write the algebraic expression

the quotient of 100 and the quantity6 plus w (6+w)/100

the quotient of 23 and u minus t
23/u-t

would these be correct?

yes, except it would be 23/(u-t)

Yes, both algebraic expressions that you provided are correct.

"The quotient of 100 and the quantity 6 plus w" is written as (6+w)/100. This expression represents dividing 100 by the sum of 6 and w.

Similarly, "The quotient of 23 and u minus t" is written as 23/(u-t). This expression represents dividing 23 by the difference between u and t.