New Elementary Algebra: Primary Elements of Algebra, for Common Schools And Academics

Cover New Elementary Algebra: Primary Elements of Algebra, for Common Schools And Academics
New Elementary Algebra: Primary Elements of Algebra, for Common Schools And Academics
Joseph Ray
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— is either the fraotion - of one unit taken m times, or it is n ft ^ the nth of m units. Hence, the numerator may be regarded as showing the number of units to be divided; and the denominator, as showing the divisor, or what part i* taken from each.
122. Proposition L — If we multiply the numerator of a fraction without changing the denominator, the value of the fraction is increased as many times as there are units in the multiplier.
If we multiply the numerator of the fraction $ by 3, withou
...t changing the denominator, it becomes $.
Now, $ and f have the same denominator, which expresses parts of the same size ; but the second fraction, $, haying three times as many of those parts as the first, is three times as large. The same may be shown of any fraotion whatever.
123« Proposition II. — If we divide the numerator of a fraction without changing the denominator, the value of the fraction is diminished as many times as there are units in the divisor.
If we take the fraction £, and divide the numerator by 2, without changing the denominator, it becomes £.


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