What is 23 remainder 1 as a fraction

23 remainder 1 as a fraction is 23/1 = 23 

23 remainder one is simply expressed as 23, however I think your teacher wants you to write it in a different notation than that just so you understand it.  With a little more information I could help you a little bit better, but when writing a remainder as a fraction you would do long division and take the remainder, in this case one, and place it over the divisor, in this case 5, and include that into your quotient.  Make sense?  For example 116/5: 23 goes into 116 23 times with one left over so your answer if you did long division the top of the division bar would look like 23 1/5, and that is your answer.  

 Understanding why the two answers are the same is what your teacher wants you to learn, also when move up to more difficult math courses the method I just described makes more sense. 1/5=.2 so 23 1/5 is the same as 23.2. Remember that to check long division you multiply your quotient times your divisor and hope it equals the number under the division bar. so for our check we multiply 23.2 times five and that comes out to equal 116.  

So in summary, do long division once you reach the point where you are ready to write the remainder on top of the division bar write the remainder as a fraction

They are somewhat similar