Basic Math Integers and Order of Operations

Welcome back to Educator.com.0000

For this next lesson on integers and order of operation,0002

now that we went over all the different ways we can solve integers,0007

we are going to put them together into the same problem and solve it by using order of operations.0012

Remember that when you solve, you have to solve in this order.0023

Parentheses is always, always first; then it is exponents.0029

Then after that, it is multiplication and division.0035

This is the same; you don't multiply before you divide.0039

You just do it in order from left to right.0045

If you have multiplication and division, then you would just solve it in that order.0049

You don't solve one over the other; same thing for addition and subtraction.0053

If you have something to subtract before you add, then you would just do that0059

in order from left to right instead of adding first and then subtracting.0064

Again parentheses; then exponents; then multiplication and division; then addition and subtraction.0070

The first problem is going to be -4 plus 8 times -3 divided by 6 minus 2.0080

Within all these operations, I have to multiply and divide first.0091

Multiplication and division, there is no order between those two.0099

I just have to solve it out whichever comes left to right.0103

I am going to solve this first right here; 8 times -3.0107

When you multiply integers, you have to look at how many negative signs there are.0114

There is only one negative sign; only this one has a negative.0122

My answer is going to be -24.0126

After you solve one thing out, write out the rest.0133

-4 plus the 8 divided by 6 minus 2.0138

I rewrote the whole problem with only this solved.0146

From here, my next step will be to divide these.0150

This is going to be -24 divided by 6.0155

Again the same rule applies for the negatives; negative sign here; positive here.0159

My answer is going to become a negative; that is going to be a -4.0166

This is not a divide; don't get confused with that.0175

-4; rewrite the whole problem again; plus that, minus that.0178

Don't forget to include these signs; this sign was included when we solved it.0184

This was part of this answer; but this wasn't.0190

You are going to write out that sign here when you rewrite the whole problem.0194

-4 plus a -4, I have the same sign.0200

When you add integers, if they have the same sign, then you are just going to add up the numbers.0207

Then you are going to give the same sign.0213

For this one, -4 plus -4 is -8.0216

I am going to write out this right here, -8 minus 2.0223

I have a minus; I am going to use the two-dash rule; one, two.0227

-8 plus -2 is -10; all of this became -10.0234

I know it looks like a lot of work.0243

But it is only a lot of work because you are doing one little step at a time.0245

But just remember, you are multiplying integers, then dividing, then adding, and then subtracting integers.0249

The next one, 3² plus 2 minus 5 times 6.0261

I have parentheses; parentheses always, always, always comes first.0270

I am going to solve this first; I have a minus problem, 2 minus 5.0276

I am going to use the two-dash rule to make this minus to a plus, the subtraction problem to an addition problem.0282

It would be one, two.0289

They have different signs; I am going to find the difference of their absolute values.0293

This is a 2; the absolute value of -5 is 5.0298

The difference will be 3.0303

I am going to give it the same sign as the 5.0306

That is a negative so this is a negative.0308

Then I am going to rewrite the whole problem.0312

This is 3²; don't forget this plus; then times 6.0316

The next step on the order of operations is exponents.0325

I have to solve this exponent next; 3² is 9; plus -3 times 6.0330

Then after that, I have adding and I have multiplying; multiplying comes first.0339

That will be again one negative sign here; my answer will be -18.0346

Write everything else out; you don't have to write everything out.0355

But that is the best way to do it because that prevents any mistakes that you might make.0358

9 plus -18; again we are adding integers.0368

They have different signs; you find the difference.0372

This is a 9; absolute value of this is 18.0376

If you find the difference of those, you get 9.0380

Give it the sign of the 18; that will be your answer, -9.0383

This next problem, I have parentheses that I have to solve out first, -15 plus 4.0397

Again we are adding integers; they have different signs.0406

Find the difference of their absolute values.0410

Absolute value of -15 is 15; absolute value of 4 is 4.0413

If you find the difference of those, it is 11 with a negative sign.0419

Then times another parentheses that I have to solve out.0429

Here is a minus problem; use the two-dash rule; one, two.0433

Again two-dash rule, do not apply it to any other negative signs.0438

This negative sign, you are not going to touch that.0441

The two-dash rule only changes the minus to a plus.0444

Then this number to either a negative or a positive.0449

-2 plus -8; they have the same sign; -2 and -8.0454

You are going to add the numbers, their absolute values; then give it that same sign.0459

-2 plus -8 is going to be -10.0464

-11 times -10; I have two negative signs.0472

That is going to make my answer a positive; 11 times 10 is 110.0479

That is it for this problem; that is the answer.0488

The fourth example, let's see, I have a negative.0494

This, divided by absolute value of that minus a -7.0501

The first thing I want to solve out is the parentheses which is right here.0507

2³; 2³, be careful, 2³ is not 2 times 3.0513

This is 2 times 2 times 2; I can just rewrite the whole thing.0519

Absolute value of -8 minus a -7; I have to solve this out first.0530

2 times 2 is 4; 4 times 2 is 8.0536

I am going to make this an 8.0541

-8 divided by absolute value of -8 minus a -7.0544

I want to solve this out too because absolute value is like parentheses.0555

Just solve that out first before you divide and do anything else.0560

Absolute value of -8 is 8 because the distance from 0 is 8.0567

I am going to write everything else out; don't forget these signs.0580

Minus a -7; write everything else out exactly the way it is.0584

-8 divided by 8 minus -7; I have to divide before I subtract.0590

Do this next; -8 divided by 8 is -1.0597

Because I have one negative sign, that is going to make my quotient a negative.0602

Then I am going to write all this out again; minus a -7.0608

I am subtracting integers; I am going to apply the two-dash rule.0612

Make this a plus; make that a plus; -1 plus a 7 here.0617

Again I have different signs so I am going to find the difference of their absolute values.0625

The absolute value of -1 is 1; absolute value of 7 is 7.0630

That is 6; then I am going to give it the sign of the 7.0635

That is it; that is your answer.0642

If any of these problems were confusing to you, if you forgot how to do some of these0646

like either dividing or multiplying, maybe adding and subtracting integers,0653

then just go back to the previous lessons and review over it.0657

Then try to come back here and figure out these problems too.0660

That is it for this lesson; thank you for watching Educator.com.0665