1. Ratios, Rates, and Proportions
Comparing

2. 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
3 4 = (20) = 4(15) 60 ≠ 60 Proportional
2 5 and
2 5 = (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.

3. 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

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

5. 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