Know the rules of the order of operations? A central concept in pre-algebra/algebra, these rules clarify which actions in any algebraic expression should be performed first. Let’s review what the rules are and why they are important. Then, you can test your knowledge with a spreadsheet quiz!
Why important?
Why do we learn the order of operations? These rules are important because they ensure no calculation confusion throughout the math, science, technology, and programming languages. Imagine if the rules did not exist: somebody could interpret the same algebraic expression very differently from someone else. Multiple answers would arise, and there would be chaos! With these rules, everyone who solves the same expression will come to a unified answer!
What is the order of operations?
The order of operations is as follows:
- Parentheses ( ) and other grouping symbols such as brackets { }
- Exponents and roots ^
- Multiplication x and Division / from left to right
- Addition + and Subtraction –– from left to right
When you are solving an expression that includes various operators, first solve the operator that comes up higher on the list above. Both the multiplication and division operators are ranked the same, so which one would you perform first? Solve the operator located from the far left and work your way to the right. The same applies for addition and subtraction.
Can you show me an example?
Let’s take a look at the 2 algebraic expressions below.
- 12 / 2 x 3
- 12 / (2 x 3)
In the first example, there are two operators: division and multiplication. Both are ranked the same, so we would complete the left-most operator (division) first. To solve the first example, we’d do the following; 12 / 2 = 6. Then 6 x 3 = 18. The final answer is 18. Take a look how this answer would change the moment you add parentheses. Parentheses ranks higher than multiplication and division, so we first perform the parentheses. Let’s solve this together. (2 x 3) = 6. Then 12 / 6 = 2. The final answer to the second example is 2.
Let’s test our knowledge!
Once you understand the concept, take the quiz shown below! To take the quiz, first open the Google spreadsheet by clicking here: Order of Operations. Once you open the Google spreadsheet, make a copy of it onto your Google Drive. Then, let’s solve it using only your head and/or a piece of paper! (No calculators, please!) Once you think you have the correct answer, enter it in the “Answer” column. If correct, the cell will be highlighted in green!
Do you use a mnemonic or learning technique to help you remember these rules? Let us know in the Comment box below!