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:

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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3 6 9 12 15Often, 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.