Do you still make saving throws for half when benefiting from Absorb Elements?

Question

I'm wondering if Absorb Elements is done in place of a saving throw or if it's in addition to a saving throw. If you succeed on your save and use this spell, would it then do a quarter damage?

The Absorb Elements Spell is described as such:

The spell captures some of the incoming energy, lessening its effect on you and storing it for your next melee attack. You have resistance to the triggering damage type until the start of your next turn. Also, the first time you hit with a melee attack on your next turn, the target takes an extra 1d6 damage of the triggering type, and the spell ends.

Answer 1

It's as you suggest: the characters makes any saving throw as normal, then Absorb Elements reduces any damage they take by half.

Example: A wizard casts Fireball on you. He rolls 24 damage. You roll your saving throw, and succeed, reducing it to half, since Fireball allows a save for half damage. You take 12 damage. You immediately choose to use your reaction to cast Absorb Elements. This interrupts and gives you resistance, so in the end you only take 6 damage.