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

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

### Subtracting Integers

#### Related Links

- Integers
- Fraction
- Absolute Value
- Natural numbers
- Negative number
- Real number
- Sign
- Value
- Substraction
- Plus and minus signs

- Use the Two-Dash Rule to change the subtraction problem into an addition problem
- Add the integers

### Subtracting Integers

7 - 8

- 7 + - 8

- 13 - 5

- - 13 + - 5

5 - 12

- 5 + - 12

- 6 - - 5

- - 6 + 5

- 15 - 8

- - 15 + - 8

21 - 29

- 21 + - 29

|−6|−|−12|

- |−6| = 6
- |−12| = 12
- 6 - 12

|−23| − |13|

- |−23| = 23
- |13| = 13
- 23 - 13

- 9 - - 12 + 5

- - 9 + 12 = 3
- 3 + 5

15 - 20 - 6

- 15 - 20 = - 5
- - 5 - 6 = - 5 + - 6

*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

### Subtracting Integers

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
- How to Subtract Integers 0:06
- Two-dash Rule
- Example: 3 - 5
- Example: 3 - (-5)
- Example: -3 - 5
- Extra Example 1: Rewrite Subtraction to Addition 4:43
- Extra Example 2: Find the Difference 7:59
- Extra Example 3: Find the Difference 9:08
- Extra Example 4: Evaluate 10:38

### Basic Math Online Course

### Transcription: Subtracting Integers

*Welcome back to Educator.com; this next lesson is on subtracting integers.*0000

*The previous lesson was on adding integers.*0011

*What we are going to do first in order to subtract integers is*0015

*use a two-dash rule to change the subtraction problem to an addition problem*0019

*because adding integers is always a lot easier than subtracting integers.*0026

*We are going to use the two-dash rule.*0033

*What that is is in order to change the minus sign to a plus sign, you are going to add a dash to it.*0036

*For example, if I have 3 minus 5, first step, I have to make two dashes.*0045

*The first dash is to make this minus sign a plus sign.*0053

*That is the whole point--to change the minus to a plus.*0057

*I am going to use the first dash to make that a plus.*0060

*Then I have to make two of them.*0063

*My second one will be to make this a negative.*0065

*My subtraction problem is now an addition problem.*0069

*Another example, if I have 3 minus -5.*0072

*This is a minus; this is a negative.*0078

*The first dash is going to make this minus a plus.*0081

*Since I have to make two dashes, this is already a negative.*0085

*My second dash would be to make that a positive.*0089

*3 minus -5 would be the same as 3 plus 5.*0092

*If I have -3 minus 5, this right here would be just a -3.*0100

*That is not a minus problem.*0108

*The minus is right here because it is -3 minus the 5.*0109

*When you use a two-dash rule, you are not going to be using it for negative signs.*0114

*All you are doing is changing the subtraction problem to an addition problem.*0118

*You are not going to use two-dash rule for this one up here.*0127

*But you are just using it for the minus sign; it will be one, two.*0130

*That is your subtraction problem to an addition problem; then you just add the integers.*0136

*If you remember from last lesson, when we add integers,*0141

*if we have the same sign here, if it is the same sign,*0145

*if this is a negative and this is a negative, then we can combine these numbers.*0149

*We can add the numbers which is 8; or take the absolute value.*0154

*Remember absolute value takes the distance from 0.*0158

*-3 is 3 from 0.*0163

*Absolute value must be a positive number because distance...*0166

*if you are looking at how far away -3 is from 0... here is 0, 1, 2... here is -3.*0170

*How many units away from 0 is it?--it is 3.*0179

*Whenever you measure distance, it cannot be a negative; it has to be a positive.*0184

*The absolute value of -3 is 3; the absolute value of -5 is 5.*0190

*If you add those, it is going to be 8.*0196

*But then be careful because you have to give it the same sign.*0200

*This is a negative; this is a negative.*0205

*Then this is going to be a negative; -3 plus -5 is -8.*0206

*If you look at these problems right here or this one, let's do this one first.*0212

