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Irreducible fraction. An irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and −1, when negative numbers are considered). [1] In other words, a fraction a b is irreducible if and only if a and ...
A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or , where a and b are both integers. [9] As with other fractions, the denominator (b) cannot be zero. Examples include 1 2 , − 8 5 , −8 5 , and 8 −5 .
For example, the ratio 4:5 can be written as 1:1.25 (dividing both sides by 4) Alternatively, it can be written as 0.8:1 (dividing both sides by 5). Where the context makes the meaning clear, a ratio in this form is sometimes written without the 1 and the ratio symbol (:), though, mathematically, this makes it a factor or multiplier.
If p and q are primes other than 2 or 5, the decimal representation of the fraction 1 / pq repeats. An example is 1 / 119 : 119 = 7 × 17 λ(7 × 17) = LCM(λ(7), λ(17)) = LCM(6, 16) = 48, where LCM denotes the least common multiple. The period T of 1 / pq is a factor of λ(pq) and it happens to be 48 in this case:
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator p and a non-zero denominator q. [1] For example, is a rational number, as is every integer (e.g., ). The set of all rational numbers, also referred to as " the rationals ", [2] the field of rationals[3] or ...
Continued fraction. A finite regular continued fraction, where is a non-negative integer, is an integer, and is a positive integer, for . In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this ...
Canonical normal form. In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form (CDNF), [1] minterm canonical form, or Sum of Products (SoP or SOP) as a disjunction (OR) of minterms. The De Morgan dual is the canonical conjunctive normal form (CCNF), maxterm canonical form, or Product of Sums (PoS or ...
Glucose (C 6 H 12 O 6), ribose (C 5 H 10 O 5), Acetic acid (C 2 H 4 O 2), and formaldehyde (CH 2 O) all have different molecular formulas but the same empirical formula: CH 2 O.This is the actual molecular formula for formaldehyde, but acetic acid has double the number of atoms, ribose has five times the number of atoms, and glucose has six times the number of atoms.