Equivalent Fractions
Some of these misconceptions all have a basis in the concept of equivalence, and we should think carefully about two significant fraction properties. Basing the teaching of fractions on two fundamental fraction properties might alleviate some of the above misconceptions. Every fraction is part of two special groups or families
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A family of fractions with the same name (denominator) but different numerator values
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A family of equivalent fractions with different denominators.
For example, 
is part of the family 
...... and it is the smallest
fraction in part of the family of fifths. Whereas is also so the simplest fraction in the
family set of equivalent fractions 
These two properties of fractions may aid the learner when moving to gaining an understanding of how to manipulate fractions using the four arithmetic operations*.
