Step 1 :The given mathematical expression is \(6 \div 2(1+2)\).
Step 2 :According to the order of operations (BIDMAS/BODMAS/PEDMAS), brackets are solved first, then indices (exponents), followed by division and multiplication (from left to right), and finally addition and subtraction (from left to right).
Step 3 :First, solve the expression in the brackets \((1+2)\), which equals to 3.
Step 4 :Then, perform the division and multiplication operations from left to right. So, \(6 \div 2 \times 3\) equals to 9.
Step 5 :The solution to the mathematical expression \(6 \div 2(1+2)\) is \(\boxed{9}\).