Lowest terms

A fraction is in lowest terms when its numerator and denominator have no common factor greater than one, so it cannot be simplified further without changing its value.

Greatest common divisor: The greatest positive integer that divides each of two or more integers. Dividing both parts of a fraction by this number produces its lowest terms.
Integer: A whole number, its negative, or zero. Fraction numerators and denominators are integers in the usual definition of lowest terms.
Fraction reduction: The process of dividing a fraction’s numerator and denominator by a shared factor. Repeated reduction, or division by the greatest common divisor, reaches lowest terms.
Improper fraction: A fraction whose numerator’s absolute value is at least its denominator’s. An improper fraction can be in lowest terms; size alone does not determine reducibility.
Euclidean algorithm: A procedure for finding the greatest common divisor by repeated division with remainders. It efficiently finds the common divisor needed to reduce large fractions.
Divisibility: The relation in which one integer is a factor of another with no remainder. A fraction is reducible precisely when a number greater than one divides both parts.
Fraction addition: The operation of combining two fractions by expressing them with a common denominator. Simplifying the result makes the final fraction easier to interpret.
Mixed number: A number written as an integer together with a proper fraction. It is an alternative notation, not the test for whether a fraction is in lowest terms.
Equivalent fractions: Fractions that represent the same value despite having different numerators and denominators. Reducing a fraction preserves its value by replacing it with an equivalent fraction.
Factor: An integer that divides another integer without a remainder. A shared factor identifies a common divisor that can simplify the fraction.

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