Thank you. I'm Joel Redford. This is the carpenter class here at Muscle Shoals Career Academy.
Today we're going to talk about construction math. This goes with the NCZER module 00. If you're in my class, you'll be getting a test on this in the next few days. Some of the problems that I'm going to work on the board as examples, they're similar to what you'll see on the test.
They're not the exact problems that you will see on the test. Also bear in mind that you will not be allowed to use a calculator on this test. So all this has got to be worked out long-hand.
Um. One thing I do want to say is some of the concepts that are covered in this module are pretty elementary, so I'm not going to spend a great deal of time on them. If you need extra instruction on some of this stuff, you can contact me, get with me outside of class and we'll work on it, or you can do a little research on your own and go about it that way.
So here we go. Okay, as I said, some of the stuff that's covered in this module is elementary. The first two things right out of the gate is addition and subtraction. And I'm not going to spend any time going over addition and subtraction.
I feel confident that most of my students, if not all of my students, can do simple addition and subtraction without a calculator. So we're going to go into multiplication, which is also sort of elementary, but it may be a little... It may have been a while since some of you have done this without a calculator, so I'm just going to hit it briefly and then we're going to keep going. Alright, the first problem that we've got is 374 times 26. So, okay. So, we've got 374 times 26. Start off from the left right hand side.
6 times 4 is 24. So we got a 4, carry the 2. 6 times 7 is 42, add the 2, that is 44. Okay, 6 times 3, 18 plus 4 is 22. Alright, now we've got to do our tens place next. So I'm going to put a placeholder here, just a zero. And then here we go with 2 times 4 is 8. 2 times 7 is 14. 2 times 3 is 6, plus 1 is 7. All right, now, all we have to do now is add these up.
4 plus 0 is 4. 4 plus 8 is 12. Put the 2 here and carry a 1. 1 plus 2 plus 4 is 7. And 2 plus 7 is 9. So the answer to this problem is 9,724. The next problem we're going to do is a long division problem. The problem is 2,638.
We're going to divide it by 24. Okay, now, right out of the gate, we know that 26 can be divided by 24, one time, 24 will go into 26 once. So we put our 1 here, 1 times 24 is 24. Now, 26 minus 24... 24 is 2. Alright.
Bring this 3 straight down here. We've got 23. 23 cannot be divided by 24, so we're going to put a 0 there. Now, 0 times 24 is 0. 23 minus 0 is 23. We've got to bring this 8 down here.
Now, 238 can be divided by 24 nine times. Okay? So 9 times 24 is going. 9 times 4 is 36. 9 times 2 is 18. plus your 3 that was left over, that gives you 216. Alright, so now we have to subtract this.
8 minus 6 is 2. 3 minus 1 is 2. So we've got 109 with the remainder of 22. Alright, as I said, this is sort of a... Elementary, hopefully everyone in here can handle this. If you need a little extra help, I would advise you to look at your chapter, section 2.70 and 2.80.
Okay, 2.8.0. Take a look in your book at those sections if you'd like to get a little bit of extra help. Okay, the next thing that we're going to talk about is the metric system.
Now, the metric... The metric system is used to measure length, weight, volume, and temperature. You might want to write that down.
The metric system is used to measure length, weight, volume, and temperature. So, speaking of length, let's just talk about what all is involved here. We have meters. Okay.
Okay. One meter is equal to... 100 centimeters.
You can remember that that term centi means 100, so that makes that easier to remember. Now, the next conversion factor that we need to remember is that there is 1,000... millimeters in a meter and there's also 10, let me write this a little bit different, but a more useful conversion factor would be that there are 10 millimeters in one centimeter.
Okay? So all of this is important. If I were you, I would write all of it down and make sure I had a good understanding of it before we take the test.
If you need a little, need to brush up on it a little bit, you can look at section 3.2.0, and that's on page 2.10 in your book, and it kind of takes all of this. and goes a little further in depth with it. I'm going to work just a few conversion problems, changing back and forth to millimeters and centimeters.
So here we go with the next portion. OK. First of all, let's convert 0.65 meters to centimeters.
Okay, now since we know that 1 meter equals 100 centimeters, we should be able to figure out from that that 0.65 meters equals 65 centimeters, right? And we also know that since 1 centimeter is equal to 10 millimeters, we can multiply. and that will tell us that we have 650 millimeters in .65 meters. Okay, like I said, pretty simple.
Let's do another one. Let's say we have 712 centimeters. Let's convert that to meters.
Okay? We know that there's 100. centimeters in a meter. Okay?
So what we would do is we would divide this 712 by 100 and that would give us 7.12 meters. Okay? So that's kind of how you convert back and forth on some of this stuff.
