How do you reduce fractions using "prime factorization"?

5/8 x 3/10 = (5)/(2*2*2) * 3/(2*5)
The 5 in the numerator of the first fraction and in the denominator of the second fraction cancel each other out.
 (5)/(2*2*2) * 3/(2*5) = 3/(2*2*2*2) = 3/16

i think it' be (5/2*4) * (3/2*5) and then 5/2*2*2 * 3/2*5 = 15/80= 3/16

i'm not sure but i think you just factor out the numbers u can. the 8 can be factred to 2 times 4 which can be taken down to 2 times 2 times 2. An the the ten in three tenths can be factored down to 5 times 2. hope it helps.

= 5/8 * 3/10
= ([5 * 1]/[2 * 2 * 2]) * ([3 * 1]/[2 * 5]) cancel out the 5
= (1/[2 * 2 * 2) * (3/2)
= 1/8 * 3/2
= 3/16

OR:
= 5/8 * 3/10
= 15/80
= (5 * 3)/(2 * 2 * 2 * 2 * 5) cancel out 5
= 3/(2 * 2 * 2 * 2)
= 3/16

Answer: in any way, that is, before or after multiplying, you may cancel out 5 at the top and the bottom of the slash sign (/). It will yield a reduced to lowest terms product of 3/16.

Check (reverse the operations to go back to the multiplicand):
= (3/16)/(3/10)
= 3/16 * 10/3
= (3/[2 * 2 * 2 * 2]) * ([2 * 5]/3) cancel out 3
= (1/[2 * 2 * 2 * 2]) * ([2 * 5]/1) cancel out a 2
= (1/[2 * 2 * 2]) * (5/1)
= 5/(2 * 2 * 2)
= 5/8