Let's do some examples dividing fractions
Let's say that I have negative 5/6
divided by 3/4.
We've already talked about, when you divide by something,
it is the exact same thing as multiplying by its reciprocal,
so this is going to be the exact same thing as negative 5/6 times the reciprocal of
3/4, which is 4/3. I'm just swapping the numerator with the denominator, its going to be 4/3.
We've already seen examples multiplying fractions, this is going to be the numerators times each other,
so we are multiplying -5 times 4. And the denominator is 6 times 3
Now the numerator here you see we have a negative number. You might already know that 5 times 4 is 20,
and you just have to remember, look we are multiplying in negative times a positive.
We are going to essentially gonna have a -5, 4 times (-5 + -5 + -5 + -5) = -20.
So the numerator here is -20, and the denominator is 18.
You get -20 over 18, but we can simplify this.
Both the numerator and the denominator are both divisible by 2, so lets divide them by 2.
If we divide the numerator and the denominator by 2 just to simplify this,
and I've picked to because it is the largest number that goes into both of these.
Its the greatest common divisor of 20 and 18. 20 divided by 2 is 10, and 18 divided by 2 is 9.
So negative 5/6 divided by 3/4.. Oh, I have to be very careful here, it is -10
Just how we always learned, if you have a negative divided by a positive,
then you're going to get a negative value.
Let's do another example, let's say that I have -4 divided by -1/2.
So using the exact logic that we just said, we said "Hey, dividing by something is equivalent to multiplying by its reciprocal".
So this is going to be equal to -4. Instead as writing it as -4, let me just write it
as a fraction, so we are clear at what its numerator and its denominator is.
So -4 is the exact same thing as -4/1
And we are going to multiply that times the reciprocal of -1/2.
The reciprocal of -1/2 is -2/1.
You could view it as 2/-1 or -2/1, or you could just have as -2. Either way, these are all the same value.
And now we are ready to multiply. Notice all I did here
I rewrote the -4 just as -4/1. -4 / 1 is -4
And here for the -1/2, since I am multiplying now by its reciprocal,
I've swapped the denominator and the numerator.
And I'm ready to multiply, this is going to be equal to
-4 times -2 in the numerator, then in the denominator,
its going to be 1 times 1. And so this gives us a negative times a negative, so we will get a positive value here
and 4 times 2 is 8, so this is a positive 8 over 1, and 8 / 1 is just 8.