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" If the numerator and denominator of a fraction be both multiplied or both divided by the same number, the value of the fraction is not altered. "
Arithmetic Modernised: Or, A Complete System of Arithmetic, Adapted to ... - Page 63
by John Davidson, Robert Scott (writing master) - 1818 - 172 pages
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Select Parts of Professor Saunderson's Elements of Algebra: For the Use of ...

Nicholas Saunderson - 1761 - 438 pages
...proportion ; and vice versa. Thus -f are twice as much as Tt and 4- is but half as much. From this principle it follows, that if the numerator and denominator...fraction be both multiplied, or both divided by the fame number, the value of the fraction will not be affecr.ed thereby ; becaufe, as much as the fraction...
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The British Encyclopedia, Or Dictionary of Arts and Sciences ..., Volume 1

William Nicholson - 1809 - 716 pages
...will not be altered. For — "A i -4-o A . ab = + 6= -j ; and = — b = — a -fa ' — a — at a If the numerator and denominator of a fraction be both multiplied, or both divided by the same quantity, its value is not altered. For •fa . arwz ry lie 6" a tic z be' Hence, a fraction is reduced...
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American Edition of the British Encyclopedia: Or, Dictionary of ..., Volume 1

William Nicholson - 1819 - 432 pages
...value will not be altered. For — a4 +a4 ab = + 4 =-$ ; and — = — 4s» — a + a — a — ab. If the numerator and denominator of a fraction be both multiplied, or both divided, by the same quantity, its value is not altered. For ac a. iurvz y — =T; and ^ ==-?. be o ate* be Hence, a fraction...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - 1824 - 542 pages
...will represent the value of the fraction y, or the quotient of the division of a by b. • b * * 118. If the numerator and denominator of a fraction be both multiplied, or both divided by the same quantity r, its value will not be, altered. For, if we multiply by m the two members of the equality...
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Elements of algebra, compiled from Garnier's French translation of L. Euler ...

Charles Tayler - 1824 - 350 pages
...by the same number. For it follows from this, that if the numerator and denominator of a fraction be both divided by the same number, the value of the fraction will be •equally unaltered. This will appear more clear by means of the general fortnula ^ ; for, by dividing...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 pages
...and retain the same denominator ; or multiply the denominator, and retain the same numerator. Hence it follows, that if the numerator and denominator of a fraction, be either both multiplied, or both divided by the same number, the value of the fraction will remain unchanged....
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A Treatise on the Elements of Algebra

Bewick Bridge - 1828 - 260 pages
...conclusion; which will be equally true, whatever be the number of divisions in the operation. 136. Hence it follows, that if the numerator and denominator of a fraction be prime to each other, there can exist no other equal fraction having its numerator and denominator respectively...
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The Penny Magazine of the Society for the Diffusion of Useful Knowledge

1832 - 406 pages
...which the rules most materially depend, is the following : If the numerator and denominator be either both multiplied or both divided by the same number, the value of the fraction is not altered. For example, take £ and multiply its numerator and denominator by 4, which gives -JJ-....
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An Elementary Treatise on Algebra, Theoretical and Practical ...

James Ryan, Robert Adrain - 1835 - 388 pages
...have Thus v will represent the value of the fraction-, or the quotient of the division of o by b. 118. If the numerator and denominator of a fraction be both multiplied, or both divided by the same quantity, its value will not be altered. For, if we multiply by m the two members of the equality (1),...
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Elements of arithmetic, with numerous examples

Richard Mosley - 1836 - 164 pages
...expressed like a fraction by putting 1 under it for a denominator : thus - is the same as 6. REDUCTION. 26. If the numerator and denominator of a fraction be...both multiplied, or both divided by the same number, its 2 2X2 4 value is not altered ; thus - = - — - = -, as will be О о X * D evident by referring...
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