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

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

### Solving Multiplication Equation

#### Related Links

- 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

4x = 20

42 = y · 7

- 5x = 35

- [( − 5)/( − 5)] ·x = [35/( − 5)]
- x = [35/( − 5)]

- 36 = 6y

- [( − 36)/6] = [6/6] ·y
- [( − 36)/6] = y

- 9t = - 36

- [( − 9)/( − 9)] ·t = [( − 36)/( − 9)]
- t = [( − 36)/( − 9)]

- 7m = 49

- [( − 7)/( − 7)] ·m = [49/( − 7)]
- m = [49/( − 7)]

- 33 = - 11a

- [( − 33)/( − 11)] = [( − 11)/( − 11)] ·a
- [( − 33)/( − 11)] = a

- 7x = 56

- [( − 7)/( − 7)] ·x = [56/( − 7)]
- x = [56/( − 7)]

- 25 = - 5s

- [( − 25)/( − 5)] = [( − 5)/( − 5)] ·s
- [( − 25)/( − 5)] = s
- s = 5

4x = - 28

- [4/4] ·x = [( − 28)/4]
- x = [( − 28)/4]
- x = − 7

*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 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

### Basic Math Online Course

### 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 math*0237

*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

*But you only see one negative sign in that problem.*0502

*Then my answer becomes a negative.*0506

*Same number; just a negative sign in front of it.*0509

*If I have two negatives signs, whether it is a negative times a negative*0513

*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

*They are asking is -2 the answer for the variable?*0777

*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 together*0810

*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 steps*1084

*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

*The answer stays a negative; equals A; that is my answer.*1168

*That is it for these multiplication equations; thank you for watching Educator.com.*1180

3 answers

Last reply by: sherman boey

Sun Jul 27, 2014 10:29 AM

Post by judy lee on August 26, 2011

And can you do cats and dogs on this?

1 answer

Last reply by: Mary Pyo

Sat Oct 29, 2011 10:40 PM

Post by judy lee on August 26, 2011

What if the product is not divisible?