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Solving Division Equation

Related Links

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

Solving Division Equation

Use mental math to solve each equation
[x/3] = 9
x = 27
Use mental math to solve each equation
[45/y] = 5
y = 9
Use the invere operation to solve each equation
[y/( − 9)] = 4
  • [( − 9)/1] ·[y/( − 9)] = 4 ·− 9
  • y = 4 ·− 9
y = − 36
Use the invere operation to solve each equation
[x/35] = − 7
  • [35/1] ·[x/35] = − 7 ·35
  • x = − 7 ·35
x = - 245
Use the invere operation to solve each equation
[x/( − 8)] = − 9
  • [( − 8)/1] ·[x/( − 8)] = − 9 ·− 8
  • x = − 9 ·− 8
x = 72
Use the invere operation to solve each equation
[y/( − 3)] = − 2
  • [( − 3)/1] ·[y/( − 3)] = − 3 ·− 2
  • x = − 3 ·− 2
x = 6
Use the invere operation to solve each equation
[y/5] = − 8
  • [5/1] ·[y/5] = 5 ·− 8
  • y = 5 ·− 8
y = − 40
Use the invere operation to solve each equation
[z/( − 8)] = 3
  • [( − 8)/1] ·[z/( − 8)] = 3 ·− 8
  • z = 3 ·− 8
z = − 24
Is - 2 a solution of the equation?
[x/( − 6)] = 3
  • [( − 6)/1] ·[z/( − 6)] = 3 ·− 6
  • z = 3 ·− 6
  • z = − 18
No
Is - 33 a solution of the equation?
[y/( − 3)] = 11
  • [( − 3)/1] ·[z/( − 3)] = 11 ·− 3
  • z = 11 ·− 3
  • z = − 33
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.

Answer

Solving Division 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
  • Division Equations 0:05
    • Inverse Operation of Division
  • Extra Example 1: Use Mental Math to Solve Each Equation 0:39
  • Extra Example 2: Use Inverse Operations to Solve Each Equation 2:14
  • Extra Example 3: Is -6 a Solution of Each Equation? 9:53
  • Extra Example 4: Solve Each Equation 11:50

Transcription: Solving Division Equation

Welcome back to Educator.com.0000

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

Just like the other equations that we were solving in the previous lessons,0009

we are going to use inverse operations to get the variable by itself.0014

The whole point of solving equations is to solve for the variable.0018

What does the variable equal?--what is the value of the variable?0022

For this one, the inverse operation of division is multiplication.0027

The opposite operation, the opposite of division is multiplication.0032

Again we are just going to solve for the variable just using mental math.0042

That means 3 equals a number divided by 2.0047

Don't forget, right here, this fraction also means divide.0054

It is the top number divided by the bottom number.0059

A divided by 2 is 3; what is A?0064

What number if you divide it by 2 is going to give you 3?0067

I know that 6 divided by 2 is 3.0071

Again instead of writing just 6, you have to write that the variable A is equal to 6.0076

Same thing here; a number divided by 3 is going to give you 5.0086

15 divided by 3 is 5; that means the variable D is equal to 15.0095

A number divided by 4 is 4; 16 divided by 4 is 4.0104

That means I have to make B equal to 16.0114

Then 100 divided by a number is going to give you 10.0121

What is K?--K has to be 10 because 100 divided by 10 is 10.0127

Now for these examples, we are going to solve for the variable using the inverse operation.0135

I am going to circle the variable just like I did for my other lessons and then separate the sides.0145

Again this is M divided by 4.0153

If I have a number on the bottom and if I multiply this by 4, a +4 is the same thing as 4/1.0158

4 is the same thing as 4/1; I could put 1 under any number.0181

If I need to turn this into a fraction, I can put a 1 under it.0189

4 divided by 1; what is 4 divided by 1?--isn't that 4?0194

Remember this also means divide; 4 divided by 1 is 4.0200

If you want, if it helps, you can put it over 1.0206

Then if you remember, to multiply fractions, this is M times 4 which is M times 4 or you can write 4M.0210