Now there's a couple of things I want you to remember. And I'll write them down up here. Alright, let's remember that a metric ruler...
It is divided into centimeters and millimeters. It's important that you remember that. You might want to write that down. Now, what fraction, let me ask you this one, this is something you'll need to know as well.
What fraction is a millimeter of a centimeter? So, one millimeter, okay, we know that there's ten millimeters in one centimeter, so one millimeter is equal to one-tenth. of a centimeter. Okay? We know that there's a thousand millimeters in a meter, so one millimeter is equal to one thousand of a meter.
It would be a good thing to remember right there. When we're speaking of volume in the metric system, we're talking about cubic. millimeters. We could be talking about cubic centimeters or we could be talking about cubic meters.
Remember the cubic is what's important. That's what tells us that we're talking about volume. When we talk about weight in the metric system, we talk about grams, and usually we talk about kilograms. If you need a little extra help on this, right now would be a good time for you to stop this video and look on page 2.19 and work the problems that you'll find there.
Okay? Okay, fractions is something we use all day, every day in construction. It's just part of what we do. So we're going to talk now just a little bit about fractions.
Some of this is elementary. again, so I'm just going to brush over it briefly. I'm sure most of you know how to manipulate fractions.
One good thing about fractions in the construction industry is we don't use any We don't use any sevenths, thirteenths, or anything like that. All we use is sixteenths, eighths, quarters, and halves. Sometimes in cabinet making and furniture building you may use thirty-seconds, but for the most part as it relates to just rough framing and general construction, those increments of an inch is all we will be using.
Now, when we're talking about fractions, just remember that the numerator is on the top and the denominator... It's on the bottom. A denominator tells us how many parts the whole is divided into.
So if we have a pie and we cut it into four parts, the denominator is four. The numerator tells you how many parts you're concerned with. So if we cut a pie into four parts and we kept three parts and gave one away, then the numerator would be three. Pretty simple.
Okay, one thing that we'll be doing is reducing fractions to their lowest terms. I'm not going to talk about that much, but if you need some help on it, you can look on page 2.22 in the book. When you add fractions, let's just say we're adding 3 eighths plus...
One half. We're going to find the lowest common denominator here, which is 8, and we're going to have to convert one half to eighths. So one half is the same thing as four eighths, right? And now we can come back here and keep this three eighths.
And all we had to do is add the 3 and the 4, which is 7, and we put that over 8. And that's our answer. If this was something like 14 sixteenths, we would just need to simplify the fraction and reduce it to its lowest terms. Okay, let's talk about subtracting fractions.
If we have 7 eighths and we want to subtract One fourth from that. Again, we have to get the lowest common denominator. We'll keep the seven eighths, because eight is our lowest common denominator. And then we will change this to two eighths.
So we have an 8th, an 8 on the denominator for both fractions. 7 minus 2, that's 5 eighths. Okay?
Easy stuff. Okay, let's multiply some fractions. Let's multiply 4 eighths, which is the same thing as 1 half, times 5 sixths. Okay, now we can go ahead right now. And simplify this fraction to one half.
I think I'm just going to go ahead with it just like it is. And what we do is we multiply this straight across. You multiply 4 times 5, that is 20. 8 times 6 is 48. Okay, now we're going to simplify that.
That'll go to... I believe 5 over 12 is a simplification of that. Yeah.
5 over 12 is the answer. So you just multiply it straight across, and then you reduce to your lowest terms. So pretty simple.
Incidentally, one... Easy way to multiply fractions by two in the construction industry, and it doesn't work if you're multiplying it times three or four. But if you want to double a fraction, all you have to do is take half of the bottom number. So if I wanted to double, say, one fourth, all I've got to do is change this fourth to a two. One half is twice as much as one fourth.
What you'll find if you go into the construction industry, you have to do that pretty frequently. You would have to double fractions and also divide fractions by two. This works the same way.
If you wanted, let's say we had 5 eighths, okay, and we wanted to take half of 5 eighths, we just double the bottom number, okay? So half of 5 eighths. is 5 16th. So just kind of a quick and easy way to do that and it'll help you if you remember that as you go through your career in the construction industry.
Okay, let's divide some fractions. Okay, let's say one half divided by three fourths. Okay, now something you can remember that will help you remember how to handle this is, I can write it right over here, I'm going to use a different color. We're going to keep it, change it, and then flip it. Alright, so how this relates to this math problem we got here.
The first term here we're going to change it. So I'm just going to bring it down here and make it one half. Now I'm going to change my sign here. So this is the change it. And then finally, I will flip it.
