Basic Math Multiplying Integers

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

When you multiply integers, it is very important to keep in mind that0007

if one of the two numbers is negative, then your answer is going to be negative.0014

If both numbers are negative, then your answer will be positive.0019

Very different than when you add or subtract integers.0023

Make sure you keep that rule in mind; this is very important.0026

If only one number is negative, if you have one negative sign in the problem, then the answer will be negative.0029

If you have two numbers, think of it as those two numbers cancel the negatives out.0036

The product will be a positive; one number, then the answer will be negative.0041

If it is two numbers, then the answer will be positive.0049

If I am going to multiply let's say A and B together,0054

if I multiply A times a ?B, then my answer is going to be... this is a positive.0057

Remember there is no sign in front, then it is a positive.0065

Positive times negative is going to be negative; this is ?AB.0068

Or if I have ?A times ?B, we have two negatives signs.0073

My answer will be a +AB.0081

Let's do a few examples; the first one, -5 times 7; -5 times 7.0088

We are going to multiply these numbers the same way; 5 times 7 is 35.0096

I only have one negative sign.0104

From the two numbers that I am multiplying, only one is negative.0107

My answer will be a negative.0110

This one, -8 times -4, I know that is a 32.0116

I have two negative signs; two negatives signs gives me a positive.0123

Another way to think of it, if you have an odd number of negatives in the problem,0131

then your answer, your product will be a negative.0137

If you have an even number of negatives, like 2, 4, 6, 8, then your answer would be a positive.0140

Every two negatives cancel each other out to make a positive.0146

Even if you are multiplying four numbers together and they are all negatives, you have four negative signs.0153

That is going to give you a positive answer, a positive product.0159

3 times -10; 30; I have only one negative sign; that is a negative product.0165

What about this one?--this one, the answer is 60.0178

If I multiply these two numbers, a positive and a positive.0183

This doesn't change; this is just 12 times 5 is 60.0186

There is no negative signs involved.0191

20 times -12; 20 times 12 is 240.0195

We have one negative sign right here; positive times a negative is a negative.0205

This next one, 11 times 10 is 110.0214

A negative sign times a negative sign, we have two negatives.0223

That makes a positive; +110.0226

Again when we are multiplying two numbers, we have only one negative sign.0234

If only one of the numbers is negative, then the product will be a negative.0241

If you have two negative signs, it is going to become a positive.0248

In this problem, 7 times 9 is 63.0253

I have a positive here; I have a negative here.0260

I have one negative sign; that is going to make my answer a negative.0262

This next problem, I have a few things I have to solve out.0269

But the first thing I always solve out is parentheses.0276

I must solve my parentheses first; this is order of operations.0279

Order of operations says parentheses; I have parentheses right here.0284

I am going to solve this out; that is -7 minus a 3.0287

From the previous lesson on subtracting integers,0292

I want to use the two-dash rule to make this subtraction problem into an addition problem.0294

I am going to do that; keep this in parentheses.0300

-7; make this a plus; then a negative; this becomes -7 plus a -3.0304

They have the same sign; I add the numbers and keep that same sign.0316

The absolute value of -7 is 7; plus the absolute value of -3 is 3.0324

If I add those two numbers together, I get 10.0331

But then since they are both negative, I have to keep that same sign.0335

This rule is very different than multiplying integers.0338

Always keep in mind what you are doing.0343

Are you adding integers?--are you subtracting?--are you multiplying?0345

The next lesson is going to be dividing integers.0349

For each of them, think of the different rules; just keep practicing the problems too.0353

This was -10; I still have another parentheses I have to solve out.0360

This one right here is already an addition problem.0369

We don't have to change this problem like we did this one because it is already a plus right here.0373

The whole point of changing this was to make it a plus.0380

A -15 plus 8, they have different signs.0385

We are going to take the difference of their absolute values.0390

-15, the absolute value of that would be 15.0393

The absolute value of 8 is 8.0397

If you find the difference of 15 and 8, that is 7.0399

The sign, we take from this one, the 15; that sign is a negative.0406

I give this a negative; just going to write this out again right here.0413

-10 times a -7; 10 times 7 is 70.0425

Then I have a negative times a negative; I have two negatives.0432

That is going to make my answer, my product, a positive.0435

Think of two negatives cancelling each other out; that is going to be +70.0440

That is it for this lesson on multiplying integers; thank you for watching Educator.com.0448