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Arithmetic operations are basic calculations we perform with numbers. They include addition, subtraction, multiplication, and division. Understanding the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), is crucial. This order tells us how to solve expressions step-by-step. When solving, always do operations inside parentheses first, then exponents, followed by multiplication or division (from left to right), and finally, addition or subtraction (from left to right). For example, in the exercise \(20 - 6 \div 2 + 1\), the division must be completed before moving on to subtraction and addition.

Division splits a number into equal parts. It is an important arithmetic operation and often comes before addition and subtraction in solving expressions. In the problem \(20 - 6 \div 2 + 1\), division occurs first according to the order of operations. Dividing 6 by 2, we get 3. This step simplifies our equation, resulting in \(20 - 3 + 1\). Understanding and performing division correctly ensures you can handle more complex equations.

Subtraction finds the difference between numbers. After division, subtraction is the next step to solve in our example. We start with \(20\) and subtract \(3\), the result of our previous division step. This gives us \(20 - 3 = 17\). Properly executing subtraction steps is vital, especially in longer and more complex equations.

Addition is the process of finding the total or sum by combining numbers. It is usually the last operation to perform when following the order of operations. In our example, after completing the division and subtraction, we add the remaining number to our current result. So, \(17 + 1\) results in \(18\). Addition is straightforward but must be done at the correct step to ensure an accurate final answer.