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Regrouping whole numbers: 76,830

Sal regroups 76,830 by its place values. Created by Sal Khan.

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  • aqualine ultimate style avatar for user Isabella Scott
    On this video it is saying 76,830. I thought it was suppose to say 7 ten thousands, 6 thousands, 8 hundreds, and 3 tens. But why is it saying 6 ten thousands then 7?
    (3 votes)
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  • purple pi purple style avatar for user Phil
    What on earth is the point of re-grouping anyway? I can't think of a single use for it. I don't even use it for subtraction.
    (3 votes)
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    • piceratops ultimate style avatar for user Denis Orlov
      Sal is demonstrating different ways to regroup numbers in order to make addition/subtraction easier, when working with more awkward and difficult numbers.

      Number he is using is quite easy. It breaks down into nice, even 'chunks': 600 + 75 + 5 , which are easy to add/subtract.

      But say you had more awkward numbers, something like this:

      437 + 789

      You could break them down into 'chunks' which are easier for you to manipulate:

      437 = 400 + 30 + 7
      789 = 700 + 80 + 9

      or whatever 'chunks' are easier for you to work with.
      And then just combine all the 'chunks' together:

      700 + 400 + 80 + 30 + 9 + 7 -> 1100 + 110 + 16
      Then
      1210 + 16 = 1226 or 1100 + 126 = 1226

      Or in any other way you want to combine you 'chunks'

      Same for subtraction

      With practice you'll be able to add/subtract large numbers in your head, without a calculator.
      (3 votes)
  • aqualine ultimate style avatar for user Swathi
    Is regrouping of whole numbers important
    (4 votes)
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  • blobby green style avatar for user Donovan
    how many times do we regorup
    (4 votes)
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  • piceratops ultimate style avatar for user codster127
    ask your teacher how to start a program so my teacher knows.
    (4 votes)
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  • blobby green style avatar for user zakary.ausmus
    how much is 5000+10000=15000
    (2 votes)
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  • blobby green style avatar for user granthart
    how does a video help others who already know this?
    (2 votes)
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  • male robot hal style avatar for user marco gonzalez
    how do you feger out the missing number
    (1 vote)
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  • male robot hal style avatar for user marco gonzalez
    how do you feger out the eqution
    (1 vote)
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  • blobby green style avatar for user cheyavo
    What is the purpose behind this regrouping? I understand how to do it but not understanding the why.
    (1 vote)
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    • stelly blue style avatar for user Kim Seidel
      It helps you understand how place values relate to each other. We also use regrouping when dealing with money. There are a lot of different ways that you can pay someone $63
      3 - twenties and 3 ones
      2 - twenties, 2 tens and 3 ones
      1 twenty, 4 tens, 2 fives and 3 ones
      etc.
      (1 vote)

Video transcript

Fill in the blanks to complete the equation. So they have 76,830 is equal to 6 ten thousands plus blank thousands plus 8 hundreds plus 3 tens. So let's just think about 76,830. So if we write 76,830-- I'm going to try to color-code it. We could write this out as being the same thing as 70,000 plus 6,000-- the 7 is in the ten thousands place. So it's 7 ten thousands, which is 70,000, plus-- the 6 is in the thousands place-- so it's 6,000, or 6 thousands, one could say, plus 800. Or you could say 8 hundreds. 800 plus 3 tens, or 30. And then there's 0 ones, so we could just write that out as 0 if we like. Now, what we have on the right here is almost what they have on the right over here. Notice the 0. They didn't write that. So we can ignore that. The 0 really doesn't affect the value. We have 3 tens. We have 3 tens. Let me do this in a color you can see. You have 8 hundreds. You have 800. But then that's where it starts to break down. They have blank thousands. Here we have 6 thousands. So we're going to have to think about this a little bit. And then they have 6 ten thousands, which is 60,000. Here we have 70 thousands. So we've got to work through these two places right over here. So they have 6 ten thousands, which is the same thing as 60,000. We have 70,000. So they essentially took 10,000 from here and regrouped it someplace. And since these two places are the same, they must have regrouped it into the thousands place. So let's try to do that. So let's get rid of 10,000 out of the 70,000. It becomes 60,000. So this becomes a 6. And then we're regrouping that into the thousands place. So we're going to add 10,000 to the thousands place. Now what's the thousands place going to be then? Well, it's 10,000 plus 6,000. It's going to become 16 thousands. This right over here is going to become a 16. So now what we wrote here looks just like what they wrote up here. This is 6 ten thousands plus 16 thousands plus 8 hundreds plus 3 tens. And we're done.