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Fraction Addition and Subtraction with a Common Denominator

When two fractions share the same denominator, their sum or difference is found by combining the numerators and placing the result over the shared denominator. Formally, for any numbers aa, bb, and cc with b0b \neq 0:

ab+cb=a+cb\frac{a}{b} + \frac{c}{b} = \frac{a + c}{b}

abcb=acb\frac{a}{b} - \frac{c}{b} = \frac{a - c}{b}

The denominator stays the same because the fractions already describe parts of the same-sized whole. Only the count of those parts (the numerator) changes. After performing the addition or subtraction, the resulting fraction should be simplified if possible.

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Updated 2026-05-02

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