The order of operations is an acronym that helps the solver with trying to solve a question. Order of operations is usually known as "PEMDAS", which stands for:
Parenthesis: The first step you take, generally, there are two types of "parenthesis" you may see, Parenthesis "(" ")", and Brackets "[" "]". Brackets are rarely used unless you need a parenthesis within a parenthesis.
For example: [10(5 + 18)], in which you first solve the parenthesis: (5 + 18) = (23), and then the brackets: [(10)(23)] = 230
Exponent (& Roots): This is the next step you take. You solve any exponents (numbers with powers, for example: 15² or 18^2).
An example can be seen in (3)² + 8, in which you solve the exponent, and then the addition: 3² = 9; 9 + 8 = 17
Multiplication: The third step, in which you solve the multiplications inside the expression. For example: 18(x + 7)
(As you cannot combine a variable and a number), you must continue on to the next step (multiplication). Distribute 18 to all terms within the parenthesis:
18(x + 7) = 18(x) + 18(7) = 18x + 126
Division: The fourth step, (however, it is interchangeable with multiplication. Remember that you should follow the left -> right rule after Parenthesis & Exponents). For example: (x + 12)/12
Distribute "divide by 12" to all terms within the parenthesis: (x + 12)/12 = x/12 + 12/12. Simplify. x/12 + 12/12 = x/12 + 1
Addition: The second to last step, in which you combine any like terms that you can (still following the left -> right rule).
Subtraction: The last step, in which you combine any like terms that you can (still following the left -> right rule).
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For example:
5 - 2 * 3 + 9
In the following order of operation, we see 3 operations: Subtract, Multiply, and Add. Remembering PEMDAS, we will solve this question.
First, multiply: 2 * 3 = 6
Next, following the left -> right rule, we will subtract: 5 - 6 = -1
Finally, add: -1 + 9 = 8
8 would be the answer for this example.
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