Remember if you have a number times a variable, you can just write it together like that.0222

Over... this number times 1 which is 4.0227

If you have the same number on top as the bottom, they will become 1.0234

4 divided by 4 is 1.0240

That is why the inverse operation, if this is M divided by 4, the opposite of divide is multiply.0246

If I want to get rid of this 4 down here, then I have to multiply the 4.0257

Again I am using the inverse operation.0264

Just in the same way, this 4 is on this side this time.0267

But it is the same thing; 4/1.0274

Or you can leave it as 4; or you can put it over a 1.0277

Times M/4; remember this becomes that same exact thing, 4M/4 because this times this is that.0281

1 times 4 is 4; 4/4 makes a 1; this is 1M.0295

If you remember, 1M is the same thing as M.0303

Here inverse operation of divide is to multiply.0312

If you multiply when it is divided from the variable, they will cancel out.0317

It will go away.0323

If you don't understand this, what I did here, just know that if you have to divide0324

or if this is M divided by 4, then you have to multiply it so that it will go away.0330

Again whatever I do to one side of the equal sign, I have to do to the other side.0340

Since I multiplied 4 to this side, I have to multiply 4 to this side.0345

You can write it like this for now.0351

Or the best way to show that you are going to multiply two numbers is to write them in parentheses.0354

What is left on the left side?0361

This side, all I have left is the M which is what I want.0364

I wanted to get rid of this 4; that is why I multiplied it.0368

Equals -3 times 4; remember... I have a negative times a positive.0371

Whenever you are multiplying or dividing, if you only have one negative sign, your answer becomes a negative.0379

You are going to multiply these two numbers just the same way.0387

3 times 4 is 12.0390

It is a -12 because I only see one negative sign.0396

Remember one negative, your answer becomes a negative.0399

If you are multiplying two negative numbers, then those negative numbers pair up to become a positive; a plus.0403

Then this is M equals -12; I have the variable by itself.0414

So I am done; I solved the equation.0419

Again next one, I am going to circle the variable.0426

That is my goal, to make the variable by itself.0429

I am going to separate the two sides like that.0433

This is A divided by 7.0436

If it is A divided by 7, the inverse operation is multiply.0439

I have to multiply this whole side by 7.0445

But these will cross cancel; they will become a 1.0450

Whatever I do to one side, I have to do to the other side.0455

7 times 6 is 42; on my left side, I get 42; then my equals.0460

On my right side, I have only A left because remember I got rid of that 7.0472

Once I have the variable by itself and I have the number, I am done.0478

That is my answer.0482

The third one, I am going to use a different color; solve for B.0486

Again this is B divided by -3; it is divided by -3.0494

I still have to get rid of this whole number right here.0499

Inverse operation, multiply this by -3; that way these will cancel out.0502

Whatever I do to one side, I have to do to the other side.0509

I have to multiply this by -3.0513

Then on this side, I only have a B left; equals... my right side.0518

I have to solve this out; 10 times -3; 10 times 3 is 30.0526

How many negative signs do I see?--I only see one.0533

That means my answer is going to be negative; B equals -30.0537

This last one, again solve for X; I am going to circle it.0548

Separate my sides; X divided by 5; inverse operation is to multiply.0553

Multiply this side; that way that number will go away.0559

Whatever I do to one side, I have to do to the other side.0565

What is left on this side?--X is left; equals... 8 times 5 is 40.0570

I only have one negative sign; that means my answer is going to be negative.0581

That is it; that is my answer.0587

For these, we are going to determine if -6 is the solution of the equation.0595

Here is my variable.0604

I want to know if -6 can be M or if M can be -6.0605

-6 divided by 2; is that 3?-- -6, I am going to replace it.0613

I am going to write it instead of M because I am trying to see if M is going to be that number.0619

