For more information, please see full course syllabus of Basic Math

For more information, please see full course syllabus of Basic Math

### 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

[x/3] = 9

[45/y] = 5

[y/( − 9)] = 4

- [( − 9)/1] ·[y/( − 9)] = 4 ·− 9
- y = 4 ·− 9

[x/35] = − 7

- [35/1] ·[x/35] = − 7 ·35
- x = − 7 ·35

[x/( − 8)] = − 9

- [( − 8)/1] ·[x/( − 8)] = − 9 ·− 8
- x = − 9 ·− 8

[y/( − 3)] = − 2

- [( − 3)/1] ·[y/( − 3)] = − 3 ·− 2
- x = − 3 ·− 2

[y/5] = − 8

- [5/1] ·[y/5] = 5 ·− 8
- y = 5 ·− 8

[z/( − 8)] = 3

- [( − 8)/1] ·[z/( − 8)] = 3 ·− 8
- z = 3 ·− 8

[x/( − 6)] = 3

- [( − 6)/1] ·[z/( − 6)] = 3 ·− 6
- z = 3 ·− 6
- z = − 18

[y/( − 3)] = 11

- [( − 3)/1] ·[z/( − 3)] = 11 ·− 3
- z = 11 ·− 3
- z = − 33

*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

### Basic Math Online Course

### 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 divide*0324

*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

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