So, I've not posed in a long time.... (I had a writing burnout) but I think I'm back sort-of..!
anyway.. I'm gonna talk today about LONG DIVISION.
I read a post by steve yegge (if you don't know his, then you are missing out) about learning math, and it inspired me to write this post.
I -as most people- don't remember how to do long division although I'm an Engineer, but having a calculator seems to fix it.
But let's go back in time and try to learn how to divide 2 numbers, and get a good enough precision in the results.
Division is just a continuous subtraction so you can get what I call the main number..
so iv we divide 17 / 6 we can just keep subtracting 6 from 17 and keep count of how many times we did that till we can't do it anymore, which is in this case 2, then we have a remainder of 5, and we now need to get the remainder as a decimal number (which is in this case 0.8333333333333334) so how do we do that??
well... we have ( 5 / 6 ) and we need to get that as ( x / 10 ) so it is just a matter of calculating x.
x = (5 * 10 / 6) = (50 / 6) which can be calculated the same way as before.
Again (50 / 6) gives you a "main number" of 8 for (48) and a remainder of 2
So the result for our main problem is 2.8 plus some remainder, which we can calculate as 2 / 6, which is 0.33333333 till the end of time
So the final result is 2.8333333333333333, which is happily the same result a calculator would get you.
Another easy example ( 13 / 11 ) you get a "main number" of one, and a remainder of (2 / 11), and we now want to calculate a decimal number so we have ( 2 / 11 ) = ( x / 10),
then x = (2 * 10 / 11 ) = ( 20 / 11) which results in a "main number" of 1 and a remainder of (9 / 11)
the result for the main problem till now is 1.1 plus some remainder ( 9 / 11) which we can calculate the same way
(9 / 11) = (x / 10) which results in x = (10 * 9 / 11) = (90 / 11) with a "main number" of 8 (for 88) and remainder if (2 / 11)
so the result for our calculation till now is 1.18 plus some remainder (2/11) which we calculated before and it seems that a pattern appears here... if we keep calculating w get (2 / 11) which will get us 0.18 plus 2/11
So the final result will be 1.181818181818181818 till the end of time.
I hope this post helps you to get a new way of how to do a division without long division, and for some strange reason without a calculator!
anyway.. I'm gonna talk today about LONG DIVISION.
I read a post by steve yegge (if you don't know his, then you are missing out) about learning math, and it inspired me to write this post.
I -as most people- don't remember how to do long division although I'm an Engineer, but having a calculator seems to fix it.
But let's go back in time and try to learn how to divide 2 numbers, and get a good enough precision in the results.
Division is just a continuous subtraction so you can get what I call the main number..
so iv we divide 17 / 6 we can just keep subtracting 6 from 17 and keep count of how many times we did that till we can't do it anymore, which is in this case 2, then we have a remainder of 5, and we now need to get the remainder as a decimal number (which is in this case 0.8333333333333334) so how do we do that??
well... we have ( 5 / 6 ) and we need to get that as ( x / 10 ) so it is just a matter of calculating x.
x = (5 * 10 / 6) = (50 / 6) which can be calculated the same way as before.
Again (50 / 6) gives you a "main number" of 8 for (48) and a remainder of 2
So the result for our main problem is 2.8 plus some remainder, which we can calculate as 2 / 6, which is 0.33333333 till the end of time
So the final result is 2.8333333333333333, which is happily the same result a calculator would get you.
Another easy example ( 13 / 11 ) you get a "main number" of one, and a remainder of (2 / 11), and we now want to calculate a decimal number so we have ( 2 / 11 ) = ( x / 10),
then x = (2 * 10 / 11 ) = ( 20 / 11) which results in a "main number" of 1 and a remainder of (9 / 11)
the result for the main problem till now is 1.1 plus some remainder ( 9 / 11) which we can calculate the same way
(9 / 11) = (x / 10) which results in x = (10 * 9 / 11) = (90 / 11) with a "main number" of 8 (for 88) and remainder if (2 / 11)
so the result for our calculation till now is 1.18 plus some remainder (2/11) which we calculated before and it seems that a pattern appears here... if we keep calculating w get (2 / 11) which will get us 0.18 plus 2/11
So the final result will be 1.181818181818181818 till the end of time.
I hope this post helps you to get a new way of how to do a division without long division, and for some strange reason without a calculator!
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