Can a fraction be negative. Is – 28/9 a fraction or a rational number?
The Correct Answer and Explanation is:
Yes, a fraction can be negative. The expression −289-\dfrac{28}{9}−928 is both a fraction and a rational number.
A fraction is defined as a number that represents parts of a whole and is expressed in the form ab\dfrac{a}{b}ba, where aaa and bbb are integers, and b≠0b \neq 0b=0. If either the numerator or denominator is negative, the entire fraction becomes negative. Therefore, −289-\dfrac{28}{9}−928 qualifies as a fraction because it is expressed in the standard form of a numerator over a denominator.
A rational number is any number that can be written as the ratio of two integers, pq\dfrac{p}{q}qp, with q≠0q \neq 0q=0. Rational numbers include positive and negative fractions, whole numbers, and decimals that terminate or repeat. Since −289-\dfrac{28}{9}−928 is a ratio of two integers and the denominator is not zero, it fits the definition of a rational number as well.
Negative fractions often arise in real-life applications, such as owing money, changes in elevation, or temperature drops. The placement of the negative sign is flexible in fractional notation. For example, −289-\dfrac{28}{9}−928, −289\dfrac{-28}{9}9−28, and 28−9\dfrac{28}{-9}−928 all represent the same value. The key point is that the overall value of the fraction is negative.
Additionally, the decimal equivalent of −289-\dfrac{28}{9}−928 is approximately −3.111…-3.111…−3.111…, which is a repeating decimal. This confirms its classification as a rational number, since repeating decimals always correspond to rational values.
Therefore, −289-\dfrac{28}{9}−928 is both a negative fraction and a rational number, and its classification depends on the mathematical context being discussed.