I am just going to substitute it in; equals 3; is this true?0626

I know that 6 divided by 2 is 3; but is -6 divided by 2, 3?0632

No, because when you have a negative divided by a positive, 0637

you only see one negative, that makes the answer a negative.0641

In this case, this is no or false.0646

This one, I am just going to write no.0650

The next one, here is my variable; 6 over... in place of the variable, -6.0653

I know that 6 divided by 6 is 1; is 6 divided by -6, -1?0665

Only one negative sign when you are dividing numbers; that makes this negative.0672

So this one is yes; this one is true.0677

Here -18 equals -6/4; does -6 divided by 4 equal -18?0682

No, so this one is no.0703

Let's solve each equation.0714

We are going to use the inverse operations to solve each of the equations.0716

The first one, I am going to circle my variable.0722

I am going to separate my sides; be careful here, this is A plus 11.0728

What is being used?--a plus; what is the inverse operation of plus again?0739

Inverse operation of plus is minus; the inverse operation of minus is plus.0748

What about times?--what is the inverse operation of times?--divide.0756

And the inverse operation of divide is times.0762

Since this is A plus 11, and I know I have to get the variable by itself,0767

I have to get rid of everything that is next to the variable.0773

I have to use the inverse operation of plus which is minus.0777

That means I have to subtract this number 11 because +10 minus 11, that makes 0; that goes away.0781

Whatever I do to one side, I do to the other; -4 minus 11.0789

Be careful here; remember we are not multiplying; we are not dividing.0799

Even though you see two negative signs, it doesn't make it go away; only when you multiply or divide.0803

When it comes to adding and subtracting, you can think of dogs and cats.0809

You can think of money; it is like saying you borrowed $4.0815

Then you borrowed another $11; whenever you see a negative, you are borrowing.0821

You borrow 4; you borrow 11; how much do you owe?0826

You owe 15; that is a negative because you still owe.0830

Whenever you don't have something, it is a negative.0837

Bring down that equal sign; then on this side, what is left?0842

Only the variable because whatever was here, we got rid of; that number that was there.0847

So this is it; this is the answer.0854

The whole point, the goal is to get the variable by itself.0858

The next one; circle the variable; separate my sides; this is N minus 8.0864

I know I have to get rid of this number because it is next to the variable.0874

Inverse operation of minus is plus.0879

That means to get rid of this ?A, I have to add A to make it go away so the variable can be by itself.0882

Then whatever you do to one side, you have to do to the other side.0892

It is the right side; only the variable is left.0895

Equals... this side, the right side... 28; 20 plus 8 is 28.0902

That is my answer; N equals 28.0909

Solving for my variable of E; separate my sides; here this is 9 times V.0915

If they are stuck together like that, that is a times; 9 times V equals -81.0924

Since it is multiplied together, I have to use my inverse operation which is divide.0932

I have to divide the 9 to get rid of it so that the variable can be by itself.0938

Then same thing; whatever you do to one side, you have to do to the other side.0943

If you did it to the left side, then you have to do it to the right side.0947

From here, this is left with V; bring down the equal sign.0953

Then 81 divided by 9; don't forget that this is divide.0960

81 divided by 9 is 9; but then you have a negative.0964

Negative divided by a positive, you only see one negative.0971

In this case, only when you multiply or divide, remember.0974

You are dividing now; one negative gives you a negative answer.0977

That is my answer; that is it.0984

The last one, D divided by -12 equals 3.0989

I am going to circle my variable; separate my sides.0997

This is D divided by -12; the inverse operation of divide is multiply.1001

To get rid of this number here, because again we need D to be by itself.1008

I need to multiply this number; make sure you divide the -12.1014

The number is -12; you are multiplying -12; that cross cancels out.1021

Whatever you do to one side, remember you have to do to the other side; 3 times -12.1027

Again the best way to write two numbers being multiplied is to write it in parentheses.1032

Can write that in parentheses too.1042

On this side, on my left side, I have D left by itself.1045

Equals... the right side, it is 3 times -12; first 3 times 12 is 36.1049

Remember the number stays the same; I have only one negative sign.1060

That makes this because it is multiplied; D is -36.1066

That is it for this lesson; thank you for watching Educator.com.1075