## Denominator Sentence Examples

- 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). - 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. - 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 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**. - 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. - The modern system of placing the numerator above the
**denominator**is due to the Hindus; but the dividing line is a later invention. - 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. - 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. - Fraction 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. - The modern method is to deal with fractions which have ioo as
**denominator**; such fractions are called percentages. - In the sexagesimal system the numerators of the successive fractions (the
of which were the successive powers of 60) were followed by', ", "', ", the**denominators****denominator**not being written. - Then the
**denominator**of the fraction, the numerical aperture, must be correspondingly increased, in order to ascertain the real resolving power. - Thus to divide by a fractional number we must multiply by the number obtained by interchanging the numerator and the
**denominator**, i.e. - 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. - B,, 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. - (iv) Each convergent is nearer to the true value than any other fraction whose
**denominator**is less than that of the convergent. - A 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. - 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.