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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
In the second step, they were divided by 3. The final result, 4 / 3 , is an irreducible fraction because 4 and 3 have no common factors other than 1. The original fraction could have also been reduced in a single step by using the greatest common divisor of 90 and 120, which is 30. As 120 ÷ 30 = 4, and 90 ÷ 30 = 3, one gets
The simplified equation is not entirely equivalent to the original. For when we substitute y = 0 and z = 0 in the last equation, both sides simplify to 0, so we get 0 = 0 , a mathematical truth. But the same substitution applied to the original equation results in x /6 + 0/0 = 1 , which is mathematically meaningless .
Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include:
Over a 45-years span — between 1975 and 2020 — improvements in cancer screenings and prevention strategies have reduced deaths from five common cancers more than any advances in treatments ...
A simple or regular continued fraction is a continued fraction with numerators all equal one, ... Simplified Reciprocal of f; 1 = ... Academic Press. pp. 25–31.
From January 2008 to December 2012, if you bought shares in companies when Cheryl W. Grisé joined the board, and sold them when she left, you would have a -46.2 percent return on your investment, compared to a -2.8 percent return from the S&P 500.
Another meaning for generalized continued fraction is a generalization to higher dimensions. For example, there is a close relationship between the simple continued fraction in canonical form for the irrational real number α, and the way lattice points in two dimensions lie to either side of the line y = αx. Generalizing this idea, one might ...