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The reciprocal of a proper fraction is improper, and the reciprocal of an improper fraction not equal to 1 (that is, numerator and denominator are not equal) is a proper fraction. When the numerator and denominator of a fraction are equal (for example, 7 / 7 ), its value is 1, and the fraction therefore is improper. Its reciprocal is ...
For example, the rational fraction is proper, and the rational fractions + + + and + + are improper. Any improper rational fraction can be expressed as the sum of a polynomial (possibly constant) and a proper rational fraction.
Fractions: A representation of a non-integer as a ratio of two integers. These include improper fractions as well as mixed numbers . Continued fraction : 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 other number as the sum of ...
This page was last edited on 23 June 2020, at 13:36 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may ...
Examples of proper fractions are 2/3, –3/4, and 4/9; examples of improper fractions are 9/4, –4/3, and 3/3. improper integral In mathematical analysis, an improper integral is the limit of a definite integral as an endpoint of the interval(s) of integration approaches either a specified real number, , , or in some instances as both endpoints
For example, the fraction is proper, and the fractions + + + and + + are improper. Any improper rational fraction can be expressed as the sum of a polynomial (possibly constant) and a proper rational fraction.
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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 ...