# Denominators sentence example

denominators
• ï¿½; the successive terms of this series, after the first, are alternately positive and negative, and consist of fractions with numerators I and denominators continually increasing.
• " Now for the interpolation of the rest, I considered that the denominators I, 3, 5, &c., were in arithmetical progression; and that therefore only the numerical coefficients of the numerators were to be investigated.
• He extended the "law of continuity" as stated by Johannes Kepler; regarded the denominators of fractions as powers with negative exponents; and deduced from the quadrature of the parabola y=xm, where m is a positive integer, the area of the curves when m is negative or fractional.
• Having proceeded so far, I considered that the terms (1 -xx) I, (I- (1 -xx) I, (i -xx)l, &c., that is I, I -x 2, I -2x 2 +x 4, I -3x 2 -} 3x 4 -x 6, &c., might be interpolated in the same manner as the areas generated by them, and for this, nothing more was required than to omit the denominators I, 3, 5, 7, &c., in the terms expressing the areas; that is, the coefficients of the terms of the quantity to be interpolated (1-xx) 4 or (1 - xx) 3/2, or generally (I -xx)"n will m m-n e.g.
• Their numerators are denoted by Pi, P2, their denominators by q,, q2, q3, We have the relations p n = an pn-1 +bn pn-2, qn = angn-1 +bngn-2.
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• - The numerators and denominators of the convergents to the general continued fraction both satisfy the difference equation un =anu„_,+bnun_2.
• (v) The difference of two successive convergents is the reciprocal of the product of their denominators; e.g.
• In the sexagesimal system the numerators of the successive fractions (the denominators of which were the successive powers of 60) were followed by', ", "', ", the denominator not being written.
• Fractional Numbers with different Denominators.
• common denominators of the complete marketing process, are the product and the ad copy.
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• However, rates cannot be provided as population denominators are not available for illnesses ascribed to these other jobs.
• denominators of the two fractions.
• Ã¯¿½; the successive terms of this series, after the first, are alternately positive and negative, and consist of fractions with numerators I and denominators continually increasing.
• In refutation of Duchesne(Van der Eycke), he showed that the ratio was 3-, %-, and thence made the exceedingly lucky step of taking a mean between the two by the quite unjustifiable process of halving the sum of the two numerators for a new numerator and halving the sum of the two denominators for a new denominator, thus arriving at the now well-known approximation 3 6 3 - or ??
• While everyone's preschool is going to look different, you will find that there are some common denominators when it comes to kids learning.
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• While graduation parties for different ages can vary widely, there are some common denominators: a fun theme, good food and drinks, lots of good friends and (for the older students, anyway) a little good-natured embarrassment.
• This denominator must, if the fractions are in their lowest terms (§ 54), be a multiple of each of the denominators; it is usually most convenient that it should be their L.C.M.
• The numerators and denominators of the successive convergents obey the law p n g n _ l - pn-1qn = (- O n, from which it follows at once that every convergent is in its lowest terms. The other principal properties of the convergents are The odd convergents form an increasing series of rational fractions continually approaching to the value of the whole continued fraction; the even convergents form a decreasing series having the same property.
• , p, ,, and for their denominators any assigned quantities ql, q2, q 2, The partial fraction b n /a n corresponding to the n th convergent can be found from the relations pn = anpn -I +bnpn -2 1 qn = anq,i l +bngn-2; and the first two partial quotients are given by b l =pi, a1 = ql, 1)102=1,2, a1a2 + b2= q2.
• - In order to deal, by way of comparison or addition or subtraction, with fractions which have different denominators, it is necessary to reduce them to a common denominator.
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