why are Negative numbers not always rational?
Negative numbers are not always rational because rational numbers are defined as numbers that can be expressed as the ratio of two integers, where the denominator is not zero. This means that the numerator and denominator must both be integers, and negative numbers do not always fit this criteria.
For example, the number -π (pi) is a negative number that cannot be expressed as the ratio of two integers. It is an irrational number because it cannot be written as a fraction with integers for its numerator and denominator.
Similarly, other examples of negative irrational numbers include the square root of -2 (√(-2)), which is also not rational as it cannot be expressed as a ratio of two integers.
On the other hand, negative rational numbers, such as -1/2 or -3/4, do exist because they can be written as the ratio of two integers, with a negative sign in front.
Negative numbers are not always rational because a rational number can be expressed as a fraction, where the numerator and denominator are both integers. However, not all negative numbers can be expressed in the form of a fraction.
For example, consider the square root of 2 (√2). This is an irrational number because it cannot be expressed as a fraction. If we try to express -√2 as a fraction, we would still have an irrational number. This is because the negative sign does not affect the irrationality of the number itself.
In summary, negative numbers can be rational, such as -1/2, -3, or -5/4. However, there are negative numbers like -√2 or -π that are considered irrational because they cannot be expressed as fractions.