A student thinks of a natural number. She divides the number by $$9$$ and the remainder is $$7$$. What is the remainder when double that number is divided by $$9$$? 
Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder 
The remainder of $$A$$ $$\div9$$ is $$7$$, and $$2A=A+A$$. Therefore the remainder of $$2A\div9$$ is $$7+7=14$$. $$14= 9+5$$, therefore the remainder is $$5$$. 