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Current time:0:00Total duration:3:51

Subtracting mixed numbers with regrouping (unlike denominators)


Video transcript

so we have the expression 17 and 4/9 minus 12 and 2/3 and I encourage you to pause the video and see if you can figure out what this is so now let's work through it so what I'm going to do is I'm going to rewrite these mixed numbers so I'm going to write this as 17 and 4/9 minus 12 and 2/3 I'm going to write the 12 right under the 17 and I'm gonna write the 2/3 right under the 4/9 let me make it very clear we are subtracting 12 and 2/3 from 17 and 4/9 so the first thing that we might want to do is we could look at the fraction parts and we might want to start subtracting until we see look we have different denominators here we have ninths and we have thirds so the first thing we'd want to do is let's get to a common denominator and a good common denominator would be the least common multiple of 9 and 3 well what's that going to be well to think think about that I like to start with the larger number 9 and say well is that divisible by 3 well yes it is divisible by 3 it is divisible by the other denominator so this actually is the least common multiple if it wasn't I would keep taking higher and higher multiples of 9 I'd go to 18 and then I would go to 27 and I would keep going until I found one the steps is what divisible by 3 but I didn't have to do that because 9 is divisible by 3 so I can rewrite both of these fractions as in terms of ninths now the one on top already is written in terms of 9 so I can just rewrite that 17 and 4/9 and the one on the bottom I can write as 12 and some number of nights so 2/3 is how many ninths well to go from thirds to ninths I had to multiply by 3 and 2 multiplied by 3 so the numerator I need to multiply by 3 as well 2 times 3 is 6 2/3 is the same thing as six ninths and now I can try to subtract but even here when I try to subtract I have a larger fraction down here that I'm trying to subtract from a smaller one I have 4/9 minus six ninths so what can I do well the answer is I can regroup I can take a whole from the 17 let me do that so if I take a whole from the 17 that's going to become 16 and then that hole that I just took from I guess you could say the whole number place I can add it to the fraction well a hole is just going to be 9/9 so all I did is I regrouped here I took 9/9 from 17 9 9 is 1 so I took nine nines from 17 I'm left with 16 and then I regrouped them and I added them to the fractions place as one way to think about it well what's 4/9 plus nine nines well that's going to be thirteen-ninths so this right over here is thirteen-ninths thirteen-ninths it's a very strange way to write it but 17 and 4/9 is the same thing as 16 and 13 9 because notice this is greater than 1 this is the same thing as 1 in 4/9 1 and 4/9 plus 16 is going to be 17 and 4/9 now why did I do all of this well 13 9 is larger than six ninths so I can subtract what's thirteen-ninths minus six ninths going to be well 13 of something in this case 9 minus 6 of that same something is going to be seven ninths 7 let me write that in a neutral color so that's going to be seven ninths thirteen-ninths minus six ninths is seven nights and then I can look over in the whole number place all I have left is 16 here 16 minus 12 is 4 and I'm done 17 and 4/9 minus 12 and 2/3 is equal to four and seven ninths