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# Which is larger?

+3
254
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+2316

(532000)/(531999) or (532000-2000)/(531999-2000)

THANK YOU

Feb 6, 2019

#1
+2316
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By the way, is there any fast way to do this?

Feb 6, 2019
#2
+105606
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Lets see

$$\frac{53^{2000}}{53^{1999}}=53^{2000-1999}=53$$

The numerator and the denominator are reduced by 2000

but proportionately the numerator has been reduced by less than the denominator because it was bigger to start with.

so proportionately... the top was reduced by a smaller factor than the bottom so the entire number got bigger.

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It is like this

$$\frac{10}{8}\;\;compared \;\;to \;\;\frac{9}{7}\\ 1\frac{2}{8}\;\;compared \;\;to \;\;1\frac{2}{7}\\$$

The second one is bigger.

Feb 6, 2019
edited by Melody  Feb 6, 2019
#3
+2316
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ohhhh i understand thank you

Feb 7, 2019