The order of operations is a rule that reports the correct sequence of steps to assess the mathematical expression. We can recall the order using PEMDAS: brackets, exhibits, multiplication and division (from left to right), adding and subtraction (from left to right).
Now that we have the foundations of the Order of Operations, let's try to solve a really hairy and monstrous problem. So, we have all kinds of brackets and numbers flying around. But in any of these problems, you just need to breathe deeply and remember, we will first make brackets. Parentheses. P for brackets. Then exhibitors. Do not worry if you do not know what indicators are, because they have no indicators. Then you are going to make multiplication and division. They are at the same level. Then you make addition and subtraction. So some people remember Pemdas. But if you remember Pemdas, remember multiplication, division, the same level. Adding and subtraction, also at the same level. So, let's look at the fact that the order of operations says that this should evaluate. So, the first thing we are going to do is our brackets. And we have a lot of brackets here. We have this expression in brackets right there, and then even inside we have these brackets. Thus, in our order of operations it is said, look, first make your brackets, but in order to evaluate these external brackets, this orange thing, we will have to evaluate this thing on yellow right there. So, let's evaluate all this. So how can we simplify this? Well, if we look at this only inside, the first thing we want to do is simplify the brackets inside the brackets. So, you see this 5 minus 2 right there? We are going to do this first, no matter what. And this is easy to evaluate. 5 minus 2- This is 3. And therefore it simplifies it, I will take this step by step. As soon as you get it, you can take a few steps at the same time. Thus, it will be 7 plus 3 times more than 5 minus 2, that is 3. And they all have brackets around it. And, of course, you have all the things from both sides- the separation of 4- no. Oops. This is not what I want. I wanted to copy and insert. I want to copy and insert it right there. So copy, then ... no, it gives me the wrong thing. It would be easier, let me just rewrite it. This is the easiest thing. I have technical difficulties. Thus, 4 times divided by 4 times 2. And on this side you had 7 times 2 plus this piece in orange brackets. Now at any step you just look again. We always want to make brackets first. Well, you continue to do, and is there really no brackets left? Thus, we must evaluate these brackets in the greenhouse here. So, we must first evaluate this thing. But in order to evaluate this thing, we must look inside this. And when you look inside this, you have more than 7 3 times 3. So if you have only 7 C plus 3 times 3, how would you rated it? Well, look back at your order of operations. We are here in brackets, so there are no more brackets inside this. So the next thing we have to do is no indicators. There is multiplication. So, we do this before you do any supplement or subtraction. Thus, we want to do 3 times 3 times before adding 7. So it will be more than 7 and 3 times 3 we want to do in the first place. We want to make multiplication first. 7 plus 9. It will be in orange brackets. And then you have 7 times 2 with a plus, on the left side. You have a divided by 4 times 2 on the right side. And now this is a thing in brackets, because we still want to make brackets first. It is quite easy to evaluate. What is 7 plus 9? 7 Plus 9 - this is 16. And therefore, all that we have simplifies up to 7 times 2 plus 16, divided by 4 times 2. Now we have no brackets, so we do not need to worry about P in Pemdas. We do not have E, there are no indicators in this. So, we go directly to multiplication and division. We have multiplication, we have some multiplication there. We have some unit and multiplication there. Thus, we must do this as follows before we make this addition right here. Thus, we could do this multiplication. We could do this multiplication. 7 times 2 - 14. We will wait to make this addition. And then here we have 16, divided by 4 times 2. This is priority in addition, so we will do this before we make this addition. But how will we evaluate it? Do we first make a separation or first multiplication? And remember, I told you in the last video, when you have 2-- when you have several operations of the same level- in this case, separation and multiplication, they are at the same level. You are best right left to the right. Or you should go left to the right. Thus, you make 16, divided into 4-4. So this thing is directly here, simplify 16, divided by 4 times 2. It simplifies up to 4 times 2. This thing is green. And then we will want to make the ability then. So it goes
Now that we have the foundations of the Order of Operations, let's try to solve a really hairy and monstrous problem. So, we have all kinds of brackets and numbers flying around. But in any of these problems, you just need to breathe deeply and remember, we will first make brackets. Parentheses. P for brackets. Then exhibitors. Do not worry if you do not know what indicators are, because they have no indicators. Then you are going to make multiplication and division. They are at the same level. Then you make addition and subtraction. So some people remember Pemdas. But if you remember Pemdas, remember multiplication, division, the same level. Adding and subtraction, also at the same level. So, let's look at the fact that the order of operations says that this should evaluate. So, the first thing we are going to do is our brackets. And we have a lot of brackets here. We have this expression in brackets right there, and then even inside we have these brackets. Thus, in our order of operations it is said, look, first make your brackets, but in order to evaluate these external brackets, this orange thing, we will have to evaluate this thing on yellow right there. So, let's evaluate all this. So how can we simplify this? Well, if we look at this only inside, the first thing we want to do is simplify the brackets inside the brackets. So, you see this 5 minus 2 right there? We are going to do this first, no matter what. And this is easy to evaluate. 5 minus 2- This is 3. And therefore it simplifies it, I will take this step by step. As soon as you get it, you can take a few steps at the same time. Thus, it will be 7 plus 3 times more than 5 minus 2, that is 3. And they all have brackets around it. And, of course, you have all the things from both sides- the separation of 4- no. Oops. This is not what I want. I wanted to copy and insert. I want to copy and insert it right there. So copy, then ... no, it gives me the wrong thing. It would be easier, let me just rewrite it. This is the easiest thing. I have technical difficulties. Thus, 4 times divided by 4 times 2. And on this side you had 7 times 2 plus this piece in orange brackets. Now at any step you just look again. We always want to make brackets first. Well, you continue to do, and is there really no brackets left? Thus, we must evaluate these brackets in the greenhouse here. So, we must first evaluate this thing. But in order to evaluate this thing, we must look inside this. And when you look inside this, you have more than 7 3 times 3. So if you have only 7 C plus 3 times 3, how would you rated it? Well, look back at your order of operations. We are here in brackets, so there are no more brackets inside this. So the next thing we have to do is no indicators. There is multiplication. So, we do this before you do any supplement or subtraction. Thus, we want to do 3 times 3 times before adding 7. So it will be more than 7 and 3 times 3 we want to do in the first place. We want to make multiplication first. 7 plus 9. It will be in orange brackets. And then you have 7 times 2 with a plus, on the left side. You have a divided by 4 times 2 on the right side. And now this is a thing in brackets, because we still want to make brackets first. It is quite easy to evaluate. What is 7 plus 9? 7 Plus 9 - this is 16. And therefore, all that we have simplifies up to 7 times 2 plus 16, divided by 4 times 2. Now we have no brackets, so we do not need to worry about P in Pemdas. We do not have E, there are no indicators in this. So, we go directly to multiplication and division. We have multiplication, we have some multiplication there. We have some unit and multiplication there. Thus, we must do this as follows before we make this addition right here. Thus, we could do this multiplication. We could do this multiplication. 7 times 2 - 14. We will wait to make this addition. And then here we have 16, divided by 4 times 2. This is priority in addition, so we will do this before we make this addition. But how will we evaluate it? Do we first make a separation or first multiplication? And remember, I told you in the last video, when you have 2-- when you have several operations of the same level- in this case, separation and multiplication, they are at the same level. You are best right left to the right. Or you should go left to the right. Thus, you make 16, divided into 4-4. So this thing is directly here, simplify 16, divided by 4 times 2. It simplifies up to 4 times 2. This thing is green. And then we will want to make the ability then. So it goes
