If one takes the tables at beginning of classes, usually on the beginning of the 2nd page of classes (ie: PHB p. 47 for Barbarian), then crop what's between the Level column/attribute and 1st of Spell Slots per Spell Level, both pairs of Eldritch Knight (EK; a 3+ Fighter (Ftr)) & Arcane Trickster (AT; a 3+ Rogue (Rog)) and Paladin (Pal) & Ranger (Rgr) have respectively the--same--spell slot tables. Taking those 2 cleaned table, if one takes the EK+AT one and make it fit to be like Pal+Rgr one (by pre-pending the 1st 2 rows/tuples and appending an empty column/attribute (with "—" for default)), one can see that the difference between the 2 is
(notice EK+AT is on the left and Pal+Rgr on the right, the lines with differences are yellow and the differences orange) and as one that have read PHB > Chapter 6: Customization Options > Multiclassing > Class Features > Spellcasting > Spell Slots (p. 164) Pal & Rgr are supposed to yield 1/2 casting level (lvl) and EK & AT 1/3 spell wielder lvl. However by comparing each table with the Multiclass Spellcaster: Spell Slots per Spell Level table soon after the previous reference (so beginning of p. 165), which 1st spell slot is at lvl 1 and EK+AT 1st spell is at 3rd lvl and Pal+Rgr is at 2nd lvl, one could deduce it's as expected as both reverse of the fractions (previous sentence) are respectively 3X & 2X. Albeit the 1st spell slot fits that logic, the 2nd spell slot doesn't as the base table (Multiclass Spellcaster: Spell Slots per Spell Level) 1st lvl 2 slot is lvl 3, EK+AT is at lvl 7 and Pal+Rgr is at lvl 5, but one would expect instead respectively lvl 9 & 6, so EK+AT is better of 2 lvl and Pal+Rgr is better of 1 lvl. The advantage continues for 1st 3rd lvl spell slot as base is lvl 5, EK+AT lvl 10, Pal+Rgr lvl 13, so respective advantages of 2 & 1 lvls. It continues for all spell slots.
So I think players that have a combination of EK+AT or(/and) Pal+Rgr would prefer to use the class tables instead of simply adding the fraction to get the overall pure casting counterpart, is it so? Also does one round down each combination (EK+AT / Pal+Rgr) or are fractions added and the final number rounded down?
Thank you kindly for your help
Update 1:
Please try to answer in a general case, with what was mentioned before, but if that's not enough the following are the specifics. I'm trying to make a EK/AT and it would be more advantageous to my character to use the EK+AT spell slot table rather than doing the (EK lvl + AT lvl) / 3 then look at the multiclass spell slot table.