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Dialogue: 0,0:00:00.64,0:00:04.16,Default,,0000,0000,0000,,Let's do some examples dividing fractions
Dialogue: 0,0:00:04.44,0:00:08.37,Default,,0000,0000,0000,,Let's say that I have negative 5/6
Dialogue: 0,0:00:08.52,0:00:15.99,Default,,0000,0000,0000,,divided by 3/4.
Dialogue: 0,0:00:15.99,0:00:19.52,Default,,0000,0000,0000,,We've already talked about, when you divide by something,
Dialogue: 0,0:00:19.52,0:00:22.94,Default,,0000,0000,0000,,it is the exact same thing as multiplying by its reciprocal,
Dialogue: 0,0:00:22.97,0:00:32.52,Default,,0000,0000,0000,,so this is going to be the exact same thing as negative 5/6 times the reciprocal of
Dialogue: 0,0:00:32.52,0:00:40.82,Default,,0000,0000,0000,,3/4, which is 4/3. I'm just swapping the numerator with the denominator, its going to be 4/3.
Dialogue: 0,0:00:40.82,0:00:47.08,Default,,0000,0000,0000,,We've already seen examples multiplying fractions, this is going to be the numerators times each other,
Dialogue: 0,0:00:47.08,0:01:03.91,Default,,0000,0000,0000,,so we are multiplying -5 times 4. And the denominator is 6 times 3
Dialogue: 0,0:01:03.91,0:01:09.94,Default,,0000,0000,0000,,Now the numerator here you see we have a negative number. You might already know that 5 times 4 is 20,
Dialogue: 0,0:01:09.94,0:01:13.53,Default,,0000,0000,0000,,and you just have to remember, look we are multiplying in negative times a positive.
Dialogue: 0,0:01:13.53,0:01:21.00,Default,,0000,0000,0000,,We are going to essentially gonna have a -5, 4 times (-5 + -5 + -5 + -5) = -20.
Dialogue: 0,0:01:21.00,0:01:27.14,Default,,0000,0000,0000,,So the numerator here is -20, and the denominator is 18.
Dialogue: 0,0:01:27.14,0:01:30.32,Default,,0000,0000,0000,,You get -20 over 18, but we can simplify this.
Dialogue: 0,0:01:30.32,0:01:38.32,Default,,0000,0000,0000,,Both the numerator and the denominator are both divisible by 2, so lets divide them by 2.
Dialogue: 0,0:01:38.32,0:01:42.92,Default,,0000,0000,0000,,If we divide the numerator and the denominator by 2 just to simplify this,
Dialogue: 0,0:01:42.92,0:01:45.86,Default,,0000,0000,0000,,and I've picked to because it is the largest number that goes into both of these.
Dialogue: 0,0:01:45.89,0:01:53.32,Default,,0000,0000,0000,,Its the greatest common divisor of 20 and 18. 20 divided by 2 is 10, and 18 divided by 2 is 9.
Dialogue: 0,0:01:53.32,0:02:02.22,Default,,0000,0000,0000,,So negative 5/6 divided by 3/4.. Oh, I have to be very careful here, it is -10
Dialogue: 0,0:02:02.22,0:02:07.46,Default,,0000,0000,0000,,Just how we always learned, if you have a negative divided by a positive,
Dialogue: 0,0:02:07.46,0:02:09.73,Default,,0000,0000,0000,,then you're going to get a negative value.
Dialogue: 0,0:02:09.73,0:02:24.33,Default,,0000,0000,0000,,Let's do another example, let's say that I have -4 divided by -1/2.
Dialogue: 0,0:02:24.33,0:02:30.14,Default,,0000,0000,0000,,So using the exact logic that we just said, we said "Hey, dividing by something is equivalent to multiplying by its reciprocal".
Dialogue: 0,0:02:30.14,0:02:36.73,Default,,0000,0000,0000,,So this is going to be equal to -4. Instead as writing it as -4, let me just write it
Dialogue: 0,0:02:36.73,0:02:41.22,Default,,0000,0000,0000,,as a fraction, so we are clear at what its numerator and its denominator is.
Dialogue: 0,0:02:41.22,0:02:45.14,Default,,0000,0000,0000,,So -4 is the exact same thing as -4/1
Dialogue: 0,0:02:45.14,0:02:51.73,Default,,0000,0000,0000,,And we are going to multiply that times the reciprocal of -1/2.
Dialogue: 0,0:02:51.73,0:02:56.82,Default,,0000,0000,0000,,The reciprocal of -1/2 is -2/1.
Dialogue: 0,0:02:56.82,0:03:05.28,Default,,0000,0000,0000,,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.
Dialogue: 0,0:03:05.28,0:03:08.26,Default,,0000,0000,0000,,And now we are ready to multiply. Notice all I did here
Dialogue: 0,0:03:08.26,0:03:13.46,Default,,0000,0000,0000,,I rewrote the -4 just as -4/1. -4 / 1 is -4
Dialogue: 0,0:03:13.46,0:03:19.22,Default,,0000,0000,0000,,And here for the -1/2, since I am multiplying now by its reciprocal,
Dialogue: 0,0:03:19.22,0:03:29.37,Default,,0000,0000,0000,,I've swapped the denominator and the numerator.
Dialogue: 0,0:03:29.37,0:03:34.100,Default,,0000,0000,0000,,And I'm ready to multiply, this is going to be equal to
Dialogue: 0,0:03:34.100,0:03:42.32,Default,,0000,0000,0000,,-4 times -2 in the numerator, then in the denominator,
Dialogue: 0,0:03:42.32,0:04:00.26,Default,,0000,0000,0000,,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
Dialogue: 0,0:04:00.26,0:04:04.26,Default,,0000,0000,0000,,and 4 times 2 is 8, so this is a positive 8 over 1, and 8 / 1 is just 8.