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