Which of the following contains both positive and negative fractions?

Which of the following contains both positive and negative fractions?

• A. Rational numbers
• B. Whole numbers
• C. Natural numbers
• D. Integers

Answer: (A)

The option that includes both positive and negative fractions is rational numbers. Rational numbers are defined as any number that can be expressed as the quotient of two integers, where the denominator is not zero. This definition encompasses a wide array of numbers, including positive and negative fractions (such as 1/2 or -3/4), as well as whole numbers and integers. Whole numbers, on the other hand, only include the non-negative integers (0, 1, 2, 3, ...), and do not account for negative numbers or fractions. Natural numbers are even more restricted, typically including only the positive integers (1, 2, 3, ...). Integers include all whole numbers as well as their negative counterparts (-1, -2, ...), but they do not include fractions. Thus, rational numbers is the only option that fully encompasses both positive and negative fractions, providing a complete representation of the set in question.

The option that includes both positive and negative fractions is rational numbers. Rational numbers are defined as any number that can be expressed as the quotient of two integers, where the denominator is not zero. This definition encompasses a wide array of numbers, including positive and negative fractions (such as 1/2 or -3/4), as well as whole numbers and integers.

Whole numbers, on the other hand, only include the non-negative integers (0, 1, 2, 3, ...), and do not account for negative numbers or fractions. Natural numbers are even more restricted, typically including only the positive integers (1, 2, 3, ...). Integers include all whole numbers as well as their negative counterparts (-1, -2, ...), but they do not include fractions.

Thus, rational numbers is the only option that fully encompasses both positive and negative fractions, providing a complete representation of the set in question.