What does "$-2\frac35$" mean?

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I have seen this notation before: $2\frac 3 5$. It means $2 + \frac 3 5$ I know it since $3$rd grade. It always seemed confusing to me because sometimes (especially in physics problems), $2\frac 3 5$ might mean $2 \cdot \frac 3 5$. But it math, I know it means addition. The problem is that I have never used this notation before with negative integers like in $-2\frac 3 5$. Logically, it means negative $2$ and $3/5$, which would be $-(2 + \frac 3 5) = -2 - \frac 3 5$. However, shouldn't this be noted as $-(2\frac 3 5)$? What does $-2\frac 3 5$ really mean?

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If you would want to multiply $2$ by $3/5$ you'd have to put a multiplication sign between $2$ and $3/5$. Always. If not, you first have to calculate "the addition" and obtain $13/5$ and then put the negative sign in front of the result, thus obtaining $-13/5$, simply because that notation has priority over the minus sign in front of it.