alanforde800Maximus wrote:Which of the following fractions has the greatest value?
(A) 1/(3^2)(5^2)
(B) 2/(3^2)(5^2)
(C) 7/(3^3)(5^2)
(D) 45/(3^3)(5^3)
(E) 75/(3^4)(5^5)
To start, we see that 2/(3^2)(5^2) > 1/(3^2)(5^2), so we can eliminate answer choice A.
Next we can simplify answers D and E.
D) 45/(3^3)(5^3) = (3^2)(5^1)/(3^3)(5^3) = 1/(3^1)(5^2)
E) 75/(3^4)(5^5) = (3^1)(5^2)/(3^4)(5^5) = 1/(3^3)(5^3)
The denominator in E is greater than in D, so we see that D is greater than E, so we can eliminate E. So we are left with:
(B) 2/(3^2)(5^2)
(C) 7/(3^3)(5^2)
(D) 1/(3^1)(5^2)
Getting common denominators we have:
(B) (2)(3^1)/(3^3)(5^2) = 6/(3^3)(5^2)
(C) 7/(3^3)(5^2)
(D) 1(3^2)/(3^3)(5^2) = 9/(3^3)(5^2)
Alternate Solution:
Since answer choices A and B have equal denominators and since B has a greater numerator, B > A.
If we multiply both the numerator and the denominator of B by 3, we obtain 6/(3^3)(5^2). The denominator is equal to the denominator of answer choice C, but the numerator of C is greater; therefore, C > B.
If we multiply both the numerator and the denominator of C by 5, we obtain 35/(3^3)(5^3). The denominator is equal to the denominator of answer choice D, but the numerator of D is greater; therefore, D > C.
Finally, in comparing D and E, we see that if we were to multiply both the numerator and the denominator of D by 3 x 5^2 = 75, we would get a denominator that is equal to the denominator of answer choice E, but the numerator of D, which is 45 x 75, would have been much greater than the numerator of E, which is only 75. Therefore, D > E.
Answer: D
