Adding Zeros in a Long Division ProblemDate: 02/26/2006 at 22:39:10 From: Mom Subject: When do we add zeros in the answer to a division problem I was trying to remember the long division rules when dividing a small number such as 6 by a larger number like 351. I am teaching my daughter and I want to make sure I understand the rules about adding zeros correctly. - Struggling Mom Date: 02/27/2006 at 11:30:38 From: Doctor Rick Subject: Re: When do we add zeros in the answer to a division problem Hi, Mom ... I prefer not to pile up too many rules, but to help a student see that what you do in this case is exactly what you always do in division. There are really no new rules; the only thing is to recall that the numbers 6, 6.0, 6.00, 6.000, and so on are all names for the same number. I start by looking at the division problem ___ 351 ) 6 How many times does 351 go into 6? None--that's 0, so I put 0 in the quotient, above the ones digit of the dividend, multiply 0 by 351, and subtract this from 6. 0 ___ 351 ) 6 -0 -- 6 Then I'm supposed to bring down the next digit. There is no next digit ... but there is, if I write 6 as 6.0. When I add the decimal point to the dividend, I also put one in the quotient directly above it. 0. _____ 351 ) 6.0 -0 -- 6 0 Now (since I ignore the decimal point at this stage) I'm trying to divide 60 by 351, and 60 still isn't big enough; 60 divided by 351 is 0 again, so ... 0.0 _____ 351 ) 6.0 -0 -- 6 0 - 0 --- 6 0 It's time to bring down the next digit of the dividend again, but again there isn't one ... unless I write the dividend as 6.00: 0.0 _______ 351 ) 6.0 0 -0 -- 6 0 - 0 --- 6 0 0 This time when I try to divide 600 by 351, it works: it goes once. I put 1 in the quotient, above the ones place of 600; multiply 1 by 351, and subtract the result; then I bring down the next digit of the dividend. To do this, I must of course add another 0 to the dividend: 0.0 1 _________ 351 ) 6.0 0 0 -0 -- 6 0 - 0 --- 6 0 0 -3 5 1 ----- 2 4 9 0 I'll just do one more step. How many times does 351 go into 2490? I estimate: 300 goes into 2100 7 times, and since I rounded both numbers down, that's probably fairly close. I multiply 351 by 7; that's 2457, which indeed is smaller than 2490, so I go ahead and write it down. 0.0 1 7 _________ 351 ) 6.0 0 0 -0 -- 6 0 - 0 --- 6 0 0 -3 5 1 ----- 2 4 9 0 -2 4 5 7 ------- 3 3 Once a child understands how this works, just following the basic rules, I can show some secrets that make it easier! You don't have to write so much, because of what you know about how numbers work. Whenever the quotient digit is zero, you know that when you multiply zero by the divisor, you'll get zero; and you know that subtracting 0 from any number leaves it just the same. You can do those operations in your head, because they amount to doing nothing! All you need to write down is this: 0.0 1 7 _________ 351 ) 6.0 0 0 -3 5 1 ----- 2 4 9 0 -2 4 5 7 ------- 3 3 The only danger in leaving out those steps is that you might lose track of where the next digit goes in the quotient. That's why I emphasize that the digit goes directly above the ones digit of the partial dividend. If you find that this leaves a blank to the left of the digit you add, it means that you forgot to write down a zero; so put it in. I hope this helps. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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