Hamid says 5/3 is a rational number and 5 is only a natural number. Asks him, “Are both numbers rational?” Who do you agree with?
The Correct Answer and Explanation is:
Both numbers are rational, but I don’t fully agree with Hamid’s interpretation.
First, let’s break down what a rational number is. A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not zero. In other words, it’s a number that can be written as a/b, where a and b are integers, and b ≠ 0.
5/3:
The number 5/3 is a rational number because it’s already in the form a/b, where a = 5 and b = 3, both of which are integers. The denominator (3) is not zero, so 5/3 is rational.
5:
The number 5 is also a rational number. Although it’s an integer, it can be written as a fraction with a denominator of 1: 5/1. This fits the definition of a rational number, because 5 = 5/1 is the ratio of two integers.
Natural Numbers:
Now, Hamid also mentions that 5 is only a natural number. This is true because 5 is indeed a natural number in most mathematical systems, as natural numbers are typically the set of positive integers: {1, 2, 3, 4, 5, …}. However, this doesn’t prevent 5 from being rational. It just means that 5 is a specific subset of rational numbers.
Conclusion:
Both 5/3 and 5 are rational numbers. 5/3 is explicitly a ratio of integers, and 5, although also a natural number, is equally a rational number since it can be written as 5/1. Therefore, I agree that 5/3 is rational, but I would clarify that 5 is also rational, not just a natural number
