...numerator, by the [new] numerator. Thus division1 [is performed.] 5. The quantity being made homogeneous,1 the square of the numerator, divided by the square of the denominator, is the square.3 The root of the homogeneous numerator, divided by the root of the denominator, is the...

...numerator, by the [new] numerator. Thus division* [is performed.] 5. The quantity being made homogeneous,* the square of the numerator, divided by the square of the denominator, is the square.5 The root of the homogeneous numerator, divided by the root of the denominator, is the...

...50 is 7, so far as it can be expressed in whole numbers, and the root of 25 exactly 5, we obtain J, or 1| for the root of 2, to within one fifth. 101....square of a number expressed by hundredths will be ten thousandths, and so on ; and consequently, that the number of decimal Jigures in the square is...

...and here it might be supposed, that the examination would be short, for the square of a fraction, is the square of the numerator divided by the square of the denominator; and by extracting the roots of each, and writing these roots as the numerator and denominator of the...

...To find the square root of 8Jf . ANS. 2.88203 +. LXXXVII. Since the square of a fraction is equal to the square of the numerator divided by the square of the denominator ; conversely, the square root of a fraction is equal to the square root of the numerator divided by...

...terms : then these terms are prime to each other, and the square of this fraction ; that is to say, the square of the numerator divided by the square of the denominator must be equal to 2. But we have seen (179) that the squares, cubes, &c. of numbers, prime to each other,...

...terms : then these terms are prime to each other, and the square of this fraction ; that is to say, the square of the numerator divided by the square of the denominator must be equal to 2. But we have seen (179) that the squares, cubes, &c. of numbers, prime to each other,...

...begin with -oo1. Vulgar Fractions. The square of a vulgar fraction presents no difficulty. It is simply the square of the numerator divided by the square of the denominator. It is to be remarked that if a fraction be in its lowest terms, its square will also be in its lowest...

...that numerator and denominator are prime to one another, the square of the fraction will be equal to the square of the numerator divided by the square of the denominator. But since the denominator is prime to the numerator it is also prime to the square of the numerator...

...root of the numerator divided by the square root of the denominator. (8) The square of a fraction is the square of the numerator divided by the square of the denominator. 2. Translate into words the following formulas expressing laws of arithmetic: (1) P = T7j7T (percentage...