Learn French: Je voudrais le tiers de ce tissu pour la veste. - I would like a third of this fabric for the jacket.

In English we usually say "a third" or "a half", but in French, these fractional quantities are treated as specific nouns that require a definite article (le or la). Therefore, you use le tiers (a third), la moitié (a half), and le quart (a quarter).

Why use Je voudrais instead of Je veux here?

Je voudrais is the conditional tense of vouloir (to want). It translates to "I would like" and is the standard, polite way to request something in a shop or restaurant. Je veux ("I want") can sound much too blunt or demanding in French.

Why is it ce tissu and not cet tissu?

Tissu (fabric) is a masculine noun that starts with a consonant, so it takes the standard masculine demonstrative adjective ce ("this" or "that"). You only use cet before a masculine noun if it starts with a vowel or a silent H (like cet arbre or cet homme).

Is tissu the same kind of "tissue" you use to blow your nose?

No, tissu is a "false friend." It means "fabric," "material," or "cloth." If you have a cold and need a paper tissue, you would ask for un mouchoir or un mouchoir en papier.