Rational numbers, symbolized by \\( \\mathbb{Q} \\), include integers, fractions, and decimals, both terminating and repeating. This overview delves into the world of fractions, a subset of rational numbers, highlighting their types—proper, improper, mixed, unit, and equivalent fractions—and the methods for performing arithmetic operations such as addition, subtraction, multiplication, and division. Understanding these concepts is fundamental for mathematical proficiency.
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Rational numbers are numbers expressed as the quotient of two integers, where the denominator is non-zero
Integers
Integers are whole numbers and their negatives, including zero
Fractions
Fractions are a form of rational numbers with a numerator and denominator that are both integers, and the denominator is positive
Decimals
Rational numbers can have finite or repeating infinite decimal representations
Rational numbers are typically presented in their simplest form, where the greatest common divisor of the numerator and denominator is one, and the denominator is positive
Fractions are numerical expressions that convey a part of a whole, consisting of a numerator and a denominator, both of which are whole numbers, with the denominator being non-zero
Proper Fractions
Proper fractions have numerators less than denominators
Improper Fractions
Improper fractions have numerators greater than or equal to denominators
Mixed Numbers
Mixed numbers combine whole numbers with proper fractions
Addition and Subtraction
Addition and subtraction of fractions require finding a common denominator before performing the operation
Multiplication
Multiplication of fractions involves multiplying the numerators and denominators, followed by simplification
Division
Division of fractions is performed by multiplying by the reciprocal of the divisor
Fractions can be classified based on the relationship between the numerator and denominator, such as proper, improper, like, unlike, equivalent, and unit fractions