Ratios, Rates, and Proportions Comparing

Writing Ratios & Rates Because rates and ratios look like fractions, smell like fractions, and taste like fraction…we’re going to treat them like fractions! In order to compare rates and ratios (fractions), CROSS MULTIPLY!!! We define these relationships as either… Proportional (they equal) Non-proportional (they don’t equal) For example: 3 4 and 15 20 3 4 = 15 20 3(20) = 4(15) 60 ≠ 60 Proportional 2 5 and 25 100 2 5 = 25 100 2(100) = 5(25) 200 ≠ 125 Non-proportional *The majority of the problems you’ll receive regarding proportional vs. non-proportional relationships will be in the form of either word problems, charts, or diagrams.

Word Problems Here’s an example of a word problem: The local fair charges $5 for entry and $1 for every ride. Is the amount you spend proportional to the amount of rides you enjoy? You need two ratios to compare; therefore, create your own ratios based upon the problem. For instance… 1 𝑟𝑖𝑑𝑒 $6 and 2 𝑟𝑖𝑑𝑒𝑠 $7 *Create your own ratios! 1 6 = 2 7 1(7) = 6(2) 7 ≠ 12 Non-proportional

Charts Here’s an example of a chart: Which table below shows a constant unit price (also known as proportional)? Publix Winn Dixie 10 20 = $2 $4 10 20 = $2 $3.50 10(4) = 20(2) 10(3.5) = 20(2) 40 = 40 35 ≠ 40 Proportional Non-proportional Publix Winn Dixie # of Apples Total Cost 10 $2.00 20 $4.00 $3.50 30 $6.00 $5.50

Diagrams Here’s an example of a word problem: If the two triangles below are similar (same shape, different size), what is the value of x? Create your own ratios! 2cm 3cm = 4cm 6cm 2(6) = 3(4) 12 = 12 Proportional