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### Solving Multiplication Equation

• To solve equations, use inverse operations to get the variable by itself
• Inverse operation of multiplication is division
• Inverse operation of division is multiplication

### Solving Multiplication Equation

Use mental math to solve the equation
4x = 20
x = 5
Use mental math to solve the equation
42 = y · 7
y = 6
Use the inverse operation to solve the equation
- 5x = 35
• [( − 5)/( − 5)] ·x = [35/( − 5)]
• x = [35/( − 5)]
x = - 7
Use the inverse operation to solve the equation
- 36 = 6y
• [( − 36)/6] = [6/6] ·y
• [( − 36)/6] = y
y = - 6
Use the inverse operation to solve the equation
- 9t = - 36
• [( − 9)/( − 9)] ·t = [( − 36)/( − 9)]
• t = [( − 36)/( − 9)]
t = 4
Solve the equation
- 7m = 49
• [( − 7)/( − 7)] ·m = [49/( − 7)]
• m = [49/( − 7)]
m = - 7
Solve the equation
- 33 = - 11a
• [( − 33)/( − 11)] = [( − 11)/( − 11)] ·a
• [( − 33)/( − 11)] = a
a = 3
Solve the equation
- 7x = 56
• [( − 7)/( − 7)] ·x = [56/( − 7)]
• x = [56/( − 7)]
x = - 8
Is - 5 a solution to the equation?
- 25 = - 5s
• [( − 25)/( − 5)] = [( − 5)/( − 5)] ·s
• [( − 25)/( − 5)] = s
• s = 5
No
Is - 7 a soultion to this equation?
4x = - 28
• [4/4] ·x = [( − 28)/4]
• x = [( − 28)/4]
• x = − 7
Yes

*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.

### Solving Multiplication Equation

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
• Multiplication Equations 0:08
• Inverse Operation of Multiplication
• Extra Example 1: Use Mental Math to Solve Each Equation 3:54
• Extra Example 2: Use Inverse Operations to Solve Each Equation 5:55
• Extra Example 3: Is -2 a Solution of Each Equation? 12:48
• Extra Example 4: Solve Each Equation 15:42

### Transcription: Solving Multiplication Equation

Welcome back to Educator.com.0000

For the next lesson, we are going to continue solving equations.0002

We are going to solve multiplication equations.0005

Equations that involve multiplication, we are going to continue to solve using inverse operations.0010

Again whenever you solve equations, you always have to try to get the variable by itself.0023

The inverse operation of multiplication is division.0030

If I have a number being multiplied to a variable, 2 times A...0037

Remember if you have a number times a variable, you can write it together like that.0044

Equals 10; that is my equation; this would be a multiplication equation.0050

This 2 times A, 2 times the variable; we can do this in our head.0056

We know that 2 times 5 equals 10; we know A is 5.0062

But if I were to solve this using inverse operations, again I want to get the variable by itself.0066

I have to get rid of whatever is next to the variable on that side.0078

On the left side, I have to get rid of everything except for the variable and get the variable by itself.0082

That means I have to get rid of this 2.0091

Since this is 2 times A, the inverse operation would be to divide.0094

To get rid of the 2, we have to divide the 2; divide this 2.0101

We know that 2 over 2 is going to go away.0107

It is going to become 1.0109

Whatever you do to this side, remember you have to do to the other side.0112

If I divide 2 from here, then I have to go to the right side and then divide 2 there.0116

This then becomes 1A; 1A is the same thing as A.0126

Whenever you have a variable with no number in front of it like this one does, there is an invisible 1 here.0139

It is just saying that you have 1 A.0148

How many As do you see?--you see 1 of them.0150

If I say I have an apple, you know I have only 1 apple.0154

I didn't say I have 1 apple.0159

But just because I said I have an apple and I made it singular, you know that I have 1.0161

In the same way, if I have an A, you know that I have 1 of them.0167

That just means that there is an invisible 1 in front of it.0172

When this number cancels out like that, you don't have to write 1A.0176

You can just write A which is the same thing as getting the variable by itself.0180

Again whether you write the 1 in front of the A or just leave it as A, it is the exact same thing.0186

By itself now, that is the whole point; you want to get it by itself.0196

We got rid of the 2; equals... on the right side, I have to actually solve that out.0199

