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This problem trains for: SAT-I, AMC-8, GMAT.

Which of the inequalities below are true?

In I, the fractions are negative. Therefore, the one with the smaller absolute value will be the larger value. Since their denominators are the same, the one with the smaller numerator is the larger value. The inequality is false.

In II, using the same reasoning as for I, we have to bring the two fractions to the same denominator before we can compare their absolute values. The inequality becomes:


which is clearly false.

In III, both fractions are negative. The fractions have the same numerator. The fraction with the larger denominator will have the smaller absolute value and will be the larger fraction (when negative):


is clearly true.

V can be written as:


Since the numbers are both positive, the greater one is the one with the larger fractional part. The inequality is true V and IV is false.