I understand the basics of conjugating sentences for the past tense in french but when do you add "s" onto the end of the infinitive? I mean for sentences like;
we paid... is it nous avons payé or nous avons payés?
we arrived... nous sommes arrivé or nous sommes arrivés?
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You only do this (make the past participle agree) when the auxiliary is "être".
J'ai dit. (I said)
Elle a fait. (She did)
Nous avons vu. (We saw)
These don't agree because the auxiliary is "avoir".
Je suis allé(e). (I went)
Elle est venue. (She came)
Nous sommes arrivé(e)s. - (We arrived)
These do agree because the auxiliary is "être".
The only other time that the past participle agrees is when there is a direct object.
Le livre. Je l'ai vu. (The book [m.] I saw it. [referring to the book])
La vache. Je l'ai vue. (The cow [f.] I saw it [referring to the cow])
Les livres. Je les ai vus. (The books [m.pl.] I saw them [referring to the books])
Les vaches. Je les ai vues. (The cows [f.pl.] I saw them [referring to the cows])
It's normally "nous avons payé", but sometimes, when the object of the sentence is referred to in the sentence, the "payé" will have to be changed to agree with it.
Les billets que nous avons payés...
La grand somme que nous avons payée....
The verb arriver is in a special category where the past participle arrivé always has to agree with the subject. So it's "nous sommes arrivés" unless everyone's female, in which case it would be "nous sommes arrivées."
http://french.about.com/od/grammar/a/passecompose_...
http://www.cliffsnotes.com/study_guide/The-Pass-Co...
you do not usually add an 's' to the participle after avoir; you add the 's' after etre:
eg. nous avons payé,
nous sommes arrivés
Where etre is used, the participle must agree with the subject. This is not necessary where avoir is used (there may be certain cases where you have to add 's' when avoir is used)- I cannot recall the exact laws of this exception. I suggest you do some further research
You never add "s" to the end of an INFINITIVE. You are talking about the PAST PARTICIPLE.
The past particle is made to agree in NUMBER and GENDER with the direct-object noun if that noun comes before the verb:
Nous avons payé les livres.
Les livres que nous avons payés.
J'ai exprimé mon opinion.
L'opinion que j'ai exprimée.
etc. etc.