...equivalent to A and ^ ; for, if the numerator or denominator of a fraction is multiplied or divided by the same number, the value of. the fraction is not changed. But, -^ is greater than T*j, the fraction ^ is then gi eater than the /faction |.. For, a fraction...

...multiplied. NB It appears from the above reasoning, that if Both the numerator and denominator of any fraction be multiplied by the same number, the value of the fraction will remain the same. It will follow also from this, that if both numerator and denominator can be...

...multiplied. NB It appears from the above reasoning, that if both the numerator and denominator of any fraction be multiplied by the same number, the value of the fraction will remain the same. It will follow also from this, that if both numerator and denominator can be...

...their common denominator. The principle of this rule is, that if the numerator and denominator be both multiplied by the same number, the value of the fraction is not altered. That both terms are multiplied by the same number, by applying the preceding rule, will readily...

...multiplied. NB It appears from the above reasoning, that if both the numerator and denominator of any fraction be multiplied by the same number, the value of the fraction will remain the same. It will follow also from this, that if both numerator and denominator can be...

...decimals. Another mode of explaining the above operation may be given. 13. Change Jg to a decimal. If both numerator and denominator of- a Fraction be multiplied by the same . number, the value will not be altered, (§ XLI.) I may therefore multiply both the 7 and the 16 in the above Fraction,...

...demonstrating certain properties in relation to known and given numbers. if To demonstrate that if both terms of a fraction be multiplied by the same number, the value of the fraction will not be changed. Let the proposed fraction be designated by p and let n be any number whatever....

...result. The most important property of a fraction is, that if both its numerator and denominator are multiplied by the same number, the value of the fraction is not altered ; that is, £ is the same as i|, or each part is the same when we divide 12 inches into 20...

...just equal to the decrease from multiplying the denominator ; hence we have, PROPOSITION V. If the numerator and denominator of a fraction be multiplied by the same number, the value of the fraction will remain unchanged. Thus, |=| X f =i| and 4=4 x |=||. § 119. It appears from Prop. II, that if...

...Demonstration. — The demonstration of the preceding rule depends upon the following principle. If both terms of a fraction be multiplied by the same number, the value of the fraction is not altered ; for, by multiplying the numerator, the fraction is multiplied (20), and by multiplying the...