If you mix (add) $5$ oranges and $2$ cars, you still get $5$ oranges and $2$ cars.
However, if you mix (add) $5$ oranges and $2$ oranges, you can compute the sum and we say that we get $7$ oranges.
The point is: to add and subtract, you need to have the same type of "things".
These examples use integer arithmetic, since it is a concept that we can visualise. However it would be easy to expand to continuous measures like:
Mixing (adding) $0.5 \ kg$ of sugar with $0.2 \ kg$ of sugar gives $0.7 \ kg$ of sugar; while mixing $0.5 \ kg$ of sugar with a ruler $0.2 \ m$ long gives the $0.5 \ kg$ of sugar and a ruler $0.2 \ m$ long.
With respect to multiplication, the multiplication can be thought as having $2$ boxes with $5$ oranges each, which results in:
$2$ box(es) $\times 5$ oranges/box = $10$ oranges. Note that oranges/box can be read as "oranges per box".
I tried to give a simple answer to your question. A more complex answer could lead us to dimensional analysis.