# improper fraction

## Definitions

• WordNet 3.6
• n improper fraction a fraction whose numerator is larger than the denominator
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Webster's Revised Unabridged Dictionary
• Improper fraction a fraction in which the numerator is greater than the denominator.
• Improper fraction See under Fraction.
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## Usage

### In literature:

Complex and improper fractions and recurring decimals are not allowed.
"Amusements in Mathematics" by Henry Ernest Dudeney
TABLE SHOWING RELATIVE VIBRATION OF INTERVALS BY IMPROPER FRACTIONS.
"Piano Tuning" by J. Cree Fischer
It has some hundreds of Eurasians, who occur as improper fractions of varying hue.
"Where the Pavement Ends" by John Russell
An improper fraction is therefore equal either to an integer or to a mixed number.
"Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 5" by Various
To have referred to this lady as his better half would be dealing in improper fractions.
"Local Color" by Irvin S. Cobb
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### In science:

Auxiliary construction In this section we construct the essential ingredient of some results: an adapted process such that w.r.t. fractional Brownian motion it integrates (in improper sense) to inﬁnity.
Random variables as pathwise integrals with respect to fractional Brownian motion
Analysis of PMT occupancy distributions from 16N data is used evaluate the average fraction of improperly functioning PMTs missed in analysis of the laser data.
Electron Energy Spectra, Fluxes, and Day-Night Asymmetries of $^{8}$B Solar Neutrinos from the 391-Day Salt Phase SNO Data Set
Secondly, it must be noted that the exponent p must necessarily be smaller than the exponent n since otherwise the fraction would be improper and the variable x would have more degrees in the numerator than in the denominator.
An easy method for finding the integral of the formula $\int (x^{n+p} - 2 x^n\cos\zeta + x^{n-p})/(x^{2n} - 2 x^n\cos\theta + 1) dx/x$ when the upper limit of integration is $x=1$ or $x=\infty$
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