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Understanding ratios

A ratio is a comparison of two numbers.

What is the ratio of tulips to cacti?

 The ratio of tulips to cacti is 2 to 3

There are 3 ways to write a ratio: 2 to 3, $\frac{2}{3}$, or 2:3

What is the ratio of pens to pencils?

 The ratio of pens to pencils is 2 to 3

The ratio of two numbers a and b is the quotient $\frac{a}{b}$

Sussan has a bag with 3 pens, 4 pencils, 7 felt tip pens, and 1 pencil sharpener. What is the ratio of pencils to pens?
Expressed as a fraction, with the numerator equal to the first quantity and the denominator equal to the second, the answer would be 4/3.
Two other ways of writing the ratio are 4 to 3, and 4:3.

In the 2009 Nathan's Hot Dog eating contest, Joey Chestnut ate 68 hotdogs in 10 minutes. Find how many hog dog per minute this is.

The ratio is $\frac{68}{10}=6.8$ hd/min