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A common, vulgar, or simple fraction (examples: and ) consists of an integer ... To add fractions containing unlike quantities (e.g. quarters and thirds), it is ...
The same fraction can be expressed in many different forms. As long as the ratio between numerator and denominator is the same, the fractions represent the same number. For example:
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 ...
Addition of fractions is much simpler when the denominators are the same; in this case, one can simply add the numerators while leaving the denominator the same: + = +, so + = + =. [ 63 ] The commutativity and associativity of rational addition is an easy consequence of the laws of integer arithmetic. [ 64 ]
The following list includes the continued fractions of some constants and is sorted by their representations. Continued fractions with more than 20 known terms have been truncated, with an ellipsis to show that they continue. Rational numbers have two continued fractions; the version in this list is the shorter one.
Unlike 19th-century America, there is no cultural, political or social movement supporting territorial conquest. America’s population is aging, not surging. Cultural superiority has given way to ...
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