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The purpose of this video is to teach you how to calculate subtractions, both without any tools, and with the help of an alignment.
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When performing a subtraction, you say that you subtract a number from another. You can also say that you calculate the difference between the numbers.
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Let's do an example.
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Peder has a 50 SEK discount on diaper packages that cost 108 SEK.
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After the discount, Peder has left to pay 108-50 = 58 SEK.
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The numbers that are being subtracted are called terms, and the result of the subtraction is called the difference.
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We will now take a look at a method for calculating a subtraction in your head.
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Here, we will first subtract the hundreds, then the tens, the ones, the tenths, etc.
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In the following example of this, we are going to calculate 880.9 - 242.7
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Here, I have marked the hundreds in blue, the tens
in red, the ones in green and the tenths in the black.
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Now let's divide the second term into these colors as well, and then we can subtract each part individually.
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First, we subtract 880.9 by 200. We will then have 680.9 -40 - 2 - 0.7 left.
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Next we subtract by 40 and get 640.9 - 2 - 0.7. Then we subtract what's left by 2 and get 638.9 - 0.7.
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Finally, we subtract by 0.7 and our final answer is 638.2.
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This method can of course be used on both larger and smaller numbers.
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We continue to work with subtraction, and now I
show you how to subtract with the help of an alignment/line-up.
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We will start by calculating 692 - 444.
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We start by placing the number that we will subtract from above that number that we subtract by. Make sure that the hundreds, tens, ones etc. are placed right below each other.
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We begin by looking at the ones. In this case we are to subtract 2 by 4. This will result in a negative number, which we can not place below our line.
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What we do, in order to place a positive number below the horizontal line, is to "borrow" one of the tens from the 9 in the column to the left. In other words we move ten away from 90 in our given number 692, and place these ten among the ones.
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Our amount of ones are now 10 + 2 = 12. We can now calculate 12 - 4 = 8 and are able to place a positive 8 under the ones below the line.
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We move over to the tens and here we have to subtract 8 - 4 = 4. The remaining 4 is then placed below the tens under the line.
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Lastly, we calculate the hundreds 6 - 4 = 2
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Our answer or difference is thereby 248.
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In the next example we will calculate 333 - 76 using the line-up.
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Again, we place the number that we will subtract from above the other.
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We begin with the ones and since 3 - 6 will be a negative number, we borrow 10 from 3 that represents 30, so that the will be a 2 there instead, and instead if 3 ones, we now have 13 ones.
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We can now subtract 13 by 6 and are able to place a positive 7 below the ones under the horizontal line.
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We move on to the tens, where we have 2 - 7. Again, we have to borrow
10 from the hundreds, so that the calculation will instead be 12 - 7 = 5. The 5 is placed below the line.
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Lastly there's a 2 remaining in the hundreds column. The calculation is thereby 2 - 0, and we can place the 2 below the line.
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Our result/difference is 257.
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We will finish this tutorial by subtracting 77.4 by 22.76.
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This is to show you that this method also works on decimal numbers.
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So again we line up the two numbers vertically.
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Here we begin with the subtraction with the hundredths, which in this case is 0 - 6. Once again we have to borrow 10 from the tenths in the given number 77.4. We then have 10 hundredths instead.
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Now we can calculate 10 - 6 = 4 and place the 4 below the hundredths under the line.
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Now we go ahead with the tenths and since we borrowed 10 before, we now have 3 - 7. That means that we have to borrow again, this time from the ones. Now we have 13 tenths to subtract from.
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The calculation is thereby 13 - 7 = 6. And we place the 6 below the line.
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Now we move on to the ones, where we have the subtraction 6 - 2 = 4. Finally we do the calculation for the tens where we have 7 - 2 = 5.
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The result/difference in this example is thereby 54.64.