Properties of Rational Numbers A rational number is a number that can be expressed as a fraction of two integers, a/b, where b is not equal to 0. Rational n...
Properties of Rational Numbers
A rational number is a number that can be expressed as a fraction of two integers, a/b, where b is not equal to 0. Rational numbers include all real numbers that can be expressed as fractions, including integers, such as 3, 4/5, and 2/3.
Basic Properties:
Addition: The sum of two rational numbers is also a rational number. For example, 1/2 + 1/4 = 3/4.
Subtraction: The difference between two rational numbers is also a rational number. For example, 3/4 - 1/4 = 2/4 = 1/2.
Multiplication: The product of two rational numbers is also a rational number. For example, 1/2 * 1/4 = 1/8.
Division: The quotient of two rational numbers is also a rational number. For example, 1/2 divided by 1/4 = 2/4 = 1/2.
Additional Properties:
Equality: A rational number is equal to itself if and only if its numerator and denominator are equal. For example, 1/2 = 2/4.
Comparison: Two rational numbers are comparable if they have the same value. For example, 1/2 and 2/4 are comparable because they both represent the same amount of the set of rational numbers.
Fractional representation: Any rational number can be expressed uniquely in a unique fraction. For example, the fraction 1/2 can be expressed as 2/4.
Irrational numbers: Rational numbers form a subset of the set of real numbers. However, there are infinitely many irrational numbers that cannot be expressed as fractions. These numbers include numbers like pi, the square root of 2, and the square root of 3