Answer:
3/11
Explanation:
Let Roberto's cards be x.
Let David's cards be y
x = (3/4) y
Roberto gives half his cards away which is 1/2*(3/4) = 3/8
David's new amount after the gift = 1/2(3/4)y + y = 3/8y+y=3y/8+8y/8 = 11y/8
So the ratio is Roberto / David = (3/8) // (11/8)
Roberto to David = 3/8 // 11.8 which you now invert and multiply the denominator
Roberto to David = 3/8 * 8/11 = 3/11
Done on my cell.