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The purpose of this video is for you to know how to use two new line-up methods for division. These are called the lying chair and the stairs.
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I will explain both these methods by starting with the example 664 / 2.
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Here 664 is called the numerator, 2 is the denominator, and the result of the division is called quota or quotient.
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First of all, I want to mention that the method for calculating, using both the lying chair and the stairs, is the same.
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The only difference is basically the set-up. In other words, where, and in what order, you place the numerator, denominator and quota in the line-up.
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In the stairs we place the numerator to the right and the denominator to the left.
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In the lying chair, we place the numerator to the left and
denominator to the right.
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In both cases, the result/quota is written above the numerator.
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The names of these methods, come from the lines that separate the numbers, which in one case looks like a lying chair, and in the other case looks like stairs.
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Both methods can also be called long division.
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So let's go ahead and see how these methods work, using some examples.
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We will divide 664 by 2, using both methods, but we will begin with the stairs.
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In the four steps in the method, we first divide, then
multiply, then subtract and lastly we move down.
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We do this over and over again until the difference, after the subtraction, is 0 and all the digits in the numerator have been used.
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We begin by asking ourselves how many times 2 runs in 6. The answer is 3, and we can thereby place a 3 in the quota.
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Now what we do is to multiply the denominator (2) by the answer (3) and place the product (6) below the 6 in the numerator.
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The next step is to subtract 6 by 6 and the difference 0, we place below.
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The next step is to move down the 6
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That was round one, and for the next round we start over.
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Again, 2 goes in 6 three times, so we place another 3 in our quota.
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Then we multiply 2 by 3 and place the product 6 below.
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Then we subtract 6 by 6 = 0, and then we move down the 4
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We do one more round, and this time 2 runs twice in 4, so we write a 2 in our quota.
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Then we multiply 2 by 2 = 4, and lastly we do the subtraction 4 - 4 = 0
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Now we have a 0 after the subtraction and we have gone through all the digits in the numerator.
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We are thereby done and the answer is 332
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Now we will perform the exact same division but instead we use the lying chair as our tool.
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This method is, for example, used when performing polynomial division in higher education, and can thereby be important to know.
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The calculation itself is, like mentioned, the exactly same as the other method, but the set-ups are different.
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We begin by calculating how many times 2 runs in 6. We get 3 and then multiply 2 by 3 = 6
Next up, we subtract 6 by 6 = 0. Lastly we move down the 6
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In the next round, we again calculate that 2 runs three times in 6. We multiply 2 by 3 = 6
Then we subtract 6 by 6 = 0, and lastly we move down the 4
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In the final round 2 runs twice in 4. We multiply 2 · 2 = 4, and then subtract 4 - 4 = 0
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Now we are done and our answer is like before 332
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We will do two more examples on the lying chair.
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We will start by calculating 868 / 7
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We take out our notes to remember how the method works.
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7 goes one time in 8. Again we multiply the result by the denominator: 1 · 7 = 7 and then subtract 8 - 7 = 1. Lastly we move down the 6
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Now 7 goes twice in 16. Next step we multiply 2 · 7 = 14
and then subtract 16 - 14 = 2. Now we move down the last 8
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Here 7 goes four times in 28. We multiply 4 · 7 = 28 and subtract 28 - 28 = 0
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Now we are finished with the division and we got the answer 124
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Let's do one more example. Now we are to calculate
77.8 / 4, again with the help of the lying chair line-up.
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We set up the division.
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In this example we begin by calculating how many times 4 runs in 7, and then we multiply 1 · 4 = 4 and then subtract 7 - 4 = 3. Lastly, we move the 7 down.
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Now 4 runs nine times in 37. We thereby multiply 9 · 4 = 36
and subtract 37 - 36 = 1, and then we move down the 8
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Here, we have to remember that the 8 in the numerator was a decimal, and we thereby have to write out another point, so the same goes for the next digit in the quota.
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4 runs 4 times in 18, and 4 by 4 is 16,
and 18-16 = 2
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What we did here was to write a point before we placed out the 4
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Now we come to a situation where we don't have any more digits to move down in the numerator, so what we do is to add a zero.
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Now 4 runs five times in 20, and we multiply 5 · 4 = 20
and then subtract 20 - 20 = 0
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Now we have gone through all the numbers in the numerator and the difference after the subtraction is 0, and we are thereby finished.
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Our answer is 19.45