How to Write a Rational Number as the Quotient of Two Integers

A rational number is any number that can be expressed in a fraction, with the exception of unsimplified square roots and if zero is the denominator (the bottom part of the fraction). Integers are the set of whole numbers, including negative numbers, positive numbers and zero. Thus, any quotient (the result of division) of two integers results in a rational number; it is only a matter of dividing them.

Instructions

    • 1

      Ensure that the two numbers you have are integers. All integers can be written as whole numbers (e.g. "2" or "-4"), and thus they are not accompanied by a decimal point, a fraction or a square root sign.

    • 2

      Arrange the two numbers in a fraction. It does not matter which one you choose to make the numerator (top, or first, number) and which you choose as the denominator, assuming the only thing that matters is that you get a rational number. For example, you can divide -4 by 2, which would be expressed as the fraction -4/2.

    • 3

      Simplify the fraction as much as possible by dividing both numbers by their greatest common factor, which is the highest number that can divide into both and leave you with a whole number. (Note that any quotient of two integers, simplified or not, will be a rational number.) The greatest common factor in the fraction -4/2 is 2, therefore the simplified fraction is -2/1, The only exception is if you divide an integer by zero (e.g. 4/0 is not a rational number).

    • 4

      Solve your equation by writing left to right: -2/1 = -2. This expresses -2 (a rational number) as the quotient of two integers (-2 and 1).

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