In the $${{9}^{\text{th}}}$$ Century BC, an Indian mathematician named Al Khwarizmi wrote a book about math calculations. Since his calculations were always written on a clay tablet, he was afraid the calculation process might be lost. So, he created a system to determine whether his calculations were correct.  Example: $$1234+18983+18922=39039$$,  $$1234$$ divided by $$9$$ yields a remainder of $$1$$,  $$18983$$ divided by $$9$$ yields a remainder of $$2$$,  $$18922$$ divided by $$9$$ yields a remainder of $$4$$,  When the remainders are added up and divided by $$9$$, the remainder is $$7$$. Dividing the number on the right-hand side of the equals sign by $$9$$ yields a remainder of $$6$$. Therefore, $$7$$ does not equal $$6$$, making the above equation incorrect.  Use the method above to determine whether the following equations are correct or not:．  ①$$2638457+3521983+6745785=12907225$$,  ②$$7832145-2167953=5664192$$. 
Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Casting Out Nines
$$(1)$$ Dividing the numbers on the left-hand side of the equals sign by $$9$$ yields remainders of $$8$$, $$4$$, and $$6$$. The sum of the remainders divided by $$9$$ is $$0$$. Dividing the right-hand side of the equals sign by $$9$$ yields a remainder of $$1$$. Therefore, $$0$$ does not equal $$1$$, making the equation incorrect.  $$(2) $$The remainders on both sides of the equation are $$6$$. We can check by performing the calculation normally. It is correct. 