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The purpose of this video it for you to learn how to add both integers and decimals by suing a method of alignment.
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But first we want to repeat what addition is and look at
a method for calculating additions in your head.
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When you calculate using the operation addition, you say that you add numbers together.
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Let's do an example of an addition.
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Peder bought 1 package of diapers for 108 SEK and toilet paper for 50 SEK.
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The sum of his purchase is 108 + 50 = 158. The numbers added are called terms and the result is called the sum.
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It may be helpful to also have a strategy for doing calculations/additions like this in your head.
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One way to do this is to separate the numbers that are being added into hundreds,
tens, ones, tenths and so on.
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Then the hundreds, tens, ones and so on can be added separately.
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We will do an example of this.
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We are adding up 156.2 to 242.7. We begin by splitting up the numbers into hundreds, tens, ones and tenths.
We then get: 100 + 50 + 6 + 0.2 + 200 + 40 + 2 + 0.7
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Here I have marked the first number in red and the other in blue, in order for us to separate them.
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Now we can add the hundreds separately as well as the tens, the ones and the tenths.
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We then get 300 + 90 + 8 + 0.9
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Now it's fairly easy for us to sum up the different parts of this number, we get 300 + 9 + 8 + 0.9 which will sum up to 398.9
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This method can of course be applied to both large and small numbers.
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We will continue by looking at how to calculate additions, this time with an alignment method as our tool.
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Let's calculate 444 + 698 with the alignment method.
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What we do is to put the numbers in a vertical alignment. In other words, we place one number above the other so that the ones, the tens and the hundreds are above/below each other.
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We start from the right with the ones. In this example 4 and 8.
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We add up 4 + 8 = 12. The 2 in 12 represents the ones in the number 12, and is thereby placed below the line and under the ones column, in our alignment.
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The 1 in 12 represents the tens in 12, and we thereby write the 1 above the tens column, in the alignment.
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We are now done with the ones and will move on to the tens.
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Here we calculate 1 + 4 + 9 = 14
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The 4 in 14 represents the tens and is thereby placed below the line and under the tens column in the alignment. The 1 in 14 represents the hundreds and we thereby write a 1 above the hundreds column.
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At last, let's calculate the hundreds: 1 + 4 + 6 = 11 and since this is the last column we place the entire number, in this case 11, below the line, and we are done with our calculation.
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Our answer is 1142
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We will do one more example where we add two integers with the help of an alignment.
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Here we are to calculate 1231 + 77
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Again, we write the numbers in a vertical line-up in which the ones are in the same column, as well as the tens, the hundreds and the thousands.
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Since the number 77 doesn't contain any hundreds or thousands, we leave these spaces blank.
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First, we add the ones together. In this case 1 + 7 = 8
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Then we go ahead and add up the tens 3 + 7 = 10. We place the 0 in the tens column, and move the 1 up to the hundreds.
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Now we add the hundreds together: 1 + 2 = 3, and place the three below the line, under the hundreds. Finally we calculate our number of thousands, and here we only have 1.
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Our answer is then 1308.
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We will finish this video with a final example.
Here I want to show that this method also works with decimal numbers.
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Here we are to add the numbers 77.4 and 22.76 together by using the alignment method.
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We put the numbers in the vertical line-up, but first we just write a 0 after the 4 in 77.4,
so we get 77.40 instead of 77.4, which is the exact same thing, but now we have the same amount of digits in both numbers.
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First, we add the hundredths together: 0 + 6 = 6.
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Then we sum up the tenths: 4 + 7 = 11, and here we put the 1, representing the tenths, in the tenths column and move the 1, representing the ones, over to the ones column.
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Now we add all the ones together: 1 + 7 + 2 = 10. Here put a 0 on below the line
in the ones column, and move over the 1 to the tens column.
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Finally, we add up all the tens: 1 + 7 + 2 = 10, and since this was our last column, we put the entire number, here 10, below the line.