Learn French: Il plie le tiers de la largeur. - He folds a third of the width.

While you can say un tiers (which is very common in math), French frequently uses the definite article (le) for fractions like le tiers (a third), le quart (a quarter), and la moitié (a half) when referring to a portion of a specific whole object. Here, because he is folding a piece of a specific width, le tiers is the most natural choice.

Since le tiers is a quantity, shouldn't it just be followed by de instead of de la?

That is a great observation! With most quantity expressions (like beaucoup or un peu), you just use de with no article (e.g., beaucoup de papier). However, fraction nouns like la moitié, le tiers, and le quart are exceptions. They are treated like regular nouns, meaning they translate strictly to "the third of the...", so they require the definite article (using du, de la, or des).

Why does tiers have an 's' at the end if he is only folding one third?

The 's' in tiers is just part of its base spelling, not a plural marker. The word is invariable, meaning it looks exactly the same in the singular and the plural. You write un tiers for one third, and deux tiers for two thirds.

Is there a trick to remembering that largeur (width) is feminine so I know to use de la?