Comparing Fractions

  Example: Which of the fractions in the following pairs are greater?

1/3   and    3/4

2/9   and     5/9

21/28    and   15/20

3/7   and   4/9

Use one of these strategies for comparing two fractions:

Strategy #1 : Ask: Are either of the fractions "benchmark fractions" that
                     you can easily compare?

                     1/3   and   3/4 :  are benchmark fractions,  and we know
                     3/4 is greater.

Strategy #2: Ask: Do the fractions have a common numerator or denominator?

                         2/9    and    5/9 :  have a common denominator, therefore
                     we can tell 5/9 is greater.

Strategy #3: If the fractions contain large numbers, put them into lowest terms
                     and see if they are more easily compared.

                     21/28  and   15/20 :  can both be reduced to 3/4,
                     therefore, they are equivalent fractions.

Strategy #4: Find a common denominator

                     3/7    and  4/9 :  A common denominator could be 63,
                    Multiply 3/7 by 9/9 to get 27/63 and  multiply 4/9
                    by 7/7 to get 28/63. You can now see that
                    4/9 is greater.