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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 .
A complex fraction is a fraction whose numerator or denominator, or both, contains a fraction. A simple fraction contains no fraction either in its numerator or its denominator. A fraction is in lowest terms if the only factor common to the numerator and the denominator is 1. An expression which is not in fractional form is an integral ...
For example, 1 / 4 , 5 / 6 , and −101 / 100 are all irreducible fractions. On the other hand, 2 / 4 is reducible since it is equal in value to 1 / 2 , and the numerator of 1 / 2 is less than the numerator of 2 / 4 . A fraction that is reducible can be reduced by dividing both the numerator ...
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Partial fraction decomposition. In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions ...
where is the volume fraction of the fibers in the composite (and is the volume fraction of the matrix).. If it is assumed that the composite material behaves as a linear-elastic material, i.e., abiding Hooke's law = for some elastic modulus of the composite and some strain of the composite , then equations 1 and 2 can be combined to give
Mass fraction (chemistry) In chemistry, the mass fraction of a substance within a mixture is the ratio (alternatively denoted ) of the mass of that substance to the total mass of the mixture. [1] Expressed as a formula, the mass fraction is: Because the individual masses of the ingredients of a mixture sum to , their mass fractions sum to unity: