I've always balanced my props whether they are 9" or 20".
I have found most plastic/composite props are not as unbalanced as wood props. Also to throw another wrench into this thread, if you have to enlarge the prop shaft hole in the prop use a prop reamer designed for the job or a bench press. Please don't use a hand held drill especially on a wood prop since the drill bit will follow the softer side of the hole. Which brings me to another complication: Off centered holes in the prop will drive you crazy trying to balance them.
Don't fly with them.
Oh BTW, don't trhow out your old broken props..they make good epoxy mixers and with the larger props 14" or better they make good paint stirrers.
Some 'old school' flyers at my field say to use wood props on trainers until your landings/taxiiing become alot smoother so you don't bend the prop shaft on your engine. I don't agree with this because I feel it would take more than an occasional ground strike to bend a shaft. Wood will take less stress to break and transfer less to the engine/airframe than plastic/composite props. Just my $.02
Another word of advice is to paint the tips of your props white or yellow so you can see the prop arch when running and will wear equally from each tip. I don't recommend painting one tip to balance as over time the paint will wear off and you'll be back to square one.
Always check your prop nut for tightness ,especially on wood props,before your flying session as wood will expand and contract more than plastic/composite props.
On four stroke engines if your engine backfires, recheck your prop nut. Chances are it came loose.
Always....always....always check your prop, spinner and prop nut whenever you even nick the ground. A flying prop without being attached to an engine can be extremely dangerous.
Do not ever.....ever....ever try to glue, attach or in any other way, repair a broken prop to fly.


Happy Flying


Tom