True
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-37 is the ratio of -37 to 1 . It's completely rational.
37 can be written as 37/1 which is a number of the from a/b where a and b are integers. This shows it is rational.
It is an irrational number
The square root of 37 is an irrational number
-37 is the ratio of -37 to 1. It's also the ratio of 37 to -1, and also the ratio of, for example, 481 to -13, and also an infinite number of other ratios of whole numbers. So it's pretty clearly rational.