Lesson 2.3 Proportional Reasoning

A proportion is an equation between two ratios or rates

Definitions and Examples

$2.85 = $0.953 pencils 1 pencil

To prove this, take your caluculator and go $2.85/3. You will get $0.95 so there for this is an equation.

Example 1

Solve the following proportions…

1cm : 25km = 4cm: ? First term is multiplied by a factor of 4, so the second term is multiplied by 425x4=100, so the answer is 100km

Example 2

200 km = ? 3h 5hTwo methods to solving1. Method 1: Find the unit rate and multiply as needed

200km/3h = 66.666km/h or 66.66km per one hour

66.666km/h x 5 hours = 333.3333km

2. Method 2: Cross-multiply and divide200km x 5h /3h = 333.333km

Example 3

Use a proportion to solve….Two out of three dentists recommend chewing sugarless gum after eating to prevent cavities. If there are 60 dentists in Stickyville, how many of them would you expect to recommend chewing sugarless gum after eating to prevent cavities?Step 1: Set up the proportion 2 = ?

3 60 dentistsStep 2: Choose method unit rate or cross-multiply

3 x 20 = 602x 20 = 40

Therefore, 40 dentists in Stickyville would recommend chewing sugarless gum after eating to prevent cavities.

Example 4