Fraction Concepts


The greatest difficulties I see for students in understanding fractions is in dealing with equivalent fractions, especially putting them into lowest terms.  To make a larger equivalent fraction, I simply encourage the students to make a table and choose any column from the table:

                 8      10
3       6       9     12     15

Often, putting fractions in lowest terms is a matter of recognizing that the fraction is already in lowest terms.  Four characteristics of a fraction in lowest terms:
1)  The numerator is 1
2) The numerator and denominator are consecutive numbers.
3)  The denominator is prime.
4)  The numerator is prime BUT will not go evenly into the denominator.  (3/8 is in lowest terms, but 3/6 is not)

Characteristics of fractions that are NOT in lowest terms:
1) Both numerator and denominator are even.
2) The numerator is exactly half the denominator.


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