Differences Between French Pairs Like An/Année

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The French word pairs an/année, jour/journée, matin/matinée, and soir/soirée can be confusing to students because each pair has a single English translation. The important thing to understand is that the difference between the words in each pair has to do with two different ways of considering time.
The short words an, jour, matin, and soir (note that they are all masculine) indicate a simple amount of time or division of time. For the purposes of this lesson, we'll call these "division words."
Je suis en France depuis deux jours.
I've been in France for two days.
Il est fatigué ce soir.
He's tired this evening.
In comparison, the longer words année, journée, matinée, and soirée (all feminine) indicate a duration of time, usually stressing the actual length of time. I'll call these "duration words."
Nous avons travaillé pendant toute la matinée.
We worked all morning.
Elle est la première de son année.*
She's the first in her year/class.
*Though année is feminine since it begins with a vowel you have to say son année (not "sa année") - see adjectives with special forms.

Division Words vs. Duration Words

Here are some general rules about when to use division words vs. when to use duration words, as well as some important exceptions. But if you consider them carefully, you'll see that the exceptions follow the basic differences outlined above.

Use division Words With

1. Numbers*   

Un homme de trente ans.  
A 30-year-old man.
Il est arrivé il y a deux jours.
He arrived two days ago.
Dans trois ans, j'aurai terminé mes études.
In three years, I'll have finished my studies.
*except when you want to emphasize the duration or when the word is modified by an adjective.
J'étais en Afrique pendant trois années, pas deux.
I was in Africa for three years, not two.
Ils ont passé sept merveilleuses journées à Paris.  
They spent seven marvelous days in Paris.
2. Temporal adverbs   

demain matin
tomorrow morning
tôt le matin
early in the morning
hier soir
last night

Use Duration Words

1. with de + a descriptive noun
l'année de base
base year
une journée de travail de huit heures
an eight-hour workday
les soirées d'été
summer evenings
2. with nearly* all adjectives, including

However, note that an/année is far more flexible than the other pairs; for "last year" you can say l'an dernier or l'année dernière, "next year" can be l'an prochain or l'année prochaine, etc.
Except demonstrative adjectives, which are used with division words:   cet an - cet an que j'ai vécu en France
that year - that year that I lived in France
(But when talking about the current year, say cette année - this year.)
ce jour - ce jour où nous sommes allés au musée
this/that day - that day we went to the museum
ce matin, ce soir
this/that morning, this/that evening
The indefinite word tout has a different meaning with division vs. duration words; it is an indefinite adjective with division words and an indefinite pronoun with duration words.

   tous les matins, tous les jours
every morning, every day
toute la matinée, toute la journée
all morning, all day

Note that when referring to the day of the week, you need the division word:
Quel jour est-on? Quel jour sommes-nous?
What day is it?
Vendredi est le jour de la fête.
Friday is the day of the party.