<P> If the equal denominators are negative, then the opposite result of comparing the numerators holds for the fractions: </P> <Dl> <Dd> 3 − 4 <2 − 4 (\ displaystyle (\ tfrac (3) (- 4)) <(\ tfrac (2) (- 4))) because a − b = − a b (\ displaystyle (\ tfrac (a) (- b)) = (\ tfrac (- a) (b))) and − 3 <− 2 (\ displaystyle - 3 <- 2). </Dd> </Dl> <Dd> 3 − 4 <2 − 4 (\ displaystyle (\ tfrac (3) (- 4)) <(\ tfrac (2) (- 4))) because a − b = − a b (\ displaystyle (\ tfrac (a) (- b)) = (\ tfrac (- a) (b))) and − 3 <− 2 (\ displaystyle - 3 <- 2). </Dd> <P> If two positive fractions have the same numerator, then the fraction with the smaller denominator is the larger number . When a whole is divided into equal pieces, if fewer equal pieces are needed to make up the whole, then each piece must be larger . When two positive fractions have the same numerator, they represent the same number of parts, but in the fraction with the smaller denominator, the parts are larger . </P>

How many two thirds are in one half