Join Karin Hutchinson for an in-depth discussion in this video Order of operations: Parentheses and exponents, part of Foundations of Algebra: Pre-Algebra.
- In this lesson, we're going to continue our study of the Order of Operations, and this time we're going to focus on Parentheses and Exponents. Don't forget that when you use the order of operations you can think of the acronym PEMDAS. Let's walk through a problem together. For this problem, we're first going to start by looking for Parentheses, and I do see Parentheses, and this time there is an expression inside. There are multiple operations going on inside of the Parentheses, so we must continue to follow the order of operations.
I'm going to look for Exponents, and I see that I do have the exponent 2, therefore, I'm going to evaluate 3 squared first. Three squared is 9, and I'm going to bring down the rest of the problem so that I can continue solving in the correct order. Now we're going to continue working inside of the Parentheses.
Since I do not have any other Exponents, I'm going to now look for Multiplication or Division. In this problem, I do have Multiplication inside of the Parentheses. We know that 5 x 2 is 10. And then again, I'm going to bring down the remaining problem. And again, I'm still working inside of the Parentheses. We now have just Addition left, 3 + 10 is 13 and 13 + 9 is 22.
Inside the Parentheses we now just have Addition left, so I'm going to add 3 + 10, which is 13, + 9 which is 22. I'm going to keep the Parentheses, because this set of Parentheses is going to indicate that I need to multiply. I need to multiply 3 x 22. It's simply separating the numbers to show Multiplication. Now that I've completed the Parentheses, I'm going to look for any Exponents.
Since I do not have Exponents, I'm going to move on to Multiplication or Division, whichever comes first. I have both, and Multiplication comes first. So I'm going to start with 3 x 22, which is 66. And then I'm going to bring down the rest of the problem, and I notice that I still have Division. So I'm going to go ahead and divide. Ten divided by 5 is 2, and I'm going to bring down the rest of the problem.
And now I have just Addition and Subtraction left. Since Addition comes first, I'm going to go ahead and add. Two + 66 is 68 and then 68 - 2 is 66. And the final answer to this problem is 66. As you can see, there are times that when you're using the order of operations you actually have to start in the middle of the problem in order to solve it correctly.
In the next video, we will focus on using the order of operations with other grouping symbols.
This course includes practice challenges and worksheets, as well as tips for educators who are helping students master pre-algebra for Common Core. Karin Hutchinson also helps you evaluate, write, and simplify expressions, and solve word problems and complex algebraic expressions.
- Adding integers
- Multiplying and dividing
- Understanding the order of operations
- Evaluating expressions
- Breaking down word problems and algebraic expressions
- Distributing positive and negative numbers
- Simplifying expressions