Fractions {aliquot part} {unit fraction} can have the number one in numerators: 1/n.
Polynomials can divide into other polynomials {complex fraction}: (a*x + b) / (b*y + d). Alternatively, fractions can have numerator and/or denominator fractions: (3/4) / (7/8).
A fraction {continued fraction}| can have an integer plus a numerator-1 fraction, and that fraction can have a denominator with an integer plus a numerator-1 fraction, and so on: a + 1/(b + 1/(c + 1/(...))), where a, b, and c are integers. a + (b + (c + (...)^-1)^-1)^-1. Rational numbers can be terminating continued fractions. Quadratic irrational numbers can be non-terminating periodic continued fractions. Real numbers can be non-terminating non-periodic continued fractions.
Two fractions, a1/b1 and a2/b2, can make a fraction {mediant fraction} whose value is between the original fractions: (a1 + a2) / (b1 + b2).
Fractions {partial fraction} can have form A / (a*x + b)^n or (A*x + B) / (a*x^2 + b*x + c)^2, and so on. Proper fractions can be sums of partial fractions whose denominators are proper-fraction denominator factors: 16/12 = 1/2 + 1/3 + 1/2.
Numerator can be less than denominator {proper fraction}. Numerator can be greater than denominator {improper fraction}.
Fractions {similar fraction} can have same denominator.
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Date Modified: 2022.0225