios, Proportions, and Percents

And you thought fractions where a pain.

Section 2: Proportions

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!

Try This On For Size…a/b = c/d• Multiplication Property of Equality (Method 1)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 (cancelcancel out stuff on the top and bottom that are the same)

• ad and bc are called the Cross ProductsCross Products of the proportion a/b = c/d.

PROOF OF PROPORTIONS:

Multiplication Property of Equality!

If a/b = c/d

Simplify

Get Common Denominators and Multiply TOP and BOTTOM.

Then Cancel!

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 ProductCross Product to find

variables in proportions to make the proportions true.

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)

Solve Using Your Favorite Method

• H/9 = 2/3

• 22/D = 6/21

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?

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.

Assignment #43

• Page 286-287: 18-29 All, 38-45 All, 53, and 55.

• MAKE SURE YOU WRITE THIS DOWN CORRECTLY!!!