Denominator Sentence Examples
Hence, so long as the denominator remains unaltered, we can deal with, exactly as if they were numbers, any operations being performed on the numerators.
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.
Hence 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).
Generally, to find the sum or difference of two or more fractional numbers, we must replace them by other fractional numbers having the same denominator; it is usually most convenient to take as this denominator the L.C.M.
A fraction written in this way is called a decimal fraction; or we might define a decimal fraction as a fraction having a power of To for its denominator, there being a special notation for writing such fractions.Advertisement
The modern system of placing the numerator above the denominator is due to the Hindus; but the dividing line is a later invention.
Hence we can treat the fractional numbers which have any one denominator as 0 o constituting a number-series, as shown in the 2 adjoining diagram.
The Romans commonly used fractions with denominator 12; these were described as unciae (ounces), being twelfths of the as (pound).
To add or subtract fractional numbers, we must reduce them to a common denominator; and similarly, to multiply or divide surds, we must express them as power-numbers with the same index.
Hindu treatises on arithmetic show the use of fractions, containing a power of io as denominator, as early as the beginning of the 6th century A.D.Advertisement
If the denominator of the fraction, when it is in its lowest terms, contains any other prime factors than 2 and 5, it cannot be expressed exactly as a decimal; but after a certain point a definite series of figures will constantly recur.
In this context, the community became the common denominator.
Every convergent is a nearer approximation to the value of the whole fraction than any fraction whose denominator is less than that of the convergent.
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.
Thus to divide by a fractional number we must multiply by the number obtained by interchanging the numerator and the denominator, i.e.Advertisement
By 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.
To avoid this difficulty, in practical life, it is usual to confine our operations to fractions which have a certain standard denominator.
The modern method is to deal with fractions which have ioo as denominator; such fractions are called percentages.
Except in the case of - and 2, the fraction was expressed by the denominator, with a special symbol above it.
The Babylonians expressed numbers less than r by the numerator of a fraction with denominator 60; the numerator only being written.Advertisement
A different method was used by Diophantus, accents being omitted, and the denominator being written above and to the right of the numerator.
Then the denominator of the fraction, the numerical aperture, must be correspondingly increased, in order to ascertain the real resolving power.
Why do we always have to use the lowest common denominator?
The only common denominator may be a shared locality.
Adopting flexible benefits can avoid the pressure of a merged company having to take all benefits up to the highest common denominator.Advertisement
Ask the students if they know what the other common denominator is.
As we all know, Western left thinking sees its minimum common denominator as being against racism and nationalism.
The significance of evidence-based nursing interventions, supported by outcome measures, may provide a powerful denominator in promoting change.
Yet somehow there seems to be a common denominator to all the music you have chosen.
Each listed inch fraction has the smallest denominator that keeps the value within the ISO 216 tolerance limits.
She counted out lots corresponding to the posited fraction denominator.
Adding and subtracting Before adding or subtracting fractions, they must be transformed so that they all have a common denominator.
It will return either fail or a new list [num, den] of canceled numerator and denominator.
A rational is represented as a pair of integers, called numerator and denominator.
The direct method was found not to be robust as it was affected by small numerator and denominator counts in specific age groups.
The peaks arise because the denominator will approach zero at sinusoidal frequencies, resulting in exceedingly sharp spectral peaks.
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 ??
This is done by multiplying both numerator and denominator by 7; i.e.
This turns out to be inconvenient, so instead we replace the q s in the denominator by their MLE.
Add and subtract fractions by writing them with a common denominator.
A common denominator in all chat room environments is the bully or spoiler.
Traditional vows can mean many things, but the common denominator is love, affection and commitment.
Luxury bath towels mean many things to different people, but the one common denominator is high quality.
Another common denominator on all of the ships is Costa's theme of "Cruising Italian Style."
This common denominator enhances cruise ship fellowship and creates a more rewarding experience.
The common denominator is a population sector which is already healthy and wishes to ensure their continued good health.
On the other hand, Acclaim was clearly shooting for the lowest common denominator with their BMXXX extreme sports title.
Children with neurological damage will have a common denominator of prolonged neonatal reflexes.
This tool also lets you control values of the numerator and denominator.
When we know the mass of the earth in gravitational measure, its product by the denominator of the fraction just mentioned gives the mass of the sun in gravitational measure.
Thus the fractions must be reduced to a common denominator.
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.
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.
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 attempt to win adherents requires the appeal to the lowest common denominator.
Your main consideration is finding the lowest common denominator of the people who will be viewing the image.
With all of us being involved in turf care we all had a common denominator to start from.
In many cases this has led to the adoption of measures reflecting the lowest common denominator among Member States.
A Europe scaling the heights of ambition; not seeking the lowest common denominator.
Management is reduced to a least common denominator of housekeeping.
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.
Descending series of the semi-convergent class, available for numerical calculation when u is moderately large, can be obtained from (12) by writing x=uy, and expanding the denominator in powers of y.
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.
Sadly, in the rush for the lowest common denominator, others are unlikely to follow our lead.
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.
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 denominator sin a is the quantity well known (after Abbe) as the " numerical aperture."