Fraction Addition and Subtraction and Mixed Number Notation

Addition and Subtraction of Fractions with Unequal Denominators

Now how can we add ?  As with problems with common denominators, we can draw a diagram. We have a problem since all the pieces are not the same size. Though, after cutting each piece to make pieces of the same size, we are able to work the problem. In other words, we change the problem so that the fractions are equivalent fractions with common denominators as illustrated below.

Note that we cut each third into fourths and each fourth into thirds so that each small piece represents one-twelfth of a whole square. Further, we note that the LCM (3, 4) = 12, so we have chosen 12 for the least common denominator.

 

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