That becomes 10 divided by 2.0207

Remember this line right here like a fraction; that represents divide.0211

This would be 10 divided by 2.0216

We know that 10 divided by 2 is 5; that would be my answer.0220

That is how you would solve multiplication equations using inverse operation.0227

Let's go ahead and do our examples.0234

The first set of examples, we are going to use mental math0237

meaning we are just going to solve it in our head.0240

We don't have to divide or use inverse operations.0241

Here again this means 3 times F; 3F means 3 times F.0247

3 times what is 9?--3 times what equals 9?0257

I know 3 times 3 equals 9; F has to be 3.0263

Again when you are solving equations, you don't want to just write 3.0268

You don't want to just write the number.0271

You have to write what that number represents; you are saying that F is 3.0273

Once you write it like that, variable by itself equaling the number, then that is your answer.0283

10 times what equals 100?--10 times 10 equals 100.0290

Then I have to say A is equal to 10.0296

18 equals C times 6; this C times 6, same thing.0305

Whether you see it like this or whether you see it like that, they both mean multiplication.0314

What times 6 is 18?--I know 3 times 6 is 18.0321

That means C has to be 3.0327

The next one, 21 equals 3 times a number; 3 times what equals 21?0335

3 times 7 equals 21; that means P has to be 7.0344

Now let's use the inverse operation to solve the equation.0357

We are going to use that method that we did earlier.0360

We are going to use that same method to go out and solve for our variable.0364

This is -10 times S equals 100.0370

I am solving for S; I am solving for my variable.0377

I can circle it just to see that that is what I want.0381

That is my goal; that is what I am solving for.0385

I am separating my sides.0388

Since this is -10, that number times S, inverse operation of times is divide.0393

To get rid of this -10, I have to divide it.0404

I am going to use the inverse operation to get rid of the number and get the variable by itself.0407

I need to divide.0415

Remember this line right here, writing it as a fraction; that means divide.0415

Whatever I do to one side, remember I have to do to the other side.0423

I have to divide this side by -10 also; what is left on this side?0428

On my left side of the equal sign, I got rid of that number.0435

I want to get the variable S by itself.0440

Now that I got rid of -10, I have S by itself now.0444

I am going to write S; that is what is left on my left side.0448

Equals... what became of my right side?--100 divided by -10.0452

Remember when you multiply or divide integers, meaning positive and negative numbers like this, you still get the same number.0459

Let's say I don't see that negative sign.0474

Then I am still going to do 100 divided by 10.0476

Whether or not this number is negative or positive, you are still going to divide 100 to 10.0480

But if you have one negative number, if only one is negative, then your answer becomes negative.0487

It is the same number when you divide.0496

You are just going to do 100 divided by 10.0498

Then my answer becomes a negative.0506

If I have two negatives signs, whether it is a negative times a negative0513

or a negative number divided by a negative number, whenever you see two of them,0520

those two negative signs will pair up and become a positive.0526

This is only when you multiply or divide; two negatives make a positive.0532

One negative, it remains a negative.0541

If you have two negatives, it becomes a positive number.0544

This is 100 divided by 10; that is still 10.0549

But because there is only one negative sign here within this problem,0553

there is only one, so then my answer becomes a negative.0558

S equals -10; that is my answer.0562

The next one; again you are solving for T; separate the sides.0571

I have to get rid of the 2.0579

To get T by itself, I have to get rid of the 2.0581

This is 2 times T; my inverse operation, I have to divide; divide the 2.0584

Remember this line means divide also; that goes away.0591

Then I have to divide this side by 2.0595

On my left side, I only have T left which is what I want.0602

Equals -16 divided by 2.0606

A +16 divided by 2 is 8; I know 2 times 8 is 16.0611

But since I have only one negative sign within this problem, my answer, it stays a negative.0619

Be careful not to confuse multiplying and dividing positive and negative numbers and adding and subtracting positive and negative numbers.0628

When you add two negative numbers, that doesn't become a positive.0635

Only when you multiply or divide two negative numbers; so that is my answer.0641

For the third one, I am solving for my variable R.0653

It is on the right side of my equal sign.0659

This is my left side; this is my right side; I am solving for R.0661

I have to get rid of the 5 because R, the variable, has to be by itself.0667

This is 5 times R.0673

I have to get rid of the 5 using the inverse operation, dividing.0675

That is my way of making that go away.0681

Since I did it to this side, I have to do to the other side.0685

Now I am going to simplify; I am going to solve everything out now.0691

25 divided by 5 is 5.0694

We don't have to worry about any positive or negative numbers because there is no negatives.0697

