If x is divided by 5 the remainder is 4. if why is divided by 5 the remainder is 1. what is the remainder when x+y is divided by 5

0

Step-by-step explanation:

We are given the following:

     (equ. 1)

     (equ. 2)

We are asked:

 (equ. 3) , what is ?

The 's represent the quotients you get.

is the remainder of dividing by 5.

We know that is a number in {0,1,2,3,4}.

(I got this by multiplying both sides of equ 1. by 5.)

(I got this by multiplying both sides of equ 2. by 5.)

Let's add these equations together:

Factoring the 5 out for the 's part and simplify 4+1 gives:

So can't be the remainder of dividing something by 5 but see that we can factor this right hand expression more as:

So while there is no remainder (the remainder is 0).

Let's do an example if you are not convinced at this point that the remainder will be 0.

So choose x=9 since 9/5 gives a remainder of 4.

And choose y=16 since 16/5 gives a remainder of 1.

x+y=9+16=25 and 25/5 gives a remainder of 0.