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Lecture Comments (1)

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Post by Milan Ray on April 18, 2014

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

Subtracting Integers

Related Links

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

Subtracting Integers

Rewrite the subtraction problem to an addition problem and solve
7 - 8
  • 7 + - 8
- 1
Rewrite the subtraction problem to an addition problem and solve
- 13 - 5
  • - 13 + - 5
- 18
Find the differences
5 - 12
  • 5 + - 12
- 7
Find the difference
- 6 - - 5
  • - 6 + 5
- 1
Find the difference
- 15 - 8
  • - 15 + - 8
- 23
Find the difference
21 - 29
  • 21 + - 29
- 8
Find the difference
  • |−6| = 6
  • |−12| = 12
  • 6 - 12
- 6
Find the difference
|−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
- 11

*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.


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

Transcription: Subtracting Integers

Welcome back to; 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 problem0019

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 plus0667

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 plus0677

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