Similarity: Ratios and Proportions

Comparing Proportions

On the last page, we cross multiplied to compare ratios.  This concept of cross multiplying can be taken one step further to compare proportions.  Two proportions are equivalent if, when you cross multiply, equivalent equations are generated.

Example:
Are the fraction a over b equals five-sixths and the fraction a over 5 equals the fraction b over 6 equivalent proportions?

Solution:
In each proportion, cross multiply and compare the equations generated.

the fraction a over b equals five-sixths; 6 a equals 5 b

the fraction a over 5 equals the fraction b over 6; 6 a equals 5 b

Since both equations are the same, the proportions are equivalent.