How to Know When One Fraction Is Larger Than Another Fraction

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.

Difficulty:

Easy

Instructions

Things You'll Need

• Pencil and
• Paper

1. 

   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.

2. 

   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.

3. 

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

4. 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).

Tips & Warnings

• It is very important that the PRODUCT,(of the denominator of the second fraction with the numerator of the first fraction), be associated with the first fraction. Also the PRODUCT,(of the denominator of the first fraction with the numerator of the second fraction), be associated with the second fraction. Since the PRODUCT (of both the denominators of the first and second fractions) will be used as the new denominator to each of the first two products, so that we now have equivalent fractions to the two original fractions given.

• Given the FIRST fraction (A / B) and the SECOND fraction (C / D)

• (A x D)/(B x D) is equal to the FIRST fraction (A / B)

• (C x B)/(B x D) is equal to the SECOND fraction (C / D)

• That is in using the two fractions given in Step 1 above...

• The FIRST fraction (6 / 11) and the SECOND fraction (5 / 9)

• (6 / 11) = (6 x 9)/(11 x 9) which equals (54 / 99) and

• (5 / 9) = (11 x 5)/(11 x 9) which equals (55 / 99).

• Since (55 / 99) is larger than (54 / 99), then...

• (5 / 9) is larger than (6 / 11).