Is -5 a rational number? This question may seem straightforward, but it delves into the fascinating world of mathematics and number theory. To answer this question, we need to understand what a rational number is and how -5 fits into this category.
Rational numbers are a subset of real numbers that can be expressed as a fraction of two integers, where the denominator is not zero. In other words, a rational number can be written in the form p/q, where p and q are integers and q is not equal to zero. This definition includes all integers, as they can be represented as fractions with a denominator of 1 (e.g., 3 = 3/1, -2 = -2/1).
Now, let’s examine -5. Since -5 is an integer, it can be written as a fraction with a denominator of 1: -5 = -5/1. This means that -5 can be expressed as a ratio of two integers, making it a rational number. In fact, any integer, positive or negative, can be represented as a rational number by placing it over 1 as the denominator.
The concept of rational numbers is essential in various mathematical fields, such as algebra, geometry, and calculus. Rational numbers provide a foundation for understanding fractions, proportions, and rates. Moreover, they help us solve real-world problems, such as calculating percentages, ratios, and proportions.
In conclusion, -5 is indeed a rational number because it can be expressed as a fraction of two integers, -5/1. This example illustrates the broad applicability of rational numbers in mathematics and their significance in solving problems in various disciplines.