25 divided by 5 is just 5; bring down the equal sign; this is R.0700

R by itself because we got rid of the 5; that is my answer.0707

Again if you want, you can leave it like that as your answer.0712

Or you can say R equals 5.0715

You can rewrite it 5 equals R or R equals 5.0718

It is the same exact thing.0722

This last one, again I am solving for D, the variable.0727

Separate my two sides; this is 8 times D.0733

To get rid of it, inverse operation would be to divide.0736

Whatever you do to one side, you have to do to the other side.0742

What is left here?--D only, equals... 64 divided by 8 is 8.0747

But because I have one negative sign when I am dividing numbers, my answer becomes a negative.0755

It is -8; that is my answer.0761

Here, is -2 a solution of each equation?0771

That means I can plug this in.0786

I can substitute a -2 for the variable to see if my equation is going to be true or false.0788

4 times S; instead of writing S, I can write -2 to see if -2 is what S is going to equal.0797

4 times -2; then remember the best way to show two numbers being multiplied together0810

is to write each of them in parentheses like that; equals -8.0818

You are just seeing if 4 times -2 equals -8.0827

4 times -2 is -8; 4 times 2 is 8.0832

You only have one negative sign; that makes that negative.0837

They do equal each other; this does equal -8; so this one is yes.0841

Is this -2 a solution for this equation?--this one is yes.0847

Next one, 10 equals 5 times -2; I want to write it out.0855

Again I can write both of these in parentheses to show that those are two numbers being multiplied together.0866

What is 5 times -2?--isn't this -10?0873

because again 5 times 2 is 10 but then you have only negative number.0880

So this is not true; this one is no or false.0884

This one, -6 times -2 equals +12.0892

Again I am going to write that in parentheses to show that I am going to multiply them.0900

6 times 2 we know is 12; here I have two negatives signs.0909

For this, the two numbers that I am multiplying, they are both negative.0915

That means I have two negatives which makes a positive.0919

When you multiply or divide, two negatives make a positive.0923

This becomes +12 or just 12; I don't even have to write the positive.0927

12 equals 12; this one is yes; this one works.0933

Let's do a few more; we are going to solve this using inverse operation.0944

Here again we are solving for the variable.0952

Circle it; draw a line to separate the sides.0954

This is -4 times W; I am going to divide -4.0959

Whatever I do to one side, I have to do to the other side.0965

That was my way of making that number go away and make the variable by itself.0970

Equals... 28 divided by 4; we have a negative divided by a negative.0975

Does that make it a positive when you divide two negatives?0987

Yes; that becomes a +7 because 4 times 7 equals 28.0992

Be careful; this is a +7.1000

Or if you just write 7 without the plus sign, that is okay.1003

Number two, you are solving for N; I am going to separate my sides.1012

Here again I need to get rid of this number.1022

Do not divide this number; do not try to move this number; don't use this.1025

We are going to try to get rid of this number because that is what is next to the variable.1032

Again we are trying to get the variable by itself.1037

Divide -8; again I divided because that was -8 times N.1041

Dividing is the inverse operation.1046

Whatever you do to one side, you have to do to the other side.1049

Negative divided by a negative is a positive.1054

This becomes 10 because 8 times 10 is 80.1057

Equals; went away; left with N; same thing here.1063

I know some of you guys can still do this in your head.1080

If you can, that is fine.1083

But it is important to know inverse operations and know how to do these steps1084

because later on, the equations are going to get a lot harder.1090

If you know how to do it this way, then solving equations becomes really easy.1094

Just try to practice it a few times; just keep practicing.1102

Circle the variable because that is what you are solving for.1105

To get the variable by itself, I have to get rid of this number.1109

Divide; divide; this goes away; this becomes -2.1113

Again positive divided by negative; I only have one negative sign so my answer is a negative.1122

11 times 2 is 22; that is why it is a 2.1129

Equals K; there is my answer.1133

If you want, you can flip this and make it K equal to -2.1140

Or not flip but switch the sides; you can write it like that.1146

The last one, going to circle the A; this is 9 times A.1151

Divide the 9; inverse operation to get rid of it.1158

45 divided by 9 is 5; I only have one negative.1163