Okay? So we keep it, change it, flip it, and then all we have is a simple multiplication problem. 1 times 4 is 4. 2 times 3 is 6. And then we have to simplify that into 2 thirds.
And that's your answer. So, pretty simple as far as fractions go. If you need to... If you need a little brush up on this, look at page 2.25 and there's some information there about manipulating fractions.
One other thing that I want you to remember is this. The question that I would pose to you is one fourth. Of a dollar.
Okay. Just think in your mind, what is one-fourth of a dollar? Now, is it, or is it... Your answer is this, okay? Because what this means is .25 of a cent.
So that's one-fourth of a penny. That's one-fourth of one cent. Okay, this is 25 pence, which is one-fourth of a dollar. You're not going to take a note of that.
Make sure you understand that concept. It's a tricky little question, and it can get you. Okay, let's talk a little bit about decimals.
Now... Okay, let's add some decimals together here. Let's take 4.76 and we'll add a point. 8, 3, 4. And when you add decimals, remember you line your decimal point up.
And this is just a simple addition problem. 4 plus nothing is 4. 6 plus 3 is 9. 7 plus 8 is 15. So we've got a 5 here. Carry the 1. 1 plus 4 is 5. And you bring this decimal straight down. 5.594.
And subtraction works the same way. You just line the decimal points up here, and you've got a simple fraction problem, just like the same fraction problems we've been doing since we were in first grade. So I'm not going to do it with subtraction. problem.
If you need some help on subtracting decimals, look up in the book. It's I think on page 2.31 or 2.30, somewhere along in there. and it will tell you about adding and subtracting decimals.
Now, when we multiply decimals, it's just a little bit different, but it's not much. Let's multiply .507 and .022. All right, now what we do here is we kind of just ignore the decimals until the very end.
We take 2 times 7, it's 14, so we've got a 4, carry the 1. 2 times 0 is 0 plus 1. 2 times 5 is 10. Okay? Now, we've got a placeholder here. And we've got the same problem. 2 times 7 is 14. Carry the 1. 2 times 0 is 0 plus 1. And then 2 times 5 is 10. All right. Now, we add these together.
4 plus 0 is 4. 4 plus 1 is 5. 1, 1, 1. Now. Now we've got our trawl done. What we do is we count the decimal places.
We've got 1, 2, 3 there. And then add these two at 1, 2, 3 for a total of 6 decimal points. and move this 1, 2, 3, 4, 5, and 6. We've got a 0. We've got to add a 0 to that.
So our answer is 0.011154. Okay? Again, this should be... Nothing new to you.
You all should understand this completely. This is something we've all been doing for many years now, since we began with our educational careers. Now, we're going to talk about... dividing decimals.
This is probably just a little bit tricky just because most of us haven't done this in a long time. We're all kind of in the habit of just punching these decimals into, punching these problems into our calculators and just sort of letting the church roll along. All right, so the first thing, the first problem I'm going to do right now, I'm going to divide 22 into 44.5. Okay.
Now, when the decimal is in the dividend, which is the number that's being divided, you don't change anything. This is just a regular math problem that we've always done. Okay.
And 44 is divided by 22. That's two times. Two times 22, 44, 0. bring down the five here so that's our remainder so we got a two with the remainder of five now the next one is just a little bit different Because what we do is we'll take this point 2, 2. The divisor is now a decimal. And the dividend remains a decimal as well.
And this is the same. It's the same procedure if there's no decimal points shown in the dividend because let's just imagine that this is 44. Well, you've still got a decimal behind 44 even if you leave the 5 off. So just treat it the same. And what we're going to do is we're going to move this decimal over here two places.
One, two, right? Now since we moved it two places in the divisor, we've got to do it two places over here as well. So our decimal point's there. Now our problem is 4,450 divided by 22. Alright, so kind of the same deal that we did a minute ago. I'm going to erase some of these marks that I made here just to keep it from being so busy.
Okay, so 44 divided by 22 is 2. 2 times 22 is 44. Okay, that's 0. Bring down this 5. 5 cannot be divided by 22, so we've got a 0 here. 0 times that, that's 0. 5 minus 0 is 5. Bring down this 0 here. Now we've got something we can work with. 22 divided into 5. 2 times, so put your 2 up here, 2 times 22, that's 44. Subtract that, we've got a 6, remainder of 6. Okay, again, if you need to work on this outside of class, just look.
It's section 5.5, 5.5, so I'll write that down on page 2.33. Okay, to convert from a decimal to a percentage, you move your decimal 0.2 places. So if we've got 0.5, that is equal to 50%. All you do is add this decimal, move this decimal two places, that gives you 50%. If you've got, let's say, 23% and you want to convert that to a decimal, that's .23.
