If a number, n, is divided by k, the remainder is 5. What is the remainder if n-k is divided by k?

Question

The answer choices are 1 or 2 or 3 or 4 or 5.

Answer 1

Since the remainder is 5, n is 5 more than a multiple of k.

 

So, if we subtract k from n, then n-k is also 5 more than a multiple (the previous multiple) of k.

 

Algebraically, let Q be the quotient when n is divided by k.

 

   Then, n = kQ + 5

 

            n-k = (kQ+5) - k

 

                  = k(Q-1) +5

 

            If n-k is divided by k, then the quotient is Q-1 and the remainder is 5.

 

Answer:  5

 

Answer 2

Hello Amy, Lets try some small numbers.

 

For the first part,   n divided k giving a remainder of five.

 

Let n=11.

 

Let k=6.  

                           So, we have      n          r 5.

                                                   ___.                      

                                                    k.                                       

 

                                   

 

                                                      11              r      5.

                                                _______.

                                                      6.                                

 

                          So, 6 divides  into 11    1 time,  with a remainder  of    5.                 

 

 

      As for    n  - k         r=5.

                  ______.                                        

                       k.                                                              

 

        n=11.

  

        k=5              11   - 5.         

                         ______.                         

                              5.                                So, we have     6            r =   1   1/5. 

                                                                                       ______.

                                                                                            5.                                               

 

                Hope this helps.