proportions

PROPORTIONS

What is a Proportion? An equation which shows two equivalent

ratios

Why do we use Proportions?

They help us to find relationships in the real world which are similar

There are two methods to evaluate a proportion

Method 1 -- Scale Factor

Method 2 -- Cross Products

Scale Factor Method

Step 1 – Setup the Problem

Julian is the best cake baker in Richmond. To make a cake, he uses 1 egg for every 2 cups of flour. If the recipe calls for 10 cups of flour, how many eggs does he need?

eggs 1 X

flour 2 10

RatioItem

Scale Factor Method

Step 2 – Find number (scale factor) that you can multiply by to get from side with two numbers to side with variable.

eggs 1 X

flour 2 10

Scale Factor Method

Step 2 – Find number (scale factor) that you can multiply by to get from side with two numbers to side with variable.

eggs 1 X

flour 2 10

x5

x5

Scale Factor Method

eggs 1 X

flour 2 10

x5

x5

Step 3 – Multiple to find the answer

2 x 5 = 10 and 1 x 5 = 5; therefore, X = 5

Cross Products Method

Step 1 – Setup the Problem

Tom is driving to New York. He travels 70 miles every 2 hours. If the trip takes 8 hours, how many miles will he travel?

Miles 70 X

Hours 2 8

Ratio

Cross Products Method

Step 2 – Multiple numbers from top left to bottom right

Miles 70 X

Hours 2 8

70 8 = 560

Cross Products Method

Step 3 - Multiply numbers from top right to bottom left

2 · x = 2x

Miles 70 X

Hours 2 8

Cross Products Method

Step 4 - Write products as an equation

Miles 70 X

Hours 2 8

560=2x

Cross Products Method

Step 5 – Divide by this number to get x by itself

560=2x

Example

Cats

Dogs

Wendy works at a kennel. There are 3 cats for every 2 dogs. If she takes in 18 cats, how many dogs will she have?

Ratio

Example

miles

hours

Simone is taking a trip to Florida for spring break. Her family travels 1250 miles in 25 hours. At their rate of travel, how many miles did they travel per hour?