...denominator divides the value of the fraction. 78. III. If the terms of a fraction be multiplied or divided by the same quantity, the value of the fraction is not changed. Let T be the fraction, and ж its value, so that -=- = я.' о о then, if the numerator be multiplied...

...answer, the same quantity as the numerator. We have also shown that where both terms of a fraction are multiplied by the same quantity, the value of the fraction is not altered. By these two principles, we obtain the following rule for reducing a complex fraction to a...

...is one of those parts called? 5 is equal to how many twelfths? Ans. -i x4=14fj ; hence we see that if the numerator and denominator of a fraction be both multiplied by the same number, the value of the fraction will not be altered. ADDITION OF FRACTIONS. 1. Add J, j, I, and f....

...therefore т is equal to the ¿th part of a. 34. // the numerator and denominator of a fraction be Ъoth multiplied by the same quantity, the VALUE of the fraction is not altered. „, a 2a 3a пa _ 2a . .» , , l hus T = — j- = -у- = &c. = —r . For —т- signifies...

...a terms (Art. 26), and 1 + 1 + &c. to a terms is a, therefore т is equal to the 6tt part of a. 34. If the numerator and denominator of a fraction be both multiplied by the same quantity, the VALusof the fraction is not altered. „, a 2я Зa „ na _, 2a . .,, ж, ^ , Thus 6 = 26 = з6 =...

...perpetually kept in mind in the whole of our operations relating to Vulgar Fractions. 10. PRINCIPLE 1. — If the numerator and denominator of a fraction be both multiplied by the same number, the value of the fraction is not altered, that is, the valu« of the fraction remains the ваше...

...get the fraction % or one foot ; bnt one foot is equal in length to -Jf or twelve iuches. 123. If tbe numerator and denominator of a fraction be both multiplied by the same number, then the numerator of the original fraction will bear the same proportion to its denominator...

...numerator and the suppressed denominator of the decimal fraction are multiplied by 10, 100, 1000, &c. : and if the numerator and denominator of a fraction be both multiplied by the same number, the fraction is both multiplied and divided by that number, and therefore remains unaltered...

...symbols, f = f . Similarly we may show that | = T*a, or H, or ££ ..... ; and, generally, it is true that if the numerator and denominator of a fraction be both multiplied by the same number the magnitude of the fraction is unaltered. For, taking as an example the multiplier 7, each...

...Cancelling these common factors, the fraction l$abcx $c becomes - . Now since both terms have been divided by the same quantity, the value of the fraction is not changed. (Art. 167, Prin. 3.) And since these terras have no common factor, it follows that — — are the...