Select the option that is related to the third term in the same way as the second term is related to the first term.
\(\frac{5}{9}\) : \(\frac{126}{728}\) :: \(\frac{3}{4}\) : ?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\frac{28}{63}\)
126 and 728 lie next to the cubes \(5^3=125\) and \(9^3=729\), so compare the numerator and the denominator of the second term with the cubes of 5 and 9.
Numerator: \(126=125+1=5^3+1\), so the numerator is cubed and 1 is added
Denominator: \(728=729-1=9^3-1\), so the denominator is cubed and 1 is subtracted
For \(\frac{3}{4}\): numerator \(3^3+1=27+1=28\)
Denominator \(4^3-1=64-1=63\)
So the missing term is \(\frac{28}{63}\).