NoHalfMeasures
Which of the following fractions has the greatest value?
(A) \(\frac{1}{(3^2)(5^2)}\)
(B) \(\frac{2}{(3^2)(5^2)}\)
(C) \(\frac{7}{(3^3)(5^2)}\)
(D)\(\frac{45}{(3^3)(5^3)}\)
(E) \(\frac{75}{(3^4)(5^5)}\)
Solution:
First, we can eliminate choice A since it’s less than choice B. We can also reduce the two fractions in the last two choices:
D) 45 / [(3^3)(5^3)] = (3^2)(5) / [(3^3)(5^3)] = 1 / [(3)(5^2)]
E) 75 / [(3^4)(5^5)] = (3)(5^2) / [(3^4)(5^5)] = 1 / [(3^2)(5^3)]
We can eliminate choice E since it’s less than choice D.
Now, we can compare the ones in choices B, C and D by expressing them in terms of their least common denominator, which is (3^3)(5^2):
B) 2 / [(3^2)(5^2)] = 6 / [(3^3)(5^2)]
C) 7 / [(3^3)(5^2)] = 7 / [(3^3)(5^2)]
D) 1 / [(3)(5^2)] = 9 / [(3^3)(5^2)]
We see that choice D has the greatest value.
Answer: D