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Lecture Comments (5)

1 answer

Last reply by: Professor Eric Smith
Tue Aug 18, 2015 1:19 PM

Post by Terrance Goins on August 17, 2015

Evaluate if x = − 5, y = 3, and z = 2x2 − 3(y2 + 4z)
In this problem i am confused is it any error that the # 2 has disappeared from the problem shouldnt it be.
2(-5)second power -3 (3second power + 42) = ?

0 answers

Post by Mohamed Elnaklawi on April 11, 2014

Thank you! This lesson was very helpful, and you have a good way of teaching!   :-)

0 answers

Post by Professor Eric Smith on October 30, 2013

You are right, the large number is 16, but since we are taking away a smaller number 10, we will still be left with a positive number, or in this case a positive 6.

If the number were switched around, with say the larger number second like 10 - 16, then it would be -6.  Keep an eye on subtraction, the order makes a huge difference!  :^D

0 answers

Post by Asia Hassan on October 23, 2013

in example 2 the answer you told is 6  and I think it should be -6 because we are subtracting and the big number is 16 therefore and should have negative sign. I might be wrong, so plz tell me. Thanks.

Related Articles:

Order of Operations

  • The order of operations is a “road map” of what operations need to be done first in a problem.
  • The order of operations tells us to do the following
    • Work inside grouping symbols
    • Simplify exponents
    • Work on remaining multiplication and division from left to right
    • Work on remaining addition and subtraction from left to right.
  • You can memorize the order of operations by using PEMDAS. (Please Excuse My Dear Aunt Sally.)
  • When working with large fractions you can think of the numerator and denominators as their own group. In other words simplify the top and bottom of the fraction before taking care of the division that the fraction represents.

Order of Operations

6 + (72 − 33)/2
  • 6 + (49 − 27)/2
  • 6 + 22/2
  • 6 + 11
17
92 − [(4 ×7) + (32/2)]
  • 92 − [28 + 16]
  • 81 − 44
37
(√{64} − 23) ×21 + 62
  • (8 − 8) ×21 + 62
  • 0 ×21 + 36
  • 0 + 36
36
[(5 + 3 ×42 − 9)/(3 ×7 − 10)]
  • [(5 + 3 ×16 − 9)/(3 ×7 − 10)]
  • [(5 + 48 − 9)/(21 − 10)]
  • [44/11]
4
21/7 + 14 ×2
  • 3 + 14 ×2
  • 3 + 28
31
[(102 − 43)/3] ×5 − 17
  • [(100 − 64)/3] ×5 − 17
  • (36/3) ×5 − 17
  • 12 ×5 − 17
  • 60 − 17
43
Evaluate if x = − 5, y = 3, and z = 2x2 − 3(y2 + 4z)
  • ( − 5)2 − 3[(3)2 + 4(2)]
  • ( − 5)2 − 3[9 + 4(2)]
  • ( − 5)2 − 3(9 + 8)
  • ( − 5)2 − 3(17)
  • ( − 5)2 − 51
  • 25 − 51
- 26
Evaluate if x = 12, y = 6, and z = 8[(5x/6 − 5)/(y2 + 2 ×z)]
  • [((5 ×12)/6 − 5)/(62 + 2 − 8)]
  • [((60)/6 − 5)/(62 + 2 − 8)]
  • [(10 − 5)/(62 + 2 − 8)]
  • [5/(62 + 2 − 8)]
  • [5/(36 + 2 − 8)]
  • [5/(38 − 8)]
  • [5/30]
[(1)/(6)]
Evaluate if x = 2 and y = 13
[36/(14 − x3)] ×[y − 4x]
  • [36/(14 − 23)] ×[13 − 4(2)]
  • [36/(14 − 8)] ×[13 − 4(2)]
  • [36/(14 − 8)] ×[13 − 8]
  • (36/6) ×[13 − 8]
  • 6 ×[13 − 8]
  • 6 ×5
30
Evaluate if x = 2 and y = 5[(y3 − 15 ×4)/((8x + 22))]
[(5315 ×4)/((8x + 22))]
Evaluate if x = 3 and y = 5[(y3 − 15 ×4)/((9x + 22))]
  • [(53 − 15 ×4)/((9 ×3 + 22))]
  • [(125 − 15 ×4)/((9 ×3 + 22))]
  • [(125 − 60)/((9 ×3 + 22))]
  • [65/((9 ×3 + 22))]
  • [65/((27 + 22))]
[(65)/(49)]

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Order of Operations

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Objectives 0:06
  • The Order of Operations 0:25
    • Work Inside Parentheses
    • Simplify Exponents
    • Multiplication & Division from Left to Right
    • Addition & Subtraction from Left to Right
    • Remember PEMDAS
  • The Order of Operations Cont. 2:27
    • Example
  • Example 1 3:55
  • Example 2 5:36
  • Example 3 7:35
  • Example 4 8:56

Transcription: Order of Operations

Welcome back to www.educator.com.0000

In this lesson we are going to take a look at the order of operations.0002

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.0009

This one involve things like what should we do at parentheses and exponents0015

and when should we do our multiplication, division, addition and subtraction. 0020

When trying to simplify much larger expression with many different types of operations present, we have to figure out what to do first.0027

Our order of operations gives us a nice run back on what we should be doing.0037

The very first thing that we should do is work inside our grouping symbols.0042

It means if you see parentheses or brackets work inside of those first.0047

Then move on to simplifying your exponents, things raised to a power.0052

Once you have both these in care, move on to your multiplication and division.0058

If you see lots of multiplication and division next to each other, remember to work these ones from left to right.0063

Now you have to do any remaining addition and subtraction.0072

And again when it comes to which of those is more important simply work those from left to right as well.0074

