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20 Apr 2018, 07:15
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Someone has asked for effect of increase in both numerator and denominator by same constant positive integer..
so we do get questions in PS asking us to compare fractions..
for example
(1) \(\frac{188845}{188849}, \frac{188876}{188880}\) and so on..
here \(\frac{188845+21}{188849+21}= \frac{188876}{188880}\)
here \(\frac{a}{b}<\frac{a+21}{b+21}\)
(2) but if we have \(\frac{100}{20}, \frac{120}{40}\)
here \(\frac{100+20}{20+20}= \frac{120}{40}\)
but now \(\frac{a}{b}>\frac{a+20}{b+20}\)
why??
increase in value of a fraction by adding a positive integer to both numerator and denominator is possible ONLY when the fraction is <1,
and if fraction>1, the value of fraction goes down by adding a positive integer to both numerator and denominator
REASON:-
increasing a smaller number by a positive integer results in a bigger increase in % as compared to similar increase in bigger number..
so where ever the smaller number lies, addition of constant will increase that part of fraction..
thus when smaller number is in numerator, that is fraction<1, the value of fraction will increase, as numerator is increasing more than denominator..
but when smaller number is in denominator, that is fraction>1, the value of fraction will decrease, as denominator is increasing more than numerator..
so we do get questions in PS asking us to compare fractions..
for example
(1) \(\frac{188845}{188849}, \frac{188876}{188880}\) and so on..
here \(\frac{188845+21}{188849+21}= \frac{188876}{188880}\)
here \(\frac{a}{b}<\frac{a+21}{b+21}\)
(2) but if we have \(\frac{100}{20}, \frac{120}{40}\)
here \(\frac{100+20}{20+20}= \frac{120}{40}\)
but now \(\frac{a}{b}>\frac{a+20}{b+20}\)
why??
increase in value of a fraction by adding a positive integer to both numerator and denominator is possible ONLY when the fraction is <1,
and if fraction>1, the value of fraction goes down by adding a positive integer to both numerator and denominator
REASON:-
increasing a smaller number by a positive integer results in a bigger increase in % as compared to similar increase in bigger number..
so where ever the smaller number lies, addition of constant will increase that part of fraction..
thus when smaller number is in numerator, that is fraction<1, the value of fraction will increase, as numerator is increasing more than denominator..
but when smaller number is in denominator, that is fraction>1, the value of fraction will decrease, as denominator is increasing more than numerator..
22 Jun 2024, 11:35
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