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Dividing negative fractions

CCSS.Math: ,

Video transcript

let's do some examples dividing fractions let's say that I have negative 5/6 divided by divided by 3/4 divided by positive 3/4 well we've already talked about when you divide by something it's the exact same thing as multiplying by its reciprocal so this is going to be the exact same thing as negative 5/6 as negative 5/6 x times the reciprocal of 3/4 which is 4 over 3 I'm just swapping the numerator and the denominator so it's going to be 4 over 3 and we've already seen lots of examples multiplying fractions this is going to be the numerators times each other so we're going to multiply negative 5 times 4 I'll give the negative sign to the 5 there so negative 5 times 4 love you for that yellow color and then the denominator is 6 times 3 6 times times 3 now in the numerator here in the numerator 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're multiplying a negative times a positive we're going to sense you're going to have negative 5 4 times so negative 5 plus negative 5 plus negative 5 plus negative 5 is negative 20 so the numerator here is negative 20 and the denominator here is 18 so we get 20 over 18 but we can simplify this both the numerator and the denominator they're both divisible by 2 so let's divide them both by 2 give myself a little more space so if we divide both the numerator and the denominator by 2 just to simplify this and I picked 2 because that's the largest number that goes into both of these that's 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 is oh I have to be very careful here it's negative negative 10 ninths just how we always learn if you have a negative divided by a positive if the signs are different then you're going to get a negative value let's do another example let's say that I have negative 4 negative 4 divided by divided by negative 1/2 negative 1/2 so using the exact logic that we just said we said hey look dividing by something is equivalent to multiplying by its reciprocal so this is going to be equal to negative 4 and instead of writing as negative 4 let me just write it as a fraction so that we are clear what its numerator is and what's denominator is so negative 4 is the exact same thing as negative 4 over 1 and we're going to multiply that times the reciprocal of negative 1/2 the reciprocal of negative 1/2 is negative 2 over 1 negative 2 over 1 you could view it as negative 2 over 1 or you could views it as positive 2 over negative 1 or you could views it as negative 2 either way these are all the same value and now we're ready to multiply notice all I did here I rewrote the negative 4 just as negative 4 over 1 negative 4 divided by 1 is negative 4 and here for the negative 1/2 since I'm multiplying now I'm multiplying by its reciprocal I've swapped the denominator in the numerator or the I swapped the denominator in the numerator what was the denominator is now the numerator what was the numerator is now the denominator and I'm ready to multiply this is going to be equal to I gave both the negative signs to the numerator so it's going to be negative 4 negative 4 times negative 2 in the numerator and then in the denominator it's going to be 1 times 1 write that down 1 times 1 times 1 and so this gives us so we have a negative 4 times a negative 2 so it's a negative times a negative so we're gonna get a positive value here and 4 times 2 is 8 so this is a positive 8 over 1 and 8 divided by 1 is just equal to 8