Okay, before we go on to the next section, I want to take a few minutes and explain a few more topics. So the first one I want to kind of explain or present is called honor of operations. An order of operations is that when I have a mathematical equation, and I have different operations in there is an order in which I want to perform them. So for instance, up here, if I have powers and routes, I want to do that first. So I want to do that mathematical operation first. Then if there's multiple patients And division.

I'll do that next. And last addition and subtraction. All right, so let's look at some of these examples. This one here, three squared times four. Well, what do I have? I have a power and multiplication.

So what do I do first? I do my powers. three squared is a power. Three times three is nine. There we go. And so then I will do nine times four, because multiplication is a second.

Now I don't have any addition and subtraction. So therefore I'm done. And my answer is 36. All right, let's look at the next example right here. And we have six times two plus three. Well, again, going up here looking I do powers and routes first.

Well, I don't have any. So now I'll do multiplication and division, which I do six times two plus three. So I'm going to multiply six times two, and I get 12. And then I do my addition or my subtraction. Well, in this case, I have a plus 312 plus three is 15. And here's my answer.

All right, let's look at the last one here. three squared times four plus five. Okay, the first thing I do is my power. three squared is nine. All right, then I multiply nine times four, plus five, and my answer is 41. So first, I do my powers three squared Nine.

Nine times four, even though I didn't show it is 36. And then I'm going to ask For, and that's going to equal 41. All right. So there you go. Just follow this. We're going to expand upon this in the next slide.

But before we go on, just take a minute, I've given you a couple of exercises, see if you can do them. And when you go to the next slide, you'll see the answers. Okay, let's look at the answers here in the exercises and what I'm, what I've done is I've brought down the calculator. Okay, hopefully you've tried to do it by hand. Okay, we let's show you how to do it with the calculator. Because basically, you're going to be out in the field.

Once you know how to do it by hand, you'll get this. You'll know if you've done something wrong. You can estimate it once you've done it by hand. You can kind of estimate the answer that way when you look at the calculator if trilly off, you'll say, wow, that's not right. Let me do it again. So let's let's, let's do the first one here, down here, this 1666 squared divided by two plus eight.

And let's use the calculator. Again, I'm using the calculator that is with the Windows operating system. You can use a, a handheld calculator. There's many types. I use this one because it's convenient. It's not better than anything else.

And I'm in scientific mode. Let me I think I can change the mode here. And let me go back into standard. And I still love I still have the functions that I want. All right. So let's, let's go six on doing the first one.

Sixth raise to the second power, which is this one. I get 36 If you look, what's the next thing I want to do? I want to divide by two. So I divide by two. All right, and now I'm going to add eight, so plus eight equals 26. So right here, six raise to the power of two divided by two plus eight is 26.

Alrighty 26. Alright, let's do this exercise the square root of 16 times four minus three. Well again, let's type in 16 square root symbol. All right, now I multiply by four times four, and then I'm going to subtract three equals 13. So my answer right here, the square root of 16 times four minus three equals equals 13. All right, so let's clear the calculator.

And let's do the last one here. square to nine divided by three, and here it is right here. So again, I plug in nine, find my square root, I divide by three, and I add one equals two. So the square root of nine divided by three plus one equals two. All right, so let's, we're going to go on, we're still in order of operations, we're going to look at something else, when we have brackets, parentheses and so forth. And that'll be on the next slide.

Okay, on this slide here was still on auto evocative. When we have things called parentheses, brackets and braces, and we do them in the order of one, two and three. Now, if you remember from the previous slide, all right, which I'm showing here again, we do powers and routes first. We do multiplication and division next, and addition and subtraction last, okay? But we do that inside the bracket, so are the parentheses so they take preference. So for example, right here.

Alright, so, again, looking at this, I've got doing this example here. Okay, two plus three. squared, but we do what's in the parenthesis first. So what do we do? We add two plus three, and we get five. Then we bring, we bring the five to the second power, which is 25.

And then we add our four. So answers 29. So again, we do what's in the parenthesis first, two plus three is five. All right. Now notice we have no parentheses, brackets or braces. So we go back to the original, or the previous slide where we do powers and routes first.

So now I have Five to the second power, which is 25. I don't have any multiplication, I just have addition. So five plus four is 29. My answer is 29. All right, so we do what's in the parenthesis, bracket, brackets, and braces. All right.

First, after we clear them, then we do our powers and our roots first, second, our multiplication or division. And then lastly, subtraction or addition. All right, let's clear this slide and do the next one. All right, the next example is right here. All right. So, if I'm looking at it, here we go.

