In many mathematics exams the situation arises when it very important to know when one fraction is greater than another fraction. Especially in a subtraction problem when the smaller fraction needs to be subtracted from the larger fraction. Also when several fractions are given to be placed in a certain order from the least to the greatest or from the largest to the smallest.

Given the two fractions, (6 / 11) and (5 / 9). Which fraction is larger? Solution : Take the denominator ( 9 ) of the second fraction and multiply the numerator ( 6 ) of the first fraction, that is ( 6 x 9 ) which equals ( 54 ). Write the number ( 54 ), above the first fraction.

Then take the denominator ( 11 ) of the first fraction and multiply the numerator ( 5 ) of the second fraction, that is ( 5 x 11 ) which equals ( 55 ). Write the number ( 55 ) above the second fraction.

Since ( 55 ) is larger than ( 54 ), then the second fraction (5 / 9) is larger than the first fraction (6 / 11).

Given any two fractions (A / B) and (C / D), such that A,B,C,D are whole numbers, each greater than zero, ( 0 ). If the product of ( A x D ) is greater than the product of ( C x B ), then the fraction (A / B) is larger than the fraction (C / D). Similarly if the product of ( A x D ) is less than the product of ( C x B ), then the fraction (A / B) is smaller than the fraction (C / D).