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# Dividing mixed numbers

CCSS.Math:

## Video transcript

let's see if we can figure out what 4 and 4/5 divided by 1 and 1/2 is and I encourage you to pause the video and see if you can figure it out on your own and I'll give you a hint see if you can rewrite these mixed numbers as as what is sometimes called improper fractions alright now let's do this together so how can we rewrite 4 and 4/5 well 4 and 4/5 is the same thing as if we take the 4 that's the same thing as 4 plus 4 fish 4 plus 4/5 and 4 is the same thing as twenty-fifths so 4 is the same thing as twenty-fifths and then plus 4 this well what are you going to get you're going to get you add the numerators you get 20 4/5 24 fish another way to think about it is take this denominator takes the fifths multiplied by 4 you get twenty fifths plus the 4/5 that you already have is 24 fish and so this is the same thing as 24 fifths divided by if you do the same idea one and a half's the same thing as 1 plus 1/2 1 is the same thing as 2 halves plus 1/2 and so that's going to be add the numerators that's going to be 3 halves so just like this we're able to rewrite our expression as 24 fifths divided by three halves and now the key realization is is that that is the same thing as 24 fifths times the reciprocal of 3 halves so times pause the video what's the reciprocal of 3 halves well the reciprocal of 3 halves you just swap the numerator in the denominator it's going to be 2 over 3 now what is this going to be well there's a couple of ways to do it you could just straight-up multiply the numerators and you would get 48 and then multiply the denominators and you would get 15 so you get 48 over 15 but you might be able to rewrite that in slower and/or and more sometimes what's called a more simplified way but another way of thinking about this is you could just say well this is the same thing as 24 times 2 times 2 over five times three and simplify things before you even multiply them out five times five times three and you realize that look 24 and 3 are both divisible by 3 so let me divide them both by 3 so 24 divided by 3 is 8 and 3 divided by 3 is equal to 1 and then you could multiply the numerators and the denominators and so and so you get in the numerator 8 times 2 is 16 in the denominator you get a 5 so you get 16 fifths and then if you want to express that as a mixed number 16 over 5 well 5 goes into 16 three times with one left over so this is 3 and one fifth and one thing to appreciate right over here I simplify then the 24 and the three of this step sometimes you'll see people simplifying at this step so they'll say hey look eventually I'm going to have a 24 in the numerator and a 3 in the denominator so let me divide both of those by 3 so they'll say 24 divided by 3 is 8 and then a 3 divided by 3 is 1 and this is sometimes called a cross reduction but this is all that's going on right over here