# Adding fractions with like denominators. When we adding fractions why do not add denominators? For example, 2/15 + 3/15 = 5/15 not 5/30.

When we adding fractions why do not add denominators? For example, $\frac{2}{15}+\frac{3}{15}=\frac{5}{15}$ not $\frac{5}{30}$.
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Ruben Horn
Because that is not how reality behaves. The number $\frac{2}{15}$ is meant to represent that you have divided something, let's say a pie, in 15 equal pieces, and then from those you want to refer to only 2 of those pieces.
So in this motivation, we have that the numerator (the number that goes in the upper part of the fraction) represents the number of pieces you have, while the denominator (the number in the lower part of the fraction) represents the size of each of those pieces.
Now, when you pick 2 of those pieces and 3 of those pieces, you end up having 5 pieces, but the size of those pieces is the same (which is equal to the 15th part of the whole pie). So the numerator changes to reflect the change in the number of pieces but the denominator stays the same to reflect that the size of each piece has not changed.
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joguejaseg
Because
$\frac{2}{15}+\frac{3}{15}=2\cdot \frac{1}{15}+3\cdot \frac{1}{15}=\frac{1}{15}\cdot \left(2+3\right)=\frac{1}{15}\cdot 5=\frac{5}{15}$