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numerator

must have a least value, which is moreover positive, since the numerator and denominator are both essentially positive.

19182In the case of fractions of the more general kind, the numerator was written first with ', and then the denominator, followed by ", was written twice.

12830If the numerator is a multiple of 5, the fraction represents twentieths.

9390a simple fraction with ioo for denominator, can be expressed by writing the two figures of the numerator (or, if there is only one figure, this figure preceded by o) with a dot or " point " before them; thus 76 means 76%, or 17 -6 6 o.

3435is less than 2 o o If the numerator of the fraction consists of an integer and 4 - e.g.

2237A 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.

2028- A fraction (or fractional number), the numerator or denominator of which is a fractional number, is called a complex fraction (or fractional number), to distinguish it from a simple fraction, which is a fraction having integers for numerator and denominator.

1925The 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.

1929The 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.

1929Hence 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).

1729We Have Then (26 1 30 (N 6)) R But The Numerator 3 Of This Fraction Becomes By Reduction I I N 40 Or 1 I N To (The 30 Being Rejected, As The Remainder Only Is Sought) =N Io(N I); Therefore, Ultimately, Must Be Deducted From J.

1629The 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.

1528If 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.

1531The Babylonians expressed numbers less than r by the numerator of a fraction with denominator 60; the numerator only being written.

14231 A2B' Where The Denominator Factors Indicate The Forms Themselves, Their Jacobian, The Invariant Of The Quadratic And Their Resultant; Connected, As Shown By The Numerator, By A Syzygy Of Degreesorder (2, 2; 2).

1429By 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.

1321The modern system of placing the numerator above the denominator is due to the Hindus; but the dividing line is a later invention.

1325with the numerator unity: in order to express such an idea as ~ the Egyptians were obliged to reduce it to a series of primary fractions through double fractions 1~+~1rt~r+1~w+ 1~ 4(1+

1222- When a fraction cannot be expressed by an integral percentage, it can be so expressed approximately, by taking the nearest integer to the numerator of an equal fraction having ioo for its denominator.

1021- When a fraction cannot be expressed by an integral percentage, it can be so expressed approximately, by taking the nearest integer to the numerator of an equal fraction having ioo for its denominator.

1021If 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.

1023Thus to divide by a fractional number we must multiply by the number obtained by interchanging the numerator and the denominator, i.e.

919Fraction in its Lowest Terms.-A fraction is said to be in its lowest terms when its numerator and denominator have no common the more correct method is to write it a: b.

820b,, Y the numerator (or denominator) of the last preceding term by the corresponding quotient and adding the numerator (or denominator) of the term before that.

718For 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.

00If we make large enough to expand the numerator using the binomial theorem (so that behaves as ), then as.

00Rule 3: Zero in the numerator of a fraction A numerator of a fraction A numerator is allowed to take on the value of zero in a fraction.

00numerator of this ratio, that is the number of older people, rising.

00numerator of this indicator.

00That day should also be counted as an overseas workday increasing the numerator by 1 to 56.

00It will return either fail or a new list [num, den] of canceled numerator and denominator.

00Dividing by a null value returns the numerator, thus here a null behaves like one.

00A rational is represented as a pair of integers, called numerator and denominator.

00The direct method was found not to be robust as it was affected by small numerator and denominator counts in specific age groups.

00numerator data - Number of missing teeth in the survey sample of children in the respective academic year.

00numerator degrees of freedom are given first.

00Data Year 2002/03 construction numerator: Number of first outpatient appointments for which the patient did not attend.

00Making 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.

00Further, the numerator factor establishes that these are not all algebraically independent,, but are connected by a syzygy of degree order 6, 6.

001 A2B' Where The Denominator Factors Indicate The Forms Themselves, Their Jacobian, The Invariant Of The Quadratic And Their Resultant; Connected, As Shown By The Numerator, By A Syzygy Of Degreesorder (2, 2; 2).

00It is usual to write this as a fraction, inverting the order of the factors in the numerator.

00In such cases a bracketed fraction is appended to the specific gravity, of which the numerator and denominator are respectively the temperatures of the substance and of the standard; thus 1.093 (0 0 14Ã‚°) means that the ratio of the weight of a definite volume of a substance at o to the weight of the same volume of water 4Ã‚° is I 093.

00The 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.

00It 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.

00In 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 ??

00We Have Then (26 1 30 (N 6)) R But The Numerator 3 Of This Fraction Becomes By Reduction I I N 40 Or 1 I N To (The 30 Being Rejected, As The Remainder Only Is Sought) =N Io(N I); Therefore, Ultimately, Must Be Deducted From J.

00If 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.

00with the numerator unity: in order to express such an idea as ~ the Egyptians were obliged to reduce it to a series of primary fractions through double fractions 1~+~1rt~r+1~w+ 1~ 4(1+

00must have a least value, which is moreover positive, since the numerator and denominator are both essentially positive.

00Hence 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).

00If 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.

00Fraction in its Lowest Terms.-A fraction is said to be in its lowest terms when its numerator and denominator have no common the more correct method is to write it a: b.

00A 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.

00Thus 2 is equal to -, and a is equal to -16Ã‚°, and conversely; in other words, any fractional number is equivalent to the fractional number obtained by multiplying or dividing the numerator and denominator by any integer.

00- A fraction (or fractional number), the numerator or denominator of which is a fractional number, is called a complex fraction (or fractional number), to distinguish it from a simple fraction, which is a fraction having integers for numerator and denominator.

00This is done by multiplying both numerator and denominator by 7; i.e.

00Thus to divide by a fractional number we must multiply by the number obtained by interchanging the numerator and the denominator, i.e.

00By 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.

00They 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.

00If the numerator is a multiple of 5, the fraction represents twentieths.

00a simple fraction with ioo for denominator, can be expressed by writing the two figures of the numerator (or, if there is only one figure, this figure preceded by o) with a dot or " point " before them; thus 76 means 76%, or 17 -6 6 o.

00is less than 2 o o If the numerator of the fraction consists of an integer and 4 - e.g.

00The Babylonians expressed numbers less than r by the numerator of a fraction with denominator 60; the numerator only being written.

00In the case of fractions of the more general kind, the numerator was written first with ', and then the denominator, followed by ", was written twice.

00A different method was used by Diophantus, accents being omitted, and the denominator being written above and to the right of the numerator.

00The modern system of placing the numerator above the denominator is due to the Hindus; but the dividing line is a later invention.

00For 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.

00(i) If we precede the series of convergents by i and - 1 6 -, then the numerator (or denominator) of each term of the series o i a, ab?-1 after the first two, is found by multiplying 1, o?

00b,, Y the numerator (or denominator) of the last preceding term by the corresponding quotient and adding the numerator (or denominator) of the term before that.

00This tool also lets you control values of the numerator and denominator.

00It is usual to write this as a fraction, inverting the order of the factors in the numerator.

01They 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.

01A different method was used by Diophantus, accents being omitted, and the denominator being written above and to the right of the numerator.

01

The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.