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Worked example: Subtracting 3-digit numbers (regrouping twice)

CCSS.Math: ,

Video transcript

so let's subtract 286 from 913 but first I'm going to do it slightly different way I've taken each of these numbers and I've expanded them out this nine and the hundreds place represents 900 this one in the tens place represents 10 this three in the ones place represents three likewise 286 is the same thing as 200 plus 80 plus six so let's try to subtract going place by place so if we start in the ones place we have a problem immediately three is less than six how do we subtract a larger number from a smaller number we also have a problem in the tens place 80 is less than ten what do we do or sorry eighty is larger than ten how do we subtract a larger number from a smaller number and you might guess the answer here is regrouping sometimes called borrowing we're going to take value from one place and give it to another so let's say this scenario right over here where we have this three and we want to take some value from one of the other places well I could take 10 from the tens place I could take 10 from the tens place so then this is going to become zero and if I give that 10 to the ones place so 10 plus 3 is 13 is 13 notice I haven't changed the value 900 plus 0 plus 13 is still 913 now this solved the problem for the ones place I can now subtract 6 from 13 but it made the problem in the tens place even worse I'd have to subtract 80 from 0 what do I do well luckily I can go to the hundreds place I could take a hundred from 900 so then I'm left with 800 and I could give it to the tens place so if I give it to the tens place then this is going to be 100 so then this is going to be 100 right over here notice this still adds up to 913 800 plus 100 plus 13 is 913 why is this valuable well now in every column I'm subtracting a smaller number from a larger you might say wait isn't there a positive sign here but we have this negative out here so we're subtracting 6 from 13 we're subtracting 80 from 100 subtracting 200 from 800 so let's do it thirteen minus six is seven 100 minus 80 is twenty eight hundred minus 200 is 600 so we're left with 600 plus 20 plus 7 which is 627 now let's do the exact same thing here but we're not going to expand out the numbers so 6 is greater than three what do we do well we can regroup from the tens place we can take ten from here so we're left with zero tens and give that one 10 to the ones place so you give 10 to the 3 you get it becomes 13 it becomes 13 but now we have a problem in the tens place how do we subtract eight from zero well we could take 100 from the hundreds place so 900 becomes 800 and give that hundred to the tens place so you give the 100 to the tens place a hundred plus zero tens is a hundred a hundred is the same thing as ten tens is the same thing as ten tens and so now we are ready to subtract 13 minus six is seven 10 minus 8 is 2 remember this is really 10 tens minus eight tens to get two tens 10 tens minus eight tens to get two tens 100 minus 80 to get 20 and then finally we have 800 minus 200 to get 600 627