Given the statement, the ratio of men to women in the room is 3 to 5, how many men are in the room?

You probably recognize pretty quickly that it is not possible to answer the question above.  Just given a ratio, it is not possible to identify the actual number of men in the room.  At this point we know the number of men in the room must be a multiple of 3, but the actual number could be 3 or 3,000 (although I am not sure I have been in a room that large).

Along with ratios in their traditional form (3 to 5 or 3:5), there are other types of numbers that are ratios, slightly disguised

a) Fractions: The container is 2/3 full.

This statement is expressing that there are 2 full parts for every 3 total parts of the container (a ratio of 2 to 3).

b) Percentages: 33% of company employees have Master’s degrees.

This statement is expressing for every 33 employees with Master’s degrees there are 100 total employees (a ratio of 33 to 100).

c) Percentage or fractional increase: The company’s profits increased 25% (or ¼) from 2010 to 2011.

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