Okay, easy stuff, right? Study problems on page 6.11. I'm sorry, section 6.11, page 2.7.
Okay. We're getting sort of close to the end here. I want to talk with you just a little bit about a few geometric formulas. I'm not going to work problems like this. I'm just going to show you, make sure you write down and know the formula.
If you don't know how to use some of this, talk to me. Go on the Internet and figure it out. Okay, for the volume of a cube or a rectangular shape is length times width times height.
Okay, now this type of formula is very common in the construction industry. are calculating maybe the volume of the concrete that we need to fill a certain area, say a slab, kind of like the one I'm standing on now, you would use this formula. Now if we're going to figure the volume of a triangle is equal to one-half, and then we're going to The base times the height times the thickness.
Okay? That would be a three-dimensional triangle. Now some other formulas that are very useful in construction deal with area.
To figure the area of a square or a rectangle, we all know that's length times width. The area of a triangle is one-half base times height. I think that would put you in pretty good shape just as far as simple formulas for performing estimates in the construction industry. So there's just a few math problems that I kind of want to work through right quick just to show you how some things are done. And if I were you, I would take copious notes on this.
I want to make sure I understood these and make sure I can do similar problems when I take a test on it. The first problem I want to work with you is concerning just some multiplication. If you have a sheet of drywall, let's say one sheet of drywall. Weights 48.6 pounds. Okay, that means pounds in the old school.
It's hashtagged now, but it's pounds in the construction industry. Let's say we ordered 50 sheets. Okay. To figure the total weight, you would take 48.6 and we're going to multiply that times 50. Alright?
The answer to this is 2,430 pounds. Okay? Let's imagine this.
We need to mix 42 pounds of water. And for each pound, we have to add 0.03 liters of water. To figure out exactly how many liters of water we need to mix this mortar, we're going to take 42 times 0.03, and that's equal to 1.26 liters of water.
Okay, let's imagine that we're an electrician and we earn $25 for every outlet that we install. The cost of the material is $7.50 an outlet. A new addition needs $25.
12 hours. So how much money are we going to net? Now when you talk about net, that is your, what you've made after you've paid all your bills.
You can remember that by just thinking of what you caught in your... debt after everything else was paid out to suppliers or employees. So let's let's write this out.
We earned, say I earned, $25 per outlet and I'm going to use the symbol for outlets. That's what we, on a set of construction drawings, that's the symbol for outlet. Let's say our cost is $7.50 per outlet. How much money am I going to make on this?
First of all, one other thing, we need 12 outlets. Okay, first thing I got to do is figure out what is my, what's my gross pay. And I'm going to do that by multiplying 25 times $12 per hour.
25 times 12 is 300. Okay? Now, that's my... Ah.
Income, gross income. Alright, my cost... It's $7.50 times, again, my 12 outlets, okay, and that is equal to $90, okay?
Now... I subtract my cost from my gross income, and that gives me my net profit. So my net profit is $210, and that's your answer. Okay? Okay, let's see, let's do another one that's similar to this.
Let's say a carpenter has to build an addition that needs 150 studs. So we're going to do a little job and we need 150 studs. Now look, a stud is a structural member of a wall.
Each stud costs... $6.75. Okay, now we need to figure out what's the total cost.
So all we've got to do is take 150 studs and multiply that times $6.75. Okay? The answer to that is $1,000.
$12.50. Okay? Let's say I'm employed as a carpenter and I earn $20 an hour. I work 40 hours one week and then the taxes that I had to pay was $61 and $19.
Okay? Now, the way you do this is we take our rate of pay, which is $20 per hour, and we multiply that times 40. Okay? So, you can see that I'm employed as a carpenter. Alright, so at that rate I made $800 that week. Now, for my taxes, I had to pay $61.
Alright, so that would be $739. And that's for state, no that's for federal. I also got to pay the state of Alabama $19. And that would be $720. Okay, that's a conclusion of our lesson as it relates to an introduction to construction math.
Again, this is NCCER Module 102. I wish you good luck on your upcoming tests. If you have any questions, feel free to get in touch with me. Thank you.
To pretend she's all the more self-assured I know, I know, the dirty world Hello, hello, hello, hello Hello, hello, hello, hello Hello, hello, hello, hello Hello Yeah! Here we go! Yeah, It wasn't what I asked for, this gift of being the best I made a group, it's always been, always will, until the end Hello, You win, yeah!
I forget just why I'm tasting, yeah, I guess it makes me smile. I found it hard, it's hard to find the well, whatever, nevermind.