Rational numbers are numbers that can be expressed as the ratio of two integers, where the denominator is not zero.
What are Rational Numbers?
In mathematics, a rational number is any number that can be expressed as the fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number.
Properties of Rational Numbers
They can be expressed as the quotient of two integers
They contain a finite or recurring decimal representation
Their sum, difference, product, and quotient (except by 0) results in a rational number.
Examples
Examples of rational numbers include: 1/2, -5, 6, 2.75, 0.3333 (0.33 recurring), etc.
Understanding Rational Numbers
The set of all rational numbers is denoted by the letter 'Q', for quotient. They play an important role in various mathematical concepts including algebra, calculus, and number theory.
The numerator and the denominator of a fraction representing a rational number are respectively represented by 'a' and 'b'. Which condition must the denominator 'b' satisfy?
What is the term for a number that can be expressed as a fraction, terminates or repeats in its decimal expansion, and can be either positive or negative?
A rational number can be expressed as the fraction of two integers. If the numerator is represented by 'p', the denominator, represented by 'q', must never be equal to _____.
The decimal representation of a rational number can either be finite or _____ .
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Addition Of Rational Numbers
Addition is a fundamental operation that can be performed on rational numbers. The procedure for adding rational numbers involves common denominators and integer addition.
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Real Numbers
Real number set includes all the rational numbers, making rational numbers a subset of real numbers.
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Addition
Addition is an operation that can be applied to rational numbers, combining them based on the rules of arithmetic.
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Division
Rational numbers can be calculated by the division of two integers. Division is the mathematical operation that generates a rational number when performed on two integers.
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Subtraction Of Rational Numbers
Subtraction operation can be performed between two or more rational numbers, giving another rational number as result.
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Integers
Rational numbers are derived from integers since they can be expressed as the quotient p/q of two integers. Thus, the understanding of integers is integral to the concept of rational numbers.
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Fractions
Rational numbers represent the relationship between two integers, which is often most clearly expressed as a fraction.
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Decimal Representation
Rational numbers can be converted or transformed into decimal representation. For example, the rational number 1/2 can be represented as the decimal 0.5, and the rational number 2/3 can be represented as the repeating decimal 0.6666...
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Arithmetic Operations
Arithmetic operations often involve rational numbers, where the operations include addition, subtraction, multiplication, and division.
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Proportions
Proportions are based on the equality of two ratios, which are essentially fractions, and thus rational numbers in nature.
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Subtraction Of Rational Numbers
Subtraction operation in Mathematics is dependent on the nature and characteristics of numbers involved, including the rational numbers. For example, the subtraction of two rational numbers results in another rational number.
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Multiplication
Rational numbers can be transformed through various mathematical operations such as multiplication to produce other rational numbers.
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Complex Numbers
Complex numbers can be expressed as the sum of a rational number and an imaginary number, where the imaginary part is a rational number multiplied by the square root of -1.
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Equations
Rational numbers can be used in the formation and solving of equations, especially linear equations.