What is the quotient of dividing 4 out of 9 into 1 out of 9 out of 18? Is it division or not

What is the quotient of dividing 4 out of 9 into 1 out of 9 out of 18? Is it division or not

[18×(1/9)]÷[3×4/9)]
=2÷(4/3)
=2×(3/4)
=3/2