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:
I agree with Hamid’s statement that 53\frac{5}{3}35 is a rational number, but I would correct him regarding the natural number classification of 5.
Explanation:
- Rational Numbers: A rational number is any number that can be expressed as the fraction of two integers (where the denominator is not zero). Both 53\frac{5}{3}35 and 5 are rational numbers because:
- 53\frac{5}{3}35 is explicitly in the form of a fraction where both the numerator (5) and the denominator (3) are integers.
- 5 can be written as 51\frac{5}{1}15, which is also a fraction of two integers, making it a rational number.
- Natural Numbers: Natural numbers are the set of positive integers typically starting from 1. In most standard definitions, this set does not include zero or negative numbers.
- Hamid’s statement that 5 is a natural number is correct based on the common definition. 5 belongs to the natural numbers because it is a positive whole number.
- However, 5 is also an integer and a rational number, as it can be written as 51\frac{5}{1}15. Therefore, it’s more general to say that 5 is a rational number, and then mention it’s a natural number within the context of whole numbers.
Conclusion:
Both 53\frac{5}{3}35 and 5 are rational numbers. However, while 5 is indeed a natural number (under the common definition), the classification of rational numbers is more inclusive and could apply to a broader range of numbers, including 5. So, I agree with Hamid that both numbers are rational, but I would add that 5 is a natural number as well.
