Detailed solutions please Need help with only 6 Detailed sol

Detailed solutions please:

Need help with only #6

Detailed solutions please: Need help with only #6 5. Let a be any integer and let h and c be positive integers. Suppose that when a is divided by h, the quotient is q and the remainder is r, so that If ac is divided by bc, show that the quotient is q and the remainder is rc. 6. Let a, h. c, and q be as in Exercise 5. Suppose that when q is divided by c, the quotient is k. Prove that when a is divided by bc, then the quotient is also k.

Solution

5.

since a=bq+r

multiply both the side by c

ac= bqc+rc

or, ac = (bc)q+rc

since ac is divided by bc.

So, quotient = q and the remainder=rc

6.

q is divided by c, the quotient is k

q=ck

multiply by b

bd = (bc)k

given that a is divided by bc

So, the quotient =k