It's a convention, but it's a convention people have had a chance to argue about for well over 1000 years. For the mathematics developed over the last thousand years, it's a better convention. If one is only looking at arithmetic on integers, though, the advantages aren't so clear.
Any math at the high school algebra level or beyond requires extensive manipulation of unknown quantities (variables). Almost always the thing you want when manipulating a variable is for there to be only one copy of it in an equation. In order to convert an equation into this form you gather terms and factor (i.e., you apply the distributive law in reverse), ending up with a single multiple of your variable in your manipulated equation. Work with linear equations, polynomials, or integrals relies very heavily on doing this sort of thing, and it's just awkward to write out the result if your convention is that addition is performed first.
euclid316 t1_iycc612 wrote
Reply to ELI5 why we first multiply, then add by TheManNamedPeterPan
It's a convention, but it's a convention people have had a chance to argue about for well over 1000 years. For the mathematics developed over the last thousand years, it's a better convention. If one is only looking at arithmetic on integers, though, the advantages aren't so clear.
Any math at the high school algebra level or beyond requires extensive manipulation of unknown quantities (variables). Almost always the thing you want when manipulating a variable is for there to be only one copy of it in an equation. In order to convert an equation into this form you gather terms and factor (i.e., you apply the distributive law in reverse), ending up with a single multiple of your variable in your manipulated equation. Work with linear equations, polynomials, or integrals relies very heavily on doing this sort of thing, and it's just awkward to write out the result if your convention is that addition is performed first.