# Numerator Sentence Examples

In the case of fractions of the more general kind, the

**numerator**was written first with ', and then the denominator, followed by ", was written twice.If the

**numerator**is a multiple of 5, the fraction represents twentieths.This is done by multiplying both

**numerator**and denominator by 7; i.e.This tool also lets you control values of the

**numerator**and denominator.A rational is represented as a pair of integers, called

**numerator**and denominator.AdvertisementFurther, the

**numerator**factor establishes that these are not all algebraically independent,, but are connected by a syzygy of degree order 6, 6.If we make large enough to expand the

**numerator**using the binomial theorem (so that behaves as ), then as.That day should also be counted as an overseas workday increasing the

**numerator**by 1 to 56.It will return either fail or a new list [num, den] of canceled

**numerator**and denominator.Dividing by a null value returns the

**numerator**, thus here a null behaves like one.AdvertisementMaking the substitution in any symbolic product the only determinant factors that present themselves in the

**numerator**are of the form (af), (bf), (cf),...and every symbol a finally appears in the form.It follows from these equations that the logarithm of the product of any number of quantities is equal to the sum of the logarithms of the quantities, that the logarithm of the quotient of two quantities is equal to the logarithm of the

**numerator**diminished by the logarithm of the denominator, that the logarithm of the rth power of a quantity is equal to r times the logarithm of the quantity, and that the logarithm of the rth root of a quantity is equal to (r/r)th of the logarithm of the quantity.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 ??It is usual to write this as a fraction, inverting the order of the factors in the

**numerator**.They only apply accurately to divisions by 2, 4, 5, 10, 20, 25 or 50; but they have the convenience of fitting in with the denary scale of notation, and they can be extended to other divisions by using a mixed number as

**numerator**.AdvertisementA different method was used by Diophantus, accents being omitted, and the denominator being written above and to the right of the

**numerator**.For multiplication by a proper fraction or a decimal, it is sometimes convenient, especially when we are dealing with mixed quantities, to convert the multiplier into the sum or difference of a number of fractions, each of which has i as its

**numerator**.The direct method was found not to be robust as it was affected by small

**numerator**and denominator counts in specific age groups.A fractional number is called a proper fraction or an improper fraction according as the

**numerator**is or is not 3 less than the denominator; and an expression 4 such as 24 is called a mixed number.Thus to divide by a fractional number we must multiply by the number obtained by interchanging the

**numerator**and the denominator, i.e.AdvertisementBy means of the present and the preceding sections the rule given in § 63 can be extended to the statement that a fractional number is equal to the number obtained by multiplying its

**numerator**and its denominator by any fractional number.The Babylonians expressed numbers less than r by the

**numerator**of a fraction with denominator 60; the**numerator**only being written.The pth root of a number (§43) may, if the number is an integer, be found by expressing it in terms of its prime factors; or, if it is not an integer, by expressing it as a fraction in its lowest terms, and finding the pth roots of the

**numerator**and of the denominator separately.The modern system of placing the

**numerator**above the denominator is due to the Hindus; but the dividing line is a later invention.If we write 74 in the form 47 we may say that the value of a fraction is not altered by multiplying or dividing the

**numerator**and denominator by any number.AdvertisementHence the value of a fraction is not altered by substituting for the

**numerator**and denominator the corresponding numbers in any other column of a multiple-table (§ 36).The frequency ratios in the diatonic scale are all expressible either as fractions, with i, 2, 3 or 5 as

**numerator**and denominator, or as products of such fractions; and it may be shown that for a given note the**numerator**and denominator are smaller than any other numbers which would give us a note in the immediate neighbourhood.If this arrangement is expressed by a fraction, the

**numerator**of which indicates the number of turns, and the denominator the number of internodes in the spiral cycle, the fraction will be found to represent the angle of divergence of the consecutive leaves on the axis.