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11 Jan 2023, 11:00
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E
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Difficulty:
35%
(medium)
Question Stats:
73% (02:08) correct
27%
(01:50)
wrong
based on 165
sessions
History
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Which of the following fractions has the least value?
A. \(\frac{1}{7^2*9^2}\)
B. \(\frac{49}{7^3*9^2}\)
C. \(\frac{63}{7^2*9^3}\)
D. \(\frac{27}{7^2*9^4}\)
E. \(\frac{343}{7^5*9^3}\)
A. \(\frac{1}{7^2*9^2}\)
B. \(\frac{49}{7^3*9^2}\)
C. \(\frac{63}{7^2*9^3}\)
D. \(\frac{27}{7^2*9^4}\)
E. \(\frac{343}{7^5*9^3}\)
14 Jan 2023, 10:53
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We need to find which of the following fractions has the least value
It is easier to compare two fractions if they have the same numerator or the same denominator.
Looking at the denominator of all the options we can make out that the highest power of 7 and 9 in all the cases is \(7^5\) and \(9^4\)
So, lets convert all options to the denominator of \(7^5\) * \(9^4\). Once we do this then we can ignore the denominators and just compare the numerators
A. \(\frac{1}{7^2*9^2}\) = \(\frac{7^3*9^2}{7^5*9^4}\)
Ignore denominator => \(7^3*9^2\)
B. \(\frac{49}{7^3*9^2}\) = \(\frac{7^2 * 7^2*9^2}{7^5*9^4}\)
Ignore denominator => \(7^4*9^2\)
C. \(\frac{63}{7^2*9^3}\) = \(\frac{7*9 * 7^3*9^1}{7^5*9^4}\)
Ignore denominator => \(7^4*9^2\)
D. \(\frac{27}{7^2*9^4}\) = \(\frac{9^{1.5} * 7^3}{7^5*9^4}\)
Ignore denominator => \(7^3*9^{1.5}\)
E. \(\frac{343}{7^5*9^3}\) = \(\frac{7^3 * 9^1}{7^5*9^4}\)
Ignore denominator => \(7^3*9^1\)
Clearly, E has the least value
So, Answer will be E
Hope it helps!
Watch the following video to learn the Basics of Exponents
It is easier to compare two fractions if they have the same numerator or the same denominator.
Looking at the denominator of all the options we can make out that the highest power of 7 and 9 in all the cases is \(7^5\) and \(9^4\)
So, lets convert all options to the denominator of \(7^5\) * \(9^4\). Once we do this then we can ignore the denominators and just compare the numerators
A. \(\frac{1}{7^2*9^2}\) = \(\frac{7^3*9^2}{7^5*9^4}\)
Ignore denominator => \(7^3*9^2\)
B. \(\frac{49}{7^3*9^2}\) = \(\frac{7^2 * 7^2*9^2}{7^5*9^4}\)
Ignore denominator => \(7^4*9^2\)
C. \(\frac{63}{7^2*9^3}\) = \(\frac{7*9 * 7^3*9^1}{7^5*9^4}\)
Ignore denominator => \(7^4*9^2\)
D. \(\frac{27}{7^2*9^4}\) = \(\frac{9^{1.5} * 7^3}{7^5*9^4}\)
Ignore denominator => \(7^3*9^{1.5}\)
E. \(\frac{343}{7^5*9^3}\) = \(\frac{7^3 * 9^1}{7^5*9^4}\)
Ignore denominator => \(7^3*9^1\)
Clearly, E has the least value
So, Answer will be E
Hope it helps!
Watch the following video to learn the Basics of Exponents
12 Mar 2025, 06:43
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