*This one doesn't have a sign in front it.*0217

*But it is a positive because numbers are going to be either positive or negative.*0219

*If there is no negative sign in front of it, then it has to be a positive.*0224

*This is a +3 plus a +5.*0228

*That is just the same thing as 3 plus 5 which is 8 or +8.*0232

*For this one, their signs are different; this is a +3 plus a -5.*0238

*Since their signs are different, again you take the absolute value.*0245

*This is 3; absolute value of this is 5.*0248

*Instead of adding them, you are going to subtract them.*0251

*You are going to find the difference; that is 2.*0253

*Then you take the number with the greater absolute value which is this one right here.*0256

*Get that sign; give it to this one; the answer is -2.*0262

*If you don't remember how to do this or if you want to look at a few more examples,*0270

*we are going to do a few more here for this lesson.*0275

*But you can also go back to the lesson on adding integers.*0278

*The first set of examples is to rewrite the subtraction problem to an addition problem.*0286

*This one, the first one is 5 minus 9.*0291

*We want to use the two-dash rule.*0296

*The two-dash rule is strictly just used to make a subtraction problem to an addition problem.*0299

*Later when you start getting really comfortable with these kind of problems, you won't have to use the two-dash rule.*0306

*The two-dash rule is just to make the problems a lot easier.*0311

*For here, the first dash I am going to make is to make that minus into a plus.*0314

*That is the first one.*0323

*My second one that I have to make will be to make that one a negative.*0325

*Now we have 5 plus -9.*0329

*Now that it is a plus problem, we have to add these two integers.*0335

*But they have different signs; this is +5; this is a -9.*0340

*We take the absolute value; the absolute value of 5 is 5.*0344

*The absolute value of -9 is 9; remember their signs are different.*0348

*So we find their difference.*0353

*Absolute value of 5 plus absolute value of -9 is going to be...*0358

*I am sorry... this is a minus; let me just make that a minus.*0365

*This is going to be 4; it is a 4.*0372

*But remember again you have to figure out which one...*0378

*If this is a 5 and this is a 9, this is the bigger number.*0382

*You look at the sign that goes with that number; it is a negative.*0387

*You are going to give that negative sign to the answer; it is -4.*0391

*This next problem, we have a minus negative; it is -10 minus a -4.*0396

*Again the first dash will be to make this one into a plus.*0404

*The second dash... for this problem, we made it into a negative.*0409

*But it is already a negative; we have to make that into a plus.*0414

*Again you are not going to use the two-dash rule for this negative sign up here.*0419

*It is only to make this a plus.*0423

*Whenever you do the two dash rule, it has to be right in there.*0426

*-10 plus 4; this is -10 plus 4; that is the same thing.*0432

*Plus positive is the same thing as just plus.*0439

*I don't have to put my positive sign.*0442

*Again they have different signs.*0445

*The absolute value of 10 minus the absolute value of 4 is 6.*0448

*Which one has the greater number?*0456

*The absolute value is going to be this one right here.*0459

*You are going to take that same sign and give it to this.*0463

*Be careful with the signs because you can get this number right.*0466

*But if the sign is wrong, then the answer will be wrong.*0470

*You have to make sure you have the correct sign along with the correct number.*0473

*The next one, you are just finding the difference.*0480

*Again we are going to use the two-dash rule to make that a plus and then there.*0483

*They are different signs, a positive and negative sign.*0489

*We are going to find the difference of their absolute values which is 7.*0494

*You are going to give that a negative sign because the 11 is the greater absolute value.*0500

*You are going to give that a negative.*0508

*The next one, again you are going to make this a plus and then a plus.*0511

*-5 plus 5; this is -5 plus 5;*0517

*-5 plus 5, again they are different signs; you take the absolute value.*0521

*That is 5; minus the 5 is 0; this is just 0.*0530

*If you have +2 minus 2, that is 0.*0536

*A -5 plus a 5, if you have opposites, then it will just be 0.*0540

*Next one, 32 minus 9, make this a plus negative; they have different signs.*0551

