WEBVTT mathematics/algebra-1/smith
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Welcome back to www.educator.com.
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In this lesson we are going to take a look at the order of operations.
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As we will see the order of operations is a great way that we can start combining numbers and figure out what we should do first.
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This one involve things like what should we do at parentheses and exponents
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and when should we do our multiplication, division, addition and subtraction.
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When trying to simplify much larger expression with many different types of operations present, we have to figure out what to do first.
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Our order of operations gives us a nice run back on what we should be doing.
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The very first thing that we should do is work inside our grouping symbols.
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It means if you see parentheses or brackets work inside of those first.
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Then move on to simplifying your exponents, things raised to a power.
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Once you have both these in care, move on to your multiplication and division.
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If you see lots of multiplication and division next to each other, remember to work these ones from left to right.
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Now you have to do any remaining addition and subtraction.
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And again when it comes to which of those is more important simply work those from left to right as well.
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One handy way that you can remember of this entire list of that is the order of operations is to remember PEMDAS.
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PEMDAS stands for parentheses, exponents, multiplication, division, addition and subtraction.
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Let us try it out.
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A great way that you can remember these is Please Excuse My Dear Aunt Sally.
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I often heard a lot of my students use that one to make sure that they came out straight.
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Start with your parentheses and then move on to exponents.
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Be very careful if you are using this to memorize what to do first because sometimes when using it, it looks like multiplication is more important.
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But work these ones from left to right.
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The same thing applies to your addition and subtraction, work those from left to right.
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Sometimes you will deal with a larger expression that has a fraction in it.
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Even though you might not see some grouping symbols, think of the top and bottom as their own group.
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That means work to simplify the numerator and get everything together up there.
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And work to simplify your denominator, get everything together down there before we continue on with the simplification process.
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As a quick example, let us look at this slide.
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We have (-2 × 5) + (3 × -2) / (-5-3).
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I'm going to work on the top part as its own group, and the bottom part as its own group.
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Let us see what does this, -2 × 5 would give me -10, 3 × -2 =-6.
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On the bottom in that group I have that -5 -3 =-8.
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Okay -10 - 6=-16 and on the bottom I still have a -8.
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We worked to look inside each of those groups and simplify them using our order of operations in there.
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I simply have a -16 / -8 and that is a 2.
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Watch for those large fractions to play a part.
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Let us try some examples now that we know more about the order of operations and see how we can bring these into a much simpler expression.
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This one is ((5 - 2)² + 1))/ -5, we also write down PEMDAS.
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This will act as our roadmap as we are going through the problem.
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I want to look for grouping symbols or parentheses to see where I need to start.
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That 5 - 2 looks like a good area, we will do that first, 5 - 2 is 3.
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The only other grouping that I'm concerned with is the top and bottom of the fraction.
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There is only one thing on the bottom so I'm just going to now focus on the numerator.
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I can see that I have some exponents, I have a 3² in there.
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And now let us do that, 3² is 9, it is getting better.
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I want to move on to my multiplication and division.
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Looking at the top and bottom of the fraction individually I do not see any multiplication or division, I can move on.
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Addition and subtraction, why I do have some addition on the top, I put those together to get 10/-5.
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We are looking at 10 ÷ -5 and now I can say that my result is a -2, this one is done.
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You can see how we move through that order of operations as our road map.
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In this next one we want to evaluate a (-12 × -4/3) - (5 × 6) ÷ 3, let us go over the map.
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I do not see too much in terms of grouping but I do have this group of numbers over here.
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Let us go ahead and take care of those.
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Inside I have (5 × 6) ÷ 3, what should I do in there? I got multiplication and division.
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Those ones remember we are working from left to right.
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On the left side there I have multiplication then we actually do the division.
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5 × 6 is a 30, now do the 30 ÷ 3 and get 10.
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We have taken care of that grouping.
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I'm just going to copy down some these other things and then we will continue on.
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Our grouping is done, now on to exponents.
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I do not see any exponents here so now on to multiplication and division.
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We will do multiplication I got a -12 × -4/3.
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A negative × a negative would give me a positive, multiplying on the top that would be 48/3.
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Because of my fraction there, I do have some division I could take 48 and divided by 3 = 60.
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On to addition and subtraction 16 – 10 = 6.
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I have completely simplified this one and I can call it done.
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This next one I have (12 ÷ 4) × (√5 - 1).
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Starting with my grouping symbols and parentheses, I could consider everything underneath the square root as its own little group.
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Let us work on simplifying that, I'm writing here 5-1 is a 4,12÷ 4 × √4, taking care of the square root entirely.
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I'm looking at 12 ÷ 4 × 2, moving on do I see any exponents? No exponents.
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On to multiplication and division, this is that tough one.
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It is tempting to say that multiplication is more important but it is not.
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Simply work these guys from left to right.
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In this case, we are going to do the division first, 12 ÷ 4 is 3.
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Then we are actually taking that and multiply it by 2 and get 6, this one is completely simplified.
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Let us look at our example that involves lots and lots of different things.
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I have (8 × 4) - (3² × 5) + (2 × the absolute value of -1) / (-3 × 2/3) +1
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With so many different things in here we have to be careful in what to do first.
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I'm dealing with a fraction here I want the top as its own group and the bottom as its own
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and work inside each of those and try to simplify them.
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Let us look at the top a little bit.
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Inside of that I do not see any additional grouping symbols so I will try and do any exponents on the top.
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I do have a 3², let us change that into a 9.
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I have the absolute value of -1, might as well we go ahead and take care of that as well.
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We are doing a little bit of simplifying on the top, let us see if there is any exponents in the bottom.
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83 × 2³ and change out into -3 × 8 and of course we still have the + 1.
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Continuing on, looking at the top I do not have any additional parentheses, I do not have any additional exponents, multiplication and division.
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A lot of multiplication on the top, 4 × 8 would give me 32, 9 × 5 =45, 2 × 1=2.
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On to the bottom, -3 × 8=-24 and then +1, multiplication and division done.
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On to addition and subtraction and we are going to do this from left to right.
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I will do 32 - 45, what do we got from there?
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Let us imagine our technique for combining numbers that have different signs.
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I'm just subtracting here, I get a result of 13.
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The one that is larger in absolute value is the -45 so my result is a -13.
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Looking at the bottom-23 almost done.
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-11 at the top divided by -23, this one is completely simplified as 11/23.
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When dealing with multiple operations it is important that we do have a roadmap in order to get through all of these.
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Feel free to use PEMDAS also that you keep everything in order.
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As you use PEMDAS, if you get down to your multiplication and division then use them from left to right.
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If you get down to your addition and subtraction, again use those from left to right.
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