Date: 03/16/99 at 22:18:56 From: Daniel Subject: Division Please show some examples in detail about long division and the process step by step. Thank you.
Date: 03/17/99 at 12:04:28 From: Doctor Peterson Subject: Re: Division Hi, Daniel. I'm not sure how much you have learned about division; I'll show you how to divide by a one-digit number. If you need something more advanced than this, look in our Dr. Math archives for other problems like what you need to do: http://mathforum.org/library/drmath/sets/elem_division.html I'll give you an example problem, and show you how to keep your mind focused on one part of the problem at a time, so all the numbers don't get too confusing. You won't write it out in pieces as I will, but what you do write is a compact way of saying the same thing. Let's divide 175 by 3: ______ 3 ) 175 We take the dividend (175) one digit at a time starting at the left. If we tried to divide 1 by 3, we would get zero, so let's skip that and use the first two digits, 17: ___5_ 3 ) 17 15 -- 2 What I did was to look through the multiplication table for 3 (in my mind), looking for the biggest multiple of 3 that is less than 17: 3, 6, 9, 12, 15, 18 - since 18 is too big, we use 3 x 5 = 15. I wrote the 5 on top, above the "ones" digit of the 17 I'm working on, and wrote the 15 under the 17. Then I subtracted, leaving a remainder of 2. This says that 17 = 3 x 5 + 2 What we really did just now was to divide 170 by 3, getting only the number of tens in the quotient: ___50_ 3 ) 170 150 --- 20 170 = 3 x 50 + 20 That's not the whole problem, though. What do we do with the next digit of 175, the 5 we left out? I'll use the remainder, 2, as the tens of a new dividend, by "bringing down" the next (and last) digit of the dividend: 175 | v 2-->25 This is really just adding the missing 5 to the remainder of 20. Now I divide that by 3: ___8_ 3 ) 25 24 -- 1 I made "25" by combining the remainder, 2, with the next digit, 5, and divided that by 3 the same way I did before: 25 = 3 x 8 + 1. This gives us the ones digit of the answer, 8, and a final remainder of 1. Putting it all together, here's what you actually write down: ___58_ 3 ) 175 15 -- 25 24 -- 1 Do you see that second problem, 25 divided by 3, hidden in there? When you work on it, you focus on that as if it were a separate problem by itself, and write the quotient, 8, above the "ones" digit of the 25. Putting it all together, the quotient is 58 and the remainder is 1: 175 = 3 x 58 + 1 If it would help you to understand WHY we do it this way, here's a simple explanation: Long Division http://mathforum.org/library/drmath/view/58499.html You should always check a division. Here's an answer I gave another student that should help you: Checking Division http://mathforum.org/library/drmath/view/58807.html Let's check our answer. I'll do the multiplication "upside down" so you can see the connection to the way we divided: 3 <--- divisor x 58 <--- quotient ---- 24 <--- notice that 24 and 15 were in your division work! 15 <--- ---- 174 + 1 <--- remainder ---- 175 <--- this matches the dividend, so it's right I hope that helps. If the this and the archives don't give you what you need, please write back with a specific problem to show where you need help. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.