Right here, looking at this part first. Okay, so parenthesis first, what do I want to do? I want to add two plus three because it's in the parenthesis. Two plus three is five. Here we go. Okay.

Now I'm in my brackets. So I do everything in the brackets first, but I follow the rules, powers and square roots first, then I do multiplication or division, then I do subtraction, or addition. So again, let's look at it. Oh, look at this. five squared is 25. I do that first.

Now I do look at it. I have No more powers. No more roots in my brackets between here. So what do I do next? Multiplication and division. So if you look, I've got three times 25.

And that's 75. All right. And if I look here, the only thing left is addition, which is the last step. So 70 plus five plus four is 79. And that's my answer. So again, all right.

When I have parenthesis, brackets, or braces, I do what's in the parentheses, brackets or braces as follows up here, parentheses first brackets second braces third And I follow what we talked about in the previous slide. Powers and routes first. Multiplication and Division second, addition and subtraction third. Okay, so here are the answers right here. Let me get my pen out. And if we look at this one here, okay, seven minus three, or we can use a calculator, I can do it in my head, but seven minus three is what is four, four plus three equals seven.

All right, all right over here. All right, I've got two plus three in parentheses. So two plus three is five. All right, what do I do? Secondly, what's in the bracket six divided by three is what? Two, five times two equals 10.

That's my answer. Over here again. Okay, looking at the last one here. Again, follow it in order. Okay, parenthesis first. Two plus three is what five.

Then we do bracket second six divided by three is two. I'm doing this in my head. Alright. And so now we've got braces, but look at what we got in braces. We got five times two plus seven right here. All right, so we go back to the first slide, where we do policies and rules.

First, then multiplication or division. Ah, look at this. I got five times two, five times two is what 10 then I do addition or subtraction 10 plus what? This seven here, what do I got 17 ah 17 times two because this here condenses down to 17. So, when I do all the operations between the braces here, that is 17. All I got to do is multiply 17 by 217 times too is what 34.

So my answer is 34. All right, again, step by step, parenthesis, braces, brackets, okay? And I look for instance, if I look at my parentheses first, then I go to my order of operations previously, powers and roots first, multiplication, division, second, addition, subtraction third, and I just keep following that. All right, keep following it. All right, let's go on. Okay, I just want to take a minute and go over that last example.

Just to make sure that you understand. Here we go up here. I put this on the white my whiteboard here and again, We have right here, we have parentheses, brackets and braces. Okay, we do parentheses first. So if you look here, what I have is braces, braces, parenthesis, parenthesis, bracket, bracket, so I do what's in the parenthesis first, which is right here. Okay, so now two plus three is what is five.

All right, I do what's in my brackets second. six divided by three is two. Okay. I'm going to break still bring this here times too high. So now We we have our braces here, here, in here, here, here. All right.

I want to do what's inside there. But if you remember at the very start, what do we do? We do. Powers and routes first. Multiplication and Division, second, addition, subtraction last. Well, I don't have any powers or roots here, but I do have multiplication.

Five times two. Five times two is 10 plus seven. Okay. So now I finished what's in my braces 10 plus seven is 17 times two equals 34. And that's my answer. Look at this again if you have some problems, but I just wanted to clear it up.

And with that said we're going on. When we have a fraction, like I'm showing you here, what we need to do is we do all addition and subtractions in the numerator, or the denominator must be must be completed before we go on. And we know that the upstairs right here that's my numerator and the denominator, the downstairs anything below the line. That's my denominator. So let me clear the slide. And if you look at the example here, what are we doing?

We're completing this operation first. All right? four plus five is nine over three plus two. Okay? Again, we go back to what we said, powers and roots first. Then multiplication or division second.

Well, isn't that a division? Nine over three. And here we go. All right, so now we do the last part of it, either addition or subtraction, which we have here. Two plus three, and my answer is five. All right, take a minute.

Do the extra assizes here and here, and we'll show the answers on the next slide. Okay, here we are, it's 730. But just to make sure you understand, eight plus 12 is what? 20. All right. 20 divided by five is what?

Four. Four plus three equals seven. All right? Right. So, right here, that becomes a four when I do my operations, then I add the three right here. And obviously four plus three is seven.

Let's let's look at this one over here. The answer is 30. But then again, what do I need to do? Well, I again, I'm not Got a parenthesis right there. So four plus eight is what? 10 divided by, I'm sorry, 12 divided by six plus three times six.

