Is -6 a Rational or Irrational Number- Decoding the Arithmetic Enigma

Is -6 a rational number or irrational? This question may seem simple at first glance, but it raises an interesting discussion about the nature of numbers and their classification. To answer this question, we need to understand the definitions of rational and irrational numbers and then apply them to the number -6.

Rational numbers are those that can be expressed as a fraction of two integers, where the denominator is not zero. This means that a rational number can be written in the form of p/q, where p and q are integers and q is not equal to zero. On the other hand, irrational numbers cannot be expressed as a fraction of two integers and have decimal expansions that neither terminate nor repeat.

Now, let’s consider the number -6. To determine whether it is rational or irrational, we need to check if it can be written as a fraction of two integers. Since -6 is an integer, we can express it as -6/1, where both the numerator and the denominator are integers. Therefore, -6 can be written in the form of p/q, satisfying the definition of a rational number.

In conclusion, -6 is a rational number because it can be expressed as a fraction of two integers. This example demonstrates that not all negative numbers are irrational, as some can be represented as fractions. The classification of numbers as rational or irrational is essential in mathematics, as it helps us understand the properties and relationships between different types of numbers.