My cat needs antibiotics assap!

hi i have 500mg tabs of amoxicillin my cat has an infection she is 2kg how many times should i divide the tablet to get the correct amount for my cat i will add each part to water in syringe i have no scales and cannot afford the vet bill unfortunately as i live rural 

Split it in half (250 mg.) and split those two in half (125 mg.) and give her one of those to start (loading dose is double the normal dose), then split the rest of the 125s in half (67.5 mg.) and give her one of those pieces every 12 hours for 10 days, even if symptoms disappear, because that way you avoid creating a resistant strain.  I hope it works and she feels better.  It cant kill a virus but can prevent secondary bacterial infection if she has a virus that knocks down her bacteria fighting white cells.  Amoxicillin doesn't taste bad so you can crush it into a powder and mix with a little cream and mix that into a small amount of whatever wet food she likes best, or else give that to her with a syringe.