Order of Operations with Parentheses, Brackets, and Braces | PEMDAS | Math with Mr. J

In this video, I'm going to cover the order of operations, and specifically, we're going to take a look at problems involving parentheses, brackets, and braces. Now remember, as far as the order of operations, we have parentheses and other grouping symbols like brackets and braces, then exponents, then multiplication and division, and lastly, we have addition and subtraction. So taking a look at parentheses, brackets, and braces, we have parentheses, brackets, and then braces. Now all of these are grouping symbols and take priority within the order of operations. They come first. You can think of brackets and braces just like parentheses. Again, they are grouping symbols, just like parentheses. Let's take a look at our examples and see how to work through problems involving multiple grouping symbols, and you may hear this called nested parentheses. Nested parentheses just means that parentheses are inside of other grouping symbols, so grouping symbols inside of grouping symbols. Let's jump into number one, where we start with brackets, and then within the brackets, we have 28 minus, and then in parentheses, 6 plus 4, end parentheses, and then we end the brackets divided by 2. Let's work through the order of operations. Do we have any parentheses or other grouping symbols? Yes, we have parentheses and brackets. So we have parentheses nested within the brackets. When we have a problem like this with multiple grouping symbols, we always start with the innermost group. These parentheses right here, so 6 plus 4, this is the innermost group, so this is where we need to start. 6 plus 4 is 10. Now we need to bring down everything we did not use. So we have 28 minus 10 in brackets divided by 2. So now we have brackets, 28 minus 10, end brackets, divided by 2. And now we can continue to work through the order of operations. So do we have any parentheses or other grouping symbols? Yes, we have brackets. So that's what we need to do next. We have 28 minus 10 within those brackets. 28 minus 10 is 18, so we have 18, and then bring down everything we did not use, so divided by 2, and we end with 18 divided by 2. That is 9. And this is our final answer. Final answer, 9. Let's move on to number 2, where we have 50 minus, and then braces, then brackets, 5 times, and then parentheses, 7 plus 1, end parentheses, end brackets, plus 3 squared, end braces. We have multiple grouping symbols here, parentheses, brackets, and braces. So we need to start with the innermost group. That's going to be these parentheses right here. We have 7 plus 1 within those parentheses. So that's where we start, 7 plus 1 is 8. Bring down everything we did not use. So we have 5 times 8 within brackets, plus 3 squared, and this is all within braces. And then we have 50 minus whatever we get within those braces. Now we have 50 minus, and then braces, then brackets, 5 times 8, end brackets, plus 3 squared, end braces. Let's continue to work through the order of operations. Do we have any parentheses or other grouping symbols? Yes, we have both brackets and braces. So we need to do the innermost group next. That's going to be the brackets. We have 5 times 8 within the brackets. 5 times 8 is 40. Bring down everything we did not use. So we have 5 times 8 within brackets, plus 3 squared, and this is all within braces. Then we have 50 minus whatever we get within those braces. Now we have 50 minus, and then braces, 40, plus 3 squared, end braces. So let's continue to work through the order of operations. Do we have any parentheses or other grouping symbols? Yes, we still have those braces. So that's what we need to work within next. We have 40 plus 3 squared within the braces. So we have addition and an exponent. Exponents come before addition, so we need to do 3 squared next. 3 squared means 3 times 3. So 3 squared is 9. So we have 9, and then 40 plus 9, and this is within braces still. And then we have 50 minus whatever we get within those braces. Now we have 50 minus, and then braces, 40 plus 9, end braces. So we need to do 40 plus 9 next. 40 plus 9 is 49. Bring down everything we did not use. And we now have 50 minus 49, and that's what we end with. 50 minus 49 is 1, and this is our final answer. Final answer, 1. So there you have it. There's how to work through order of operations problems involving multiple grouping symbols, so parentheses, brackets, and braces. Just remember, start with the innermost group and work from there. I hope that helped. Thanks so much for watching. Until next time, peace.