One handy way that you can remember of this entire list of that is the order of operations is to remember PEMDAS.0081

PEMDAS stands for parentheses, exponents, multiplication, division, addition and subtraction.0090

Let us try it out.0096

A great way that you can remember these is Please Excuse My Dear Aunt Sally.0105

I often heard a lot of my students use that one to make sure that they came out straight.0110

Start with your parentheses and then move on to exponents.0116

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.0120

But work these ones from left to right.0129

The same thing applies to your addition and subtraction, work those from left to right.0135

Sometimes you will deal with a larger expression that has a fraction in it.0150

Even though you might not see some grouping symbols, think of the top and bottom as their own group.0157

That means work to simplify the numerator and get everything together up there.0163

And work to simplify your denominator, get everything together down there before we continue on with the simplification process.0166

As a quick example, let us look at this slide.0173

We have (-2 × 5) + (3 × -2) / (-5-3).0176

I'm going to work on the top part as its own group, and the bottom part as its own group.0183

Let us see what does this, -2 × 5 would give me -10, 3 × -2 =-6.0191

On the bottom in that group I have that -5 -3 =-8.0202

Okay -10 - 6=-16 and on the bottom I still have a -8.0212

We worked to look inside each of those groups and simplify them using our order of operations in there.0220

I simply have a -16 / -8 and that is a 2.0226

Watch for those large fractions to play a part.0232

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.0237

This one is ((5 - 2)2 + 1))/ -5, we also write down PEMDAS.0245

This will act as our roadmap as we are going through the problem.0257

I want to look for grouping symbols or parentheses to see where I need to start.0261

That 5 - 2 looks like a good area, we will do that first, 5 - 2 is 3.0266

The only other grouping that I'm concerned with is the top and bottom of the fraction.0278

There is only one thing on the bottom so I'm just going to now focus on the numerator.0283

I can see that I have some exponents, I have a 32 in there.0290

And now let us do that, 32 is 9, it is getting better.0294

I want to move on to my multiplication and division.0302

Looking at the top and bottom of the fraction individually I do not see any multiplication or division, I can move on.0306

Addition and subtraction, why I do have some addition on the top, I put those together to get 10/-5.0314

We are looking at 10 ÷ -5 and now I can say that my result is a -2, this one is done.0322

You can see how we move through that order of operations as our road map.0330

In this next one we want to evaluate a (-12 × -4/3) - (5 × 6) ÷ 3, let us go over the map.0338

I do not see too much in terms of grouping but I do have this group of numbers over here.0354

Let us go ahead and take care of those.0361

Inside I have (5 × 6) ÷ 3, what should I do in there? I got multiplication and division.0363

Those ones remember we are working from left to right.0370

On the left side there I have multiplication then we actually do the division.0374

5 × 6 is a 30, now do the 30 ÷ 3 and get 10.0383

We have taken care of that grouping.0394

I'm just going to copy down some these other things and then we will continue on.0396

Our grouping is done, now on to exponents.0406

I do not see any exponents here so now on to multiplication and division.0410

We will do multiplication I got a -12 × -4/3.0416

A negative × a negative would give me a positive, multiplying on the top that would be 48/3.0421

Because of my fraction there, I do have some division I could take 48 and divided by 3 = 60.0434

On to addition and subtraction 16 – 10 = 6.0444

I have completely simplified this one and I can call it done.0451

This next one I have (12 ÷ 4) × (√5 - 1).0458

Starting with my grouping symbols and parentheses, I could consider everything underneath the square root as its own little group.0469

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.0475

I'm looking at 12 ÷ 4 × 2, moving on do I see any exponents? No exponents.0499

On to multiplication and division, this is that tough one.0509

It is tempting to say that multiplication is more important but it is not.0512

Simply work these guys from left to right.0516

In this case, we are going to do the division first, 12 ÷ 4 is 3.0519

Then we are actually taking that and multiply it by 2 and get 6, this one is completely simplified.0527

Let us look at our example that involves lots and lots of different things.0538

I have (8 × 4) - (32 × 5) + (2 × the absolute value of -1) / (-3 × 2/3) +1 0542

With so many different things in here we have to be careful in what to do first.0562

I'm dealing with a fraction here I want the top as its own group and the bottom as its own0567

and work inside each of those and try to simplify them.0572

Let us look at the top a little bit.0575

Inside of that I do not see any additional grouping symbols so I will try and do any exponents on the top.0578

I do have a 32, let us change that into a 9.0587

I have the absolute value of -1, might as well we go ahead and take care of that as well.0594

We are doing a little bit of simplifying on the top, let us see if there is any exponents in the bottom.0602

83 × 23 and change out into -3 × 8 and of course we still have the + 1.0607

Continuing on, looking at the top I do not have any additional parentheses, I do not have any additional exponents, multiplication and division.0621

A lot of multiplication on the top, 4 × 8 would give me 32, 9 × 5 =45, 2 × 1=2.0629

On to the bottom, -3 × 8=-24 and then +1, multiplication and division done.0644

On to addition and subtraction and we are going to do this from left to right.0655

I will do 32 - 45, what do we got from there?0660

Let us imagine our technique for combining numbers that have different signs.0665

I'm just subtracting here, I get a result of 13.0673

The one that is larger in absolute value is the -45 so my result is a -13.0677

Looking at the bottom-23 almost done.0685

-11 at the top divided by -23, this one is completely simplified as 11/23.0693

When dealing with multiple operations it is important that we do have a roadmap in order to get through all of these.0705

Feel free to use PEMDAS also that you keep everything in order.0711

As you use PEMDAS, if you get down to your multiplication and division then use them from left to right.0715

If you get down to your addition and subtraction, again use those from left to right.0720

Thank you for watching www.educator.com0725