A fraction can be understood as a sum of unit fractions with the same denominator, or as sums of larger like-denominator fractions; for example, . The decomposition preserves the whole because the numerator counts equal-sized parts, and it supports adding and subtracting fractions with common denominators; decompositions involving unlike denominators or more generalized algebraic forms are beyond this scope.
A fraction’s denominator tells the size of the parts, and its numerator tells how many of those parts there are. To decompose a fraction, split the numerator into smaller numbers while keeping the denominator the same.
Example: Decompose into a sum of two fractions.
This is correct because there are still five sevenths altogether: two sevenths plus three sevenths.
You can also decompose it into unit fractions:
The denominator stays the same because all the parts are sevenths.
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