Lesson 2.3 Proportional Reasoning

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Presentation transcript:

Lesson 2.3 Proportional Reasoning

Definitions and Examples A proportion is an equation between two ratios or rates

Example 1 $2.85 = $0.95 3 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 2 Solve the following proportions… 1cm : 25km = 4cm: ? First term is multiplied by a factor of 4, so the second term is multiplied by 4 25x4=100, so the answer is 100km

Example 3 200 km = ? 3h 5h Two methods to solving 1. 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 divide 200km x 5h /3h = 333.333km

Example 4 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 dentists Step 2: Choose method unit rate or cross-multiply 3 x 20 = 60 2x 20 = 40 Therefore, 40 dentists in Stickyville would recommend chewing sugarless gum after eating to prevent cavities.