*I take the difference of the absolute values.*0561

*This is 32, the absolute value; this is 39.*0565

*If I find the difference of that, it is 7.*0569

*With that negative sign belonging to the 39, to the greater value, that becomes a negative.*0573

*For this, absolute value of -15 minus absolute value of -9.*0582

*The absolute value of -15, how far is -15 from 0?--it is 15.*0589

*You can also think of it, whenever you take the absolute value of something, it is just the positive of that number.*0597

*If it is -15, then the positive of -15 is 15.*0602

*Minus... this is not inside the absolute value sign.*0608

*This doesn't change; this has to stay the same; absolute value of -9 is 9.*0612

*15 minus 9, that is 6; we don't have to change this.*0619

*If you want to, you can change this minus to a plus using the two-dash rule.*0626

*But 15 minus 9, we know that that is just 6.*0632

*The last couple examples; here we have -3 minus -8 plus 5.*0640

*The first thing I want to do is -3 minus -8;*0648

*I want to solve this first; but I have a minus.*0653

*Remember we want to change our subtraction problems to additions problems.*0656

*We do that by using the two-dash rule.*0662

*For the two-dash rule, the first step will be to make that minus into a plus*0667

*because that is the whole point of using it.*0672

*The minus will change to a plus.*0675

*Then I have to make one more little dash either to make this a negative or make it a plus*0677

*because it already is a negative so I have to make that a plus.*0683

*I change -3 minus -8 to -3 plus 8; -3 plus 8.*0686

*Plus positive is the same thing as just plus; -3 plus 8.*0695

*-3 plus 8, again they have different signs.*0701

*This is a negative; this is a positive.*0708

*I am going to take the absolute value.*0711

*If it is different signs, then you are going to take the difference of the absolute values.*0714

*-3, the absolute value of that, which is the distance from 0, how far away is -3 from 0?*0718

*That is 3; this absolute value is 8.*0725

*When you find how far apart they are from 8 and 3, the absolute values, you get 5.*0730

*This is 5.*0737

*You look at which number has the greater absolute value; that is 8.*0740

*You are going to give it the same sign as that number.*0747

*Since 8 is a greater number, it has the sign of a positive.*0751

*You are going to give that 5 a positive sign.*0755

*We don't have to write the positive sign.*0758

*If you just don't write anything, then that is the same thing as giving it a positive sign.*0760

*This right here became 5; then I have to do 5 plus this 5.*0766

*My answer is going to be 10.*0773

*The last example, this is 4 minus 10 minus a -9.*0779

*I am going to solve that first.*0785

*Again since it is a subtraction problem, 4 minus 10,*0789

*I am going to change that subtraction to an addition problem by using the two-dash rule.*0793

*The first dash will be to change this minus to a plus.*0800

*My next dash is going to make that into a negative.*0805

*Remember both dashes have to be within those two numbers.*0809

*You can't make this number negative instead of this number.*0813

*Both dashes you make are going to be within the two numbers.*0818

*It is 4 plus -10; again their signs are different.*0822

*This has no sign which means it is a positive; +4 plus -10.*0827

*They have difference signs which means you are going to take the difference of the absolute values.*0834

*This is 4; this is 10; their difference is going to be 6.*0839

*This has the greater value; it has the sign of a negative.*0851

*That is going to go there too.*0855

*Then I am going to do that; -6 minus a -9.*0859

*Again we have a minus problem.*0866

*I am going to change this to addition by doing that; that is 1.*0867

*It is already negative; I have to make that a +2.*0874

*-6 plus +9, opposite signs; they are different signs so you find the difference.*0878

*This is 6; this is 9; they are 3 units apart.*0887

*Which one has the greater value?--the 9; that has a positive sign.*0896

*This is going to be a positive sign; the answer is +3.*0901

*That is it for this lesson on subtracting integers.*0908

*If you want to go back and review over some more problems, the previous lesson on adding integers,*0912

*that will probably help you freshen up a little bit for the next lesson.*0919

*Thank you for watching; we will see you soon.*0923

0 answers

Post by Milan Ray on April 18, 2014

Can you use the two dash rule two times in one problem?