All right, well 12 divided by six is two, plus three plus three is five. All right, so what do we got? We got five times six, and add equals 30. And we go, there's my answer. Okay, so take a look at them. Arm we've got one or two more.

Very, very quick points to make and we're off to a new section. All right, right now, we're going to Talking about rounding off a number. And just let's just look at these two rules at the beginning here when a digit dropped to six or more, raise the last digit by one. And when the digit dropped is four or less, keep the last digit the same. So let's look at these examples here. And what I have is round off 469 469 to the nearest 10th place.

Well, right there is my 10s place. All right, and I've got 469. All right, so let's look up here when the digit dropped is six or more, raise the last digit by one. All right, so I'm rounding off to the nearest 10th place right there. So this number is either going to be 460 or 470? All right, and depending on which one I choose is determined by this last number, the nine.

So let's go look at my rules. And I think we want one because look, when the digit drop is six or more, raise the last digit by one. Okay, well, the digit drop is nine. It's greater than six. So what we want to do is raise the last digit, in this example six to seven. So my answer is 470.

If I round off to the nearest 10th place again, which is right here, then the answer is 470. Let's again look at look at this one. Okay, I've got 461 461. And again, I want to round off to the nearest 10s place. Again, right there. Let's look at the digit afterwards.

It's a one. Let's look at here when the digit drop is four or less, keep the last digit the same. Well, one is definitely less than less than four. So I want to keep six the same. So in this case, my answer is 460. All right.

So whatever place we want to round off to, we go to the next digit down. In this example, we want to round off to the 10s. So we go to our ones place and if six or more. We raise the 10s up the digit in the 10s. Place up one. If it's four or less, we keep that digit the same.

That's it. That's it. Now what happens when we got five hits right smack in the middle? Well, we'll go to the next slide and see. Okay, once again, before we go on, I'm just showing you the answers to that. Okay, in this example, we want to go to the hundreds we round a round off to the hundreds place, which is this place right here.

But look at what we've got with our hundreds places, followed by a five and a five a smack dab in the middle. So there's some rules gear that Tell us what to do. So let's look at the first one here. The five is followed by digits more than zero, then raise the digit before the five by one. Well, let's look at this one here. We got 4651.

Well, the digit following the five is one that is certainly greater than zero. Okay, so now what do we say we then raise the digit before the five by one, which is again, this one. So we raise the six, which is the digit before the five by one, and we get 4700. Okay, same thing with this one here. All right. This we're going to the hundreds Place, we got a five right after the number six right there.

All right, nine is definitely greater than zero. So again, then raise the digit before the five by ones right here. All right, so we have again 4700. Let's look at this example. Here we got force 4750. And again, we want to round off to the hundreds place.

And let's look at this rule here. The second one, the five is followed by one or more zeros. You can raise the previous digit, only if it becomes an even number. So look at this 4750 Okay, five is followed by a zero right there. So I can only raise the number prior to the five. If it becomes an even number is seven odd or even seven is an odd number.

So therefore, I can raise the seven to eight. And I get this my answer. Let's look at the last one again. 4650. My five is followed by a zero. I can only raise the number prior to the five this one here.

If it becomes an even number will six isn't it? Even number, so therefore it stays the same. So my answer is 4600. All right, I'm rounding off to the one hundredths place here. I didn't write it down, but I'll do it there now, one hundredths place. Okay, take a few minutes and do these exercises.

The answers are all will be in the next slide. We're going to the 10 places on on all four of these, which is right here. All right, so stop the presentation, do the exercises, and you'll see the answers on the next slide. Okay, here are the answers right here. I'm Dan, you have any questions send me an email. This was pretty straightforward.

Okay, the last subject here is a valuation of formulas, I'm really not going to spend a whole lot of time on this. And the reason being is when we get when you take some electronic circuit analysis, we go into this in a deep way. I just want to introduce it here. But basically, we've got some some variables are some formulas with letters in there. And then we assign numbers to them. Like for instance, I equals two r equals five.

So a V equals i times R, and I say I equals two and r equals five, then two times five is 10. So V equals 10. And that's it. up. That's that's basically it. Right now, we do get a little bit more complicated, but again, that's in the circuit analysis portion.

And that's all I'm going to say I give you some examples here and find up v. And basically what you would do is you would just plug these values in to this formula, okay? v equals i times R, and you would get the, get the answer for V as I'm showing you here. Okay. What I also do is give you another rough, give you another formula i squared times R and give you a value of i and are right here and if you plug it in, you're going to get 16 And again, I give you some more examples that you can do. All right.