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Adding decimals: 9.087+15.31

Sal solves 9.087+15.31 using the "standard algorithm". Created by Sal Khan.

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  • piceratops ultimate style avatar for user kaity rosey morrow. hi hi hi there
    how did you get the decimals to line up with each other and why do you put a number off to the side
    (200 votes)
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  • blobby green style avatar for user aisha ahmad
    how does this help us in a real life situation
    (13 votes)
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  • aqualine seedling style avatar for user smorga41
    how do you do it
    (10 votes)
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    • hopper cool style avatar for user Seed Something
      Use the decimals to guide the place value alignment.

      • line up the decimals above and below,
      then add each column of numbers,
      • empty spaces are equal to zero


      9.087 + 15.31 = ?
         9.087
      + 15.31
      —————————
      24.397 ←🥳 answer

      ★In Addition order doesn't matter, because it's Commutative, meaning we can rearrange addition and get the same answer,
      1 + 7 = 8
      7 + 1 = 8
      So either decimal value can be first or second, but always line up the place values.
        15.31
      + 9.087
      —————————
      24.397 ←🥳 same answer

      ★This method works for more than two values as well, as long as we always line up the decimals so that the place values form columns!

      2.14 + 0.3421 + 3 + 11.2 = ?
         2.14
      0.3421
      3
      + 11.2
      ——————————
      16.6821 ←🥳 answer

      Rearranged,
      with place keeper zeros…
        11.2000
      3.0000
      0.3421
      + 2.1400
      ——————————
      16.6821 ←🥳 same answer

      ★ Just remember: we must line up the decimals and keep the place values aligned throughout the calculation, move the decimal straight down, so it is aligned in the answer too, then it's just adding the columns like usual…

      Start adding in the far right column, carry values to the left, etc…

      (ㆁωㆁ) Hope this helps someone!
      (11 votes)
  • blobby green style avatar for user joshichinmay0409
    Is it compulsory to line the decimals
    (4 votes)
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    • hopper cool style avatar for user Seed Something
      Corresponding place values must be added together, the decimals naturally align when the columns are in the correct order.

      Therefore aligning the decimals is an easy way to align the place values correctly into columns for manual addition.

      So, when creating accurate addition columns, it is also compulsory to line up the decimals.
      (0 votes)
  • duskpin seedling style avatar for user unique
    is it allowed to add an zero at the whole number?
    (4 votes)
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  • blobby green style avatar for user 20141140
    I made a chart and placed them into the chart to solve it, is that smart?
    (3 votes)
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  • female robot ada style avatar for user Shulie
    Do you align the decimals even if you are multiplying decimals
    (2 votes)
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    • ohnoes default style avatar for user BenjaminH
      if you are multiplying decimals, you do not have to line up the decimal points. You keep the decimal points in the correct space in the numbers, but otherwise, write it out like a normal multiplication problem. You solve it like a normal problem too. so if it is 1.5 X 3.4, you would write it out like a normal multiplication problem:
      2
      3.4
      x1.5
      --------
      1
      1 7 0
      +3 4 0
      -------
      5 1 0, but to put in the decimal point, you have to think of the original numbers, which were 1.5, and 3.4, 1.5 had one number to the right of the decimal point, so note that, and 3.4 also had one number to the right of the decimal point, So note that as well, add that up and it means that you have to put the decimal point in the problem so that it is to the left of two numbers, so the answer is not 510, it is 5.10.
      (1 vote)
  • male robot hal style avatar for user jaw100888
    The easiest thing in 6th grade, but it's not the fastest to solve.
    (4 votes)
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  • blobby green style avatar for user AAdiscountmerchandise
    how to add 2.15 + 3.85+ 2.5 + .5
    (0 votes)
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    • blobby green style avatar for user ojanusz111
      First make all the numbers have the same place value after the decimals by adding in zeros:
      2.15
      3.85
      2.50 (is same as 2.5)
      0.50 (is same as .5)
      ___
      9.00

      start by adding up the column on the far
      right and carry over to the next column to
      its left, then repeat.
      (2 votes)
  • duskpin ultimate style avatar for user bmahoney0002
    you line up your decimal in subtraction also
    (4 votes)
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Video transcript

Let's see if we can add 9.087 to 15.31. And I encourage you to pause the video and try to do it on your own. So I'm assuming you have tried to do it on your own. And now let's see how we could actually tackle this. Now, one thing I want to point out, some of you all might have seen these numbers all lined up and immediately want to say, hey, 7 plus 1 is 8, and 8 plus 3 is 11, carry the 1, et cetera, et cetera. And if you did that, you would be making a mistake. Because, you see, right over here, these decimals aren't lined up. Here, if you did that, you would be adding the 7 thousandths to 1 hundredths. You would be adding 0 tenths to 5 ones. You would be adding 9 to 1 tens, or essentially, this is a 10 right over here. So the places would be all mixed up. So what you need to do is to actually align the decimals so that your place values are aligned. So what you want to do is you want to align things up. So we could write 9.087. And then we want to align the decimal. So let's align the decimal. This is what has to match up. And this is going to be 15.31. And this should hopefully make sense to you as well. This is 9 point something plus 15 point something so it's going to be-- If you add 9 to 15, it will be 24 point something, give or take a little bit. And you see that here. Here you have a 9 plus the 15. So you have lined up the appropriate place values. And now we are ready to add. It's a good idea to start with the smallest place value, so if you have any extra at a certain place, you can bring something into the next place value. So here you say 7 plus-- well, this is 7 thousandths. It's in the thousandths place. And you might want to-- you say, well, what do I add it to? There are no thousandths right over here. And you're right. There are no thousandths. So we could literally write 0 thousandths. So 7 thousandths plus 0 thousandths is 7 thousandths. 8 hundredths plus 1 hundredth is 9 hundredths. 0 plus 0 tenths plus 3 tenths is 3 tenths. We got our decimal. Then you have 9 ones plus 5 ones is 14 ones. Well, 14 ones is the same thing as 4 ones and 1 ten. So we'll carry that 1 right over there. This is just 1 ten plus 4 ones, which is 14. And so then finally, you have 1 ten plus another ten is 2. So we get 24.397.