[MUSIC PLAYING] Let's look at our objectives for today. We will start by introducing the importance of order of operations. We'll then look at PEMDAS, which is the acronym for remembering the order of operations. And finally, we'll do some examples using the order of operations.
Let's talk about the importance of order of operations. In math, an operation is a way to combine numbers, such as addition or subtraction. You can think of it as a calculation between two or more numbers. We have to have an agreed upon order for performing operations so that when there are several operations in an expression or an equation, everyone simplifies or solves in the same way to get the correct answer.
So the order of operations is the rule that tells us the order to perform those operations. The correct order of operations is parentheses, exponents, multiplication, division, and then addition and subtraction. We'll go more into depth with these operations in a moment.
Here's an example of how we would use the order of operations to simplify an expression. We want to simplify 10 plus 4 divided by 2 minus 1. Using order of operations, we start with division. So we divide 4 divided by 2, which is 2. And our expression is now 10 plus 2 minus 1. We then move on to addition and subtraction. So we have 10 plus 2, which is 12, and then 12 minus 1, which is 11.
Here's what happens if we simplify in the wrong order, moving just from left to right and not using the order of operations. We would start with 10 plus 4, which is 14. 14 divided by 2 is 7, and 7 minus 1 is 6, which is incorrect. Not the correct answer. So we can see that without having a standard order of operations, we can find two different answers. Order of operations is used when performing all mathematical calculations, especially when solving equations and evaluating functions, which will be discussed in this course.
Now let's look a little bit more closely at PEMDAS, which is the acronym we use to remember the order of operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. There are a few important things to remember when using PEMDAS. First, parentheses includes other grouping symbols, such as brackets or radical signs. Multiplication and division are performed together from left to right in the order that they appear. And similarly, addition and subtraction are performed together from left to right in the order that they appear.
So let's look at an example of using order of operations. We want to simplify the expression 8 minus 7 minus 5 squared plus 3 times 2. We start with our parentheses. In our parentheses, we have 7 minus 5, which is 2. There are another set of parentheses at the end of the expression around the 2, but in this case, the parentheses are telling us that we multiply the 3 by the 2, so that operation comes later. So now our expression is 8 minus 2 squared plus 3 times 2.
Our next operation is exponent, so we do the 2 squared, which is 4. So now our expression becomes 8 minus 4 plus 3 times 2. We now move onto multiplication and multiply 3 times 2, which is 6. So we now have 8 minus 4 plus 6. Finally, we have addition and subtraction, which we perform from left to right in the order they appear. So we first subtract 8 minus 4, which is 4, and finally, add 6, which gives us 10.
We're going to do another example using order of operations, but before we do, let's look at a common mistake that people make with negative numbers and exponents. Let's look at two similar, but different, equations or statements. In our first equation, we have negative 3 in parentheses squared, which equals a positive 9. Negative 3 squared means negative 3 times negative 3, which is a positive 9.
In the second equation, we have a negative 3 squared, which equals negative 9. That's because the negative here is like a negative 1 being multiplied by the 3 squared. So the answer becomes negative 9.
So now let's look at another example showing how to avoid this common mistake. We want to simplify the expression negative 4 squared plus 12 divided by 2 times 3. We start with our exponent, 4 squared. Here again, the negative in front of the 4 is like a negative 1 being multiplied, so we don't include it in our exponent operation. Instead, we have 4 squared, which is 16. So our expression becomes negative 16 plus 12 divided by 2 times 3.
We now move on to multiplication and division, which we perform from left to right. So we first divide 12 by 2, which gives us 6, and then multiply 6 times 3, which is 18. So now our expression is negative 16 plus 18. Finally, we add negative 16 and 18 for a final answer of 2.
Let's go over our important points from today. Make sure you get these in your notes so you can refer to them later. Using the order of operations is important so that expressions and equations are simplified to find the correct answer. We use the acronym PEMDAS to remember the order of operations. Multiplication and division are performed together from left to right in the order that they appear. And addition and subtraction are performed together from left to right in the order which they appear.
And finally, when raising a negative number to an exponent, parentheses must be used around the negative sign as well. So I hope that these key points and examples helped you understand a little bit more about order of operations. Keep using your notes and keep on practicing, and soon you'll be a pro. Thanks for watching.
