Next, we're going to do division with negative numbers, and the rules for division are the same as the rules for multiplication.
And the reason why is because division is multiplication by the reciprocal. So, when we divide, we simply divide absolute values.
If the two numbers have the same sign, the answer is positive; and if the two answers have different signs, the answer is negative.
Problem number 1: we have 8 ÷ -4, so I'll simply do my division, 8 ÷ 4 = 2.
when I just divide absolute values; and then, I see that the two numbers in my division problem had different signs so my answer is negative.
So, the answer is -2. Problem number 2: I have -48 ÷ 16. Again, I just divide absolute values:
16 divides into 48, 3 times, and the two numbers have different signs, so the answer is negative.
So, you can see that if I divide two numbers with, that have different signs, I simply divide absolute values.
And the answer is negative because the original two numbers had different signs.
Our next problem: we have two numbers with the same sign. I have -39 ÷ -13. Again, I simply divide 39 by 13, and get 3.
The two numbers have the same sign, so the answer is positive. So, the answer to that is positive 3.
The rules for division are the same as the rules for multiplication. Here's a problem that involves fractions.
How about -3/4 ÷ -3/4? Well, this time I'm going to take my -3/4 here,
and I'm going to change division to multiplication by the reciprocal. That would be -4/3. When I multiply, I multiply absolute value;
so, 3(4) = 12; in the denominator 4(3) is also 12.
The two numbers have the same sign, so the answer is positive, and 12 ÷ 12 = 1.
So, applying our rules for division, we see that -3/4 ÷ -3/4 does in fact come out 1, exactly the way we thought it should.
Let's look at a problem that's a little more complicated. Problem 5: I have 15(-5) - 25 divided by 2(-10).
The fraction bar separates the numerator from the denominator. It's like a grouping symbol, so I'm going to simplify in the numerator first.
15(-5) is going to be -75. Then, I have my subtraction sign here, 25; in the denominator 2 (-10) = -20.
In the numerator, I have -75 - 25, which is -75 + (-25), or a -100 ÷ -20.
Now, my last step, I do my division: 100 ÷ 20 = 5. The two numbers have the same sign, so the answer is positive.
So, more complicated expressions like this that involve multiplication, subtraction, and division,
I work on the numerator and denominator separately, until I get down to the last part right here, where I have a single number
in both the numerator and denominator. Then, I can do my division.
Let's try another one of these. Here, I have to simplify the numerator first, and I'll do that by working with the exponents.
I have -4(3² = 9); subtract 5(2² = 4). And that's all divided by -8(7), which is -56.
Now, 4(9) = 36, and I'm multiplying numbers with different signs, so the answer is negative; subtract, that's that subtraction sign;
5(4) = 20, that's all divided by -56. -36 + (-20) is going to be -56, divided by -56,
and that will come out to be just the number 1.
So, you see, again, I have subtraction right here: -36 - 20, I think in terms of addition;
-36 + (-20) that gives me -56. Then, I divide by -56, and the result is 1.
One more problem: I'll work inside the parentheses first. When I do, 2 - 9 is the same as 2 + (-9);
that's right, it's -7; subtract; 5 - 7 = 5 + (-7), which is -2.
In the denominator, 10 - 15, 10 + (-15), which is -5.
In the numerator, I have -7 subtracting -2 is the same as adding positive 2. That's all over -5.
I continue to simplify in the numerator: -7 + 2 = -5, divided by -5; and that comes out to be, again, just the number 1.
So, there's how we do division with positive and negative numbers.
The rules for division are the same as the rules for multiplication, as far as what sign the answer has.