We define a quotient
[
B
/
A
]
[B/A]
of bounded operators
A
A
and
B
B
on a Hilbert space
H
H
with ker
A
⊂
A \subset
ker
B
B
as the mapping
A
x
→
B
x
,
x
∈
H
Ax \to Bx,x \in H
, and show explicit formulae for computing quotients which correspond to sums, products, adjoints and closures of given quotients.