Is -5/6 irrational, rational, an integer, or a natural number?

An integer is any number that does not have a fractional part:

... {..., -3, -2, -1, 0, 1, 2, 3, ...}

A whole number is a non-negative integer. As a mnemonic device, you can consider the O in whOle to indicate that whole numbers include zero:

... {0, 1, 2, 3, ...}

A natural number is a positive integer, a counting number. Some authors also include zero, making whole numbers and natural numbers the same set.

... {1, 2, 3, ...}

A rational number is a fraction with a numerator that is an integer and a denominator that is a non-zero integer. All integers are rational numbers. Any number you can write completely is a rational number. Any number with a repeating fractional part is also a rational number (1.09090909..., for example, is 12/11.) -5/6 is a rational number.

An irrational number is a number that cannot be expressed as a rational number. It has an infinite, non-repeating fractional part, so can never be written completely--only represented symbolically, as π or √2, for example.

-5/6 is a rational number