Two different fractions each have a difference of 2 between their numerators and their denominators. All of the following are true except:
A)the fraction with the larger numerator is the larger fraction.
B)the fraction with the larger denominator is the larger fraction.
C)the fraction that has a terminating decimal is larger.
D)the fraction with the larger sum of numerator and denominator is the larger fraction.

Question

Quizplus · Accepted Answer

The fraction with the larger numerator is not necessarily the larger fraction. For example, 3/1 and 5/3 both have a difference of 2 between their numerators and denominators, but 5/3 is the larger fraction even though it has the smaller numerator. 
The fraction with the larger denominator is not necessarily the larger fraction. For example, 1/3 and 3/5 both have a difference of 2 between their numerators and denominators, but 3/5 is the larger fraction even though it has the smaller denominator. 
The fraction with the larger sum of numerator and denominator is not necessarily the larger fraction. For example, 2/4 and 4/6 both have a difference of 2 between their numerators and denominators, but 2/4 is the larger fraction even though it has the smaller sum. 
Therefore, the only statement that is not necessarily true is C: the fraction that has a terminating decimal is larger. Some fractions with terminating decimals are larger, but this is not true in general. For example, 7/4 and 9/5 both have a difference of 2 between their numerators and denominators, but 7/4 is the larger fraction even though it does not have a terminating decimal.

Two Different Fractions Each Have a Difference of 2 Between