∑Math Atelier
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P2B · Fractions & decimals · FRAC.ADD.SUB

Add and subtract fractions

Fractions are added or subtracted by using a common denominator.

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Intuition

Understand first, compress later.

The denominator tells you the size of each piece. You can add pieces directly only when they have the same size.

Switch representations
Fraction bars2/3
2 of 3 parts
inked partsremaining parts
The whole is cut into 3 equal parts and 2 of them are inked — that is 2/3. The denominator names how many equal parts there are, the numerator counts the inked ones.
Formal view

Find a common denominator, rewrite both fractions, add or subtract the numerators, then simplify.

Why does it work?

Equivalent-fraction scaling does not change a fraction's value because numerator and denominator are multiplied by the same number. This makes the pieces comparable.