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:
2 4 6 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.
2 4 6 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.