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Current time:0:00Total duration:6:22

Relate place value to standard algorithm for multi-digit addition


Video transcript

what we're going to do in this video is get some practice adding multiple digit numbers but the point of it isn't just to get the answer but to understand why the method we use actually works so we're going to add 40 thousand seven hundred sixty-two 230 thousand four hundred and seventy-three and you can pause the video and try to solve it on your own but I encourage you to watch this one because it's really about understanding how things happen so what I'm going to do is first think about this in terms of place values so let me write out my place value so see this goes all the way up to the ten thousands place so let's see ten thousands and then we have a thousands thousands then we have a hundreds I could write these words out but it's a little bit faster to write it this way and then we could have a tens place and then we could have a ones place I want to do that in a different color so then we have a ones place let me make a table here I'm going to express both of these numbers in terms of ten thousands thousands hundreds tens and ones and then I'm gonna at the same time use what's sometimes known as the standard method or the standard algorithm algorithms a fancy word for a system a way of doing something but let's first represent these numbers so here I have for ten thousands one two three four here I have three ten thousands one two three I'm gonna add these two together eventually in both of these numbers I have zero thousands so I have nothing in this column right now here I have seven hundreds one two three four five six seven here I have four hundreds one two three four then I go to this the tens place here I have six tens one two three four five six here I have seven tens one two three four five six seven and then last but not least here I have two ones one two and here I have three ones one two three now let's just rewrite this number up here this is just this is four ten thousands so this is 40,000 I have zero thousands right over there and then I have 700 700 I have six tens six tens and I have two ones I'm just rewriting the number I want let me write the tens in that blue color so six tens and then two ones having trouble switching colors to ones so there you have it this and this are just different ways of representing the same number and then this down here I have three ten thousands and then I have zero thousands I have four hundreds here and then I have was the seven tens seven tens and then I have three ones and so now let's add up everything so I can add it here and then I can also add up things right over here so in the standard method we would start at the lowest place and we'd say okay two ones plus three ones is equal to five ones and similarly two 1s plus three ones would be one two three four five ones fair enough nothing fancy there now let's go to the tens place well in the tens place we have six tens plus seven tens and the standard method what you say is that that's 13 tens but 13 tens is the same thing as three tens and one hundred so what you do is you would regroup you would say hey look this is three tens and one hundred sometimes people say oh you're carrying the 1 6 plus 7 is 13 carry the 1 and it seems somewhat magical but all you're doing is you're taking ten of the tens and you're regrouping it as a hundred it'll be a little bit clearer here so we have six one six tens and then we have seven tens you add them all together you get 1 2 3 4 5 6 7 8 9 10 11 12 13 tens and all we're doing right over here is we're saying look this is equal to a hundred so let's let's just convert that into into into a hundred right over here let's just convert that and so what we do is we just write the 3 in the tens place and then we add an extra one in the hundreds place and so what are we gonna have in the hundreds place now and actually let me do it here because it's a little bit more interesting so I have one two three four five six seven eight nine ten eleven twelve hundreds so I could write them down here one two three four five six seven eight nine 10 11 and 12 but with the same thing we don't have a digit for the number 12 in our traditional number system and so what I could do is I could take 10 of these and I can convert it to 8,000 so I'm going to take 10 of those and give myself a thousand and we're going to do the exact same thing over here 1 plus 7 plus 4 is 12 so you'd write that's 2 hundreds because this is 12 hundredths that's 2 hundreds plus a thousand so we just regrouped again now in the thousands place 1 plus 0 plus 0 is 1,000 and you see that right over here you have 1,000 and then finally in the ten thousands place for 10 thousands plus 3 10 thousands is 7 10 thousands for 10 thousands plus 3 10 thousands is 1 2 3 4 5 6 7 10 thousands and so this number is 70 1235 70 1235 so hopefully it all makes sense how these two things will fit together that what's going on over here you're not just magically carrying numbers or magically regrouping you're just representing the same number in different ways