fract

The root fract comes from Latin frangere, "to break," whose past participle was fractus — "broken." That split between the present stem and the past stem is exactly why English shows two faces of this root: frag- (from the present frangere) and fract- (from the participle fractus).

Start with the most literal member: fracture. A fracture is simply a break — most often a broken bone, but also a crack in rock, metal, or a relationship. From there the root branches in several directions.

When you break a whole into pieces, each piece is a fraction — literally "a broken-off part." Mathematics borrowed the word: one-quarter is a piece broken off from a whole, written as a number over a number. Fractional just means "of a fraction," hence "tiny, partial."

Break something into many small bits and you get fragments — fragmentum, "a piece broken off." A thing that breaks too easily is fragile (fragilis) — easily snapped.

Now watch the metaphor stretch. Refraction is re- (back) + fract — light "broken back" or bent as it passes from air into water; the ray looks snapped at the surface. Refractory literally "breaking back against" you — a person or material that resists and won't yield (a refractory child, a refractory metal that won't melt).

Rules can be broken too. To commit an infraction is to "break into" (in- + fract) a rule — a small violation. Infringe is the same idea down a different path: Latin infringere (in- + frangere), "to break in on" someone's rights or territory — to encroach.

Finally, the feelings: someone fractious is, almost literally, of a "breakable" temper — irritable, quarrelsome, ready to snap at any moment.

One family member is Germanic, not Latin: the everyday verb break (and compounds like unbroken, windbreaker). It descends from Old English brecan, but it traces back to the same ancient Indo-European root bhreg- ("to break") that fed Latin frangere. So break and fracture are long-lost cousins — same original meaning, two separate journeys into English.