Similarity: Ratios and Proportions

Proportions

Proportions are a comparison of two ratios. Proportions are always written as an equation that compares two ratios.

 

The following are all proportions:

  1. 3:4 = 30:40
  2. two-thirds equals twenty-two-thirty-thirds
  3. 5 to 8 = 25 to 40

Did you notice that they all have an equal sign?  An equal sign with ratios on either side is a proportion.

How do we know if two ratios are actually proportional?  To see if two ratios are proportional, we can set up the equation and cross-multiply.  If the products are equal, then the ratios are proportional.

Let’s look at that closer.
Is the ratio of 4 to 7 equal to the ratio of 48 to 84?

Set up an equation and cross multiply:

four-sevenths equals forty-eight-eighty-fourths; four-sevenths equals forty-eight-eighty-fourths; 4 times 84 equals 7 times 48; 336 equals 336

Since the products are equal, the ratios are proportional.