Which of the following fraction is the smallest?

rrobiinn wrote:Which of the following fraction is the smallest?

a. 33/128
b. 45/138
c. 53/216
d. 83/324
e. 15/59

How to take approach for such kind of math?

Looking at the ratios it seems that the denominator is roughly 4x the numerator for all the choices except B, where the ratio is roughly 1:3. 1/3 > 1/4 so we can eliminate B.

Next step would be to break down the fractions in its simpliest form

A. 33/128= 32/128 + 1/128 = 1/4 + 1/128
C. 53/216 = 54/216 -1/216 = 1/4 - 1/216
D. 83/324 = 81/324 + 2/324 = 1/4 + 1/162
E. 15/59 = 15/60 + 15/(59 x 60) = 1/4 + 1/236

The only fraction less than 1/4 is 55/216
Ans = c

rrobiinn wrote:Which of the following fraction is the smallest?

a. 33/128
b. 45/138
c. 53/216
d. 83/324
e. 15/59

How to take approach for such kind of math?

A:
33*4 = 132.
Thus, 33/132 = 1/4,
Since 33/128 has smaller denominator, its value is a bit more than 1/4.

B:
45*3 = 135.
Thus, 44/135 = 1/3.
Since 45/138 has a greater denominator, its value is a bit less than 1/3.
Eliminate B, since A is smaller.

C:
53*4 = 212.
Thus, 53/212 = 1/4.
Since 53/216 has a greater denominator, its value is a bit less than 1/4.
Eliminate A, which is greater than 1/4.

D:
83*4 = 332.
Thus 83/332 = 1/4.
Since 83/324 has a smaller denominator, its value is a bit more than 1/4.
Eliminate D, since C is less than 1/4.

E:
15*4 = 60.
Thus, 15/60 = 1/4.
Since 15/59 has a smaller denominator, its value is a bit more than 1/4.
Eliminate E, since C is less than 1/4.

The correct answer is C.