How does one divide 456,792 by 34.897? Steps required!

[rosamundjohn]

These numbers are too big

[sophie_1003]

Without using a calculator I take it? We've been taught 'chunking' at uni; http://www.croydonmaths.org.uk/division.htm about halfway down this link it is explained better than I could. However, for the numbers you are looking at this would take a while but it would be possible, the other thing to bear in mind is that using this method you would be left with a remainder rather than a 'proper' answer.

[factor-fiction]

Division is taught at university now is it?

I assume you need to do it without a calculator- either by chunking or the traditional long division method. Chunking works well for this one.

I suggest you start by estimating the answer so you can recognise whether your final answer is sensible.
450000 ÷ 30 = 15000

When dividing ignore the decimal point initially, then reinsert it at the end. Alternatively multiply both numbers by 1000 first. That makes the calculation 45679200÷34897.

I'll ignore the decimal point. Then use chunking.
Try say 13 x 34897= 453661. That's close. Deduct 453661 from your 456792 to find the remainder. Then divide remainder by 34897.

Then continue chunking.

Have a go. The final answer is answer is 13089.72

But I admit i'd alsways use a calculator/spreadsheet.

[bibblebub]

long division

[sophie_1003]

I'm doing a degree in education so we were taught how to teach chunking to children; many of us in the class hadn't used the method or even heard of it before so we were taught how to use it as well as how to teach it.

[another-view]

Why not just use a calculator?

[ladyalex]

It is an awfully big sum, but long division is possible.

First you have to get rid of the decimal point, so instead of dividing 456,792 by 34.897, you divide 456792000 by 34897. (This is exactly the same sum, you've just multiplied both sides by 1000).
34897 is 5 digits long, so:
Estimate how many times you think 34897 would go into the first 5 digits of 456792000, ie 45679.
This would be 1. 1 is the first number of your answer.
Multiply 34897 by one =34897.
Subtract 34897 from 45679 =10782 this is the remainder
Bring down the next figure from 456792000 and attach it to the end of the remainder, ie 107822.
Now estimate how many times you think 34897 would go in to 107822.
That would be probably be 3.

Multiply 34897 by 3 =104691 It fits, 3 is the second number of your answer. (13 so far)

[ladyalex]

Subtract 104691 from 107822 = 3131
Bring down the next digit from 456792000 and attach it to the remainder. That gives
31310
Estimate how often 34897 would go into 31310...it would not, so the next figure in your answer is 0 (130 so far)
Multiply 34897 by 0 =0 (anything multiplied by zero is zero). Subtract 0 from 31310 =31310
Bring down the next digit from 456792000 and attach it to 31310 . that gives 313100
Estimate how often 34897 goes into 313100.
Probably 9.
Multiply 34897 by 9 =314073...that is bigger than 313100, so try 8
Multiply 34897 by 8= 279176 so the next figure in your answer is 8 (1308 so far)
Subtract 279176 from 313100 =33924
Bring down the next digit from 456792000 gives 339240
Estimate how often 34897 goes into 339240
That would be 9
Multiply 34897 by 9 gives 314073 so 9 is the next digit of your answer (13089 so far)
Subtract 314073 from 339240 gives 25167.
You have now come to the end of the number you are dividing, so your answer is 13089 remainder 25167.
If you want to continue getting figures, keep on adding zeros to the end of the remainder and repeating the estimating, multiplying and subtracting process until you get a zero after subtraction...or forever whichever is the soonest.
I learned this in primary school, which gives an indication of my age.

[LoftyLottie]

I am 63 (nearly) and have never heard of 'chunking'. Long Division for me. Thank heaven for calculators. However, nowadays it doesn't seem that estimating actually ever happens.

[squarebear]

Wow! I've got to admit, putting it into a calculator would be a lot easier than all that.

[LoftyLottie]

Just thinking back to exams where you had to put all your workings in the margins. Long Division took up lots of margins!!

[ladyalex]

Yes it is...but if you know how to do long division, you do have a better idea of whether you have made a mistake with the calculator....not unknown in this house.....:-))
Y'see when we were at school, we didn't have to learn all about the rainforest and global warming and suchlike, so there was more time to spend on long division.
Please don't get me started on square roots..yes i do know how to do them without a calculator.

[LoftyLottie]

It's amazing that a lot of young people using calculators haven't got the faintest idea of estimating the result of a calculation. I'm all for using calculator, but the basics should be taught in the old fashioned way first.

[factor-fiction]

LoftieLottie -it's even worse than that. Giving many kids a calculator won't help them solve problems. Ask some typical 13 year olds how much change you'd get from a £10 note if you bought 3 cards at £2.30 each and many wouldn't know which buttons to press- whether to multipy, divide, subtract etc.
Oh, and I don't see much differnce between chunking and long division- when doing teh latter you will have to do some chunking as part of the thought process- e.g. to decide how many 13s in 348
Sophie_1003- yes it's right to teach this method to prospective primary teachers, but sadly I think you'll find very few kids ever get to grips with it, however hard you work on teaching it. Even dividing by a single digit number such as 6 is found to be too difficult for half of secondary school pupils.

[Vagrant]

There are 2 other methods of attack from the pre-calculator days.
First, factorise each number, then cancel common factors - this may yield an easier calculation (it's no use in this particular case, as 34897 is prime).
Second - use Log tables - remember them?

[factor-fiction]

rosamundjohn- what degree of accuracy do you need (how many significant figure or how many decimal places?). What's the context of the question? That may help determine the best method.

[sophie_1003]

I actually found chunking really useful, I suppose it depends on personal preference really, but we weren't taught long division at uni so I am guessing chunking is the current government issued way of teaching division! I've never been confident with maths so anything that makes it easier for me is nice but I try not to worry about it too much because am more interested in teaching younger children!

[rosamundjohn]

WHAT IS CHUNKING?!