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are solved using cross-multiplication, since the missing b term is implicitly equal to 1: =. Any equation containing fractions or rational expressions can be simplified by multiplying both sides by the least common denominator. This step is called clearing fractions.
The first step is to determine a common denominator D of these fractions – preferably the least common denominator, which is the least common multiple of the Q i. This means that each Q i is a factor of D , so D = R i Q i for some expression R i that is not a fraction.
To add fractions containing unlike quantities (e.g. quarters and thirds), it is necessary to convert all amounts to like quantities. It is easy to work out the chosen type of fraction to convert to; simply multiply together the two denominators (bottom number) of each fraction. In case of an integer number apply the invisible denominator 1.
In academic literature, when inline fractions are combined with implied multiplication without explicit parentheses, the multiplication is conventionally interpreted as having higher precedence than division, so that e.g. 1 / 2n is interpreted to mean 1 / (2 · n) rather than (1 / 2) · n.
Multiplication is often defined for natural numbers, then extended to whole numbers, fractions, and irrational numbers. However, abstract algebra has a more general definition of multiplication as a binary operation on some objects that may or may not be numbers. Notably, one can multiply complex numbers, vectors, matrices, and quaternions.
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