When the positive integer k is divided by 7, the remainder is 6. What is the remainder when k + 2 is divided by 7? Need to show algebra work.

Question

When the positive integer k is divided by 7, the remainder is 6. What is the remainder when k + 2 is divided by 7?  Need to show algebra work

Answer 1

 

if the remainder is 6 when k is divided by 7, then k is 1 less than a multiple of 7

if you add 1 to k, that is, k+1, you have a multiple of 7

if you add 2 to k, that is k+2, where k+2 is 1 more than a multiple of 7, then when you divide k+2 by 7 you get a remainder of 1

 

using algebra...

k/7=n remainder 6 for some n

k=7n+6 for some n

(k+2)/7 gives what remainder ?

k+2/7=?

substitute k=7n+6

[(7n+6)+2]/7

(7n+8)/7

(7n+7+1)/7

[7(n+1)+1]/7

dividing gives the following...

(n+1)+1/7 which means k+2 divided by 7 gives an answer of n+1 remainder 1

 

example

27/7=3 R6

29/7=4 R1

3 is n and the remainder is 6

4 is n+1 and the remainder is 1