Answer :

Well first since its .344 this would be in the thousandths place so to start it would be 344/1000. Divide both the numerator and denominator by 2 which would be 172/500. Divide both by 2 once again 86/250. Divide by 2 once again, now its 43/125. Now since 43 is a prime number, it cannot be reduced anymore. 

.344 as a fraction in lowest terms is 43/125
apologiabiology
so 0.344 means 344/1000
(0.1=1/10  0.21=21/100    0.213=213/1000)
factor out the 'ones' (exg 4/8=1/2 times 4/4[4/4=1 so it can be canceled out])
344=2*2*2*43
1000=2*2*2*5*5*5
we notice that there is a 2*2*2 in both groups so we can cross it out (or 2*2*2=8 so divide top number and bottom number by 8)
43/(5*5*5)
43/125