Hi, and welcome back. My name is Anthony Varela. And today, we're going to talk about multiplying and dividing positive and negative numbers.
So we're going to tap into what we already know about basic multiplication and division, but we're just going to talk about sign-- or positive and negative. So we're going to take a look at how sign affects the product in multiplication, how the sign affects the quotient in division. And along the way, we're going to be developing general rules involving the sign of numbers in multiplication and division. So let's get started by talking about sign.
This means positive or negative. And when we're talking about changing sign, we're talking about going from positive to negative or going from negative to positive. And in general, the big idea for this lesson is that when multiplying or dividing by a negative, this changes the sign of our solution. So we're going to write this down because this is going to be the common thread throughout the entire video.
So let's start out with a very basic multiplication problem, 5 times 4. We know that this equals 20, but let's talk about the sign. So we're starting with a positive number, the positive 5, and we're multiplying by a positive 4. Now, going back to this idea that multiplying or dividing by a negative change is the sign of a solution, 4 is not negative, so we're not going to change the sign. We're going to remain positive in our product.
So 5 times 4 is 20, a positive number. And we're going to write this down as a general rule for multiplying two positive numbers. The product of two positive numbers is always positive. Let's see how this works with division. We have 32 divided by 4. Now, I know that this equals 8. And looking at the sign, 32 is a positive number. So is 4, so our sign does not change in our quotient. So the quotient of two positive numbers is always positive as well.
So now let's throw a negative number in here and see how this changes our answer. 7 times negative 3. Well, I know that this is negative 21, so let's take a look at the sign. Well, I'm starting with a positive number and, hey, multiplying or dividing by a negative changes the sign of the solution. So I can think of this as 7 times 3 equals 21. So 7 times negative 3 equals negative 21 because the sign must change.
So this is one of our general rules. When multiplying a positive number by a negative number, our product is always negative. Let's see if this holds true with division as well, 49 divided by negative 7. I know that this is a negative 7. Again, starting with a positive number, we're dividing by a negative number, so the sign of our quotient must change from positive to negative. So sure enough, if you have a positive number divided by a negative number, your quotient will be negative.
Now, take a look at this. I also have one positive number and one negative number, but I've switched them around. Let's see if this makes any difference. Negative 6 times 3. Well, I know that this is negative 18, and here's how we can think about that. Negative 6 is a negative number. We're multiplying that by a positive, and positive numbers does not change the sign of our product, so we remain negative. We don't change to positive.
So a negative number times a positive number equals a negative number, and we really have that written right here. So it doesn't matter if I swap the negative and positive in this statement right here. The product of a positive and a negative number will always be negative.
And you might have guessed, this holds true for division as well. I have a negative number divided by a positive number, so the sign of my cautions will not change from negative to positive. It will remain negative. So that's just another statement right here that a negative number divided by a positive number is negative.
So now what do we do if we have two negative numbers? Negative 6 times negative 5 equals a positive 30, and this is how we can think about that. We're starting with a negative number. Multiplying by a negative number changes the sign of our product from negative to positive. So negative 6 times negative 5 is a positive 30. And this is one of our general rules. The product of two negative numbers is always positive.
And you guessed it, this holds true for division as well. We're starting with a negative number. Dividing by a negative number change the sign of our quotient from negative to positive. So negative 36 divided by negative 12 is a positive 3. And as a general rule, the quotient of any two negative numbers is always positive.
So let's take a look at your notes. The big idea was that multiplying or dividing by a negative changes the sign of the product or quotient. So we looked at cases involving two positive numbers, a positive and a negative, and then two negative numbers. And we noticed that these general rules were the same whether we're multiplying or dividing. In the case of two positives the product of two positives is a positive number, the quotient of two positives is a positive number.
When we have one positive and one negative-- doesn't matter which order-- the product is always negative or the quotient is always negative. And when we're dealing with two negative numbers, both in multiplication and division, the product of two negative numbers is positive, and the quotient of two negative numbers is positive. Well, thanks for joining me in this tutorial about multiplying and dividing positive and negative numbers. I'll hope to catch you next time.