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May 12th, 2019, 12:26 PM   #1
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Unhappy Simple Long division issue is stressing me out.

Hi All

I'm reading a book I physically own and I'm doing some Long Division from it.
I'm trying to work out: a Double figure Divisor with a 4 figure Dividend.
16 / 4496.

So I divide 16 into 44, giving me 2, and a remainder.
I drop down and input 32, 44 Subtract 32, gives me 12 and I bring down the 9.
Making 129 to work with:

So I'm trying to divide 16 into 129, to give me 028 into the Quotient.
I am using Pencil and paper and don't want to use a Calculator - I want to solve it.

I rounded 16 to 20 and 129 to 30, to give me an Estimate of 6. - But I know 6 is wrong because the answer is 8 in the Book.

So if I was to do,
16 x 7 = 112
4496 - 112 = 4384

and:

16 x 8 = 128
4496 - 128 = 4368

Etc.

I also did
16 x 6 = 96
4496 - 96 = 4400

The answer for 6 is 4400 & is closest to the Dividend of 4496, than the other values, However the answer is still 8.

I'm so so lost and confused, I've been doing this for hours.
I understand I'm over complicating myself and everything is a complete mess.

But I don't know how to solve it.
Any help is much appreciated!

Thank you!
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May 12th, 2019, 05:04 PM   #2
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Quote:
Originally Posted by Violex View Post
I'm trying to work out: a Double figure Divisor with a 4 figure Dividend.
16 / 4496.

So I divide 16 into 44, giving me 2, and a remainder.
I drop down and input 32, 44 Subtract 32, gives me 12 and I bring down the 9.
Making 129 to work with:
All good to here.

Quote:
Originally Posted by Violex View Post
So I'm trying to divide 16 into 129, to give me 028 into the Quotient.
I am using Pencil and paper and don't want to use a Calculator - I want to solve it.

I rounded 16 to 20 and 129 to 30, to give me an Estimate of 6. - But I know 6 is wrong because the answer is 8 in the Book.
Here's how I did it. What's 16 into 129? Well 16 is one of those numbers that after a while, you sort of just know. It's a power of 2: 2, 4, 8, 16, 32, 64, 128, ...

Or if you didn't remember that, you could just go, "Ok two times 16 is 32, and two times that is 64, and two times that is ... aha! 128. Just fits.

So 16 integer-divided into 129 is 8 with remainder 1. We got 8 because we had to double 16 three times to get 128. And 2 x 2 x 2 = 8.
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May 12th, 2019, 05:06 PM   #3
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So basically how I'd solve it: 16/4496 44:16=2

2×16=32 44-32=12 bring the 9 down to get 129, 129:16=8


8×16=128 128-129=1 bring 6 down 16, 16:16=1 1×16=16, 16-16=0


so we have 281

hope this helps.

Last edited by skipjack; May 12th, 2019 at 05:22 PM.
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May 12th, 2019, 05:20 PM   #4
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As 16 × 6 = 96 and 129 - 96 = 33, the estimate of 6 is too low.

Using 8 instead, the division proceeds as shown below.
divide16.png
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May 13th, 2019, 02:19 AM   #5
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Quote:
I'm reading a book I physically own and I'm doing some Long Division from it.
I'm trying to work out: a Double figure Divisor with a 4 figure Dividend.
16 / 4496.
Sounds like an old book from the days of pounds and ounces.



In those days pupils used to learn up to their 16 times table for this reason.

You started off brilliantly and worked out part of the 16 times table, but confused yourself when you did this

Quote:
4496 - 112 = 4384
and this 4496 - 128 = 4368
and this 4496 - 96 = 4400
When you do long division, you only work on the digits on the line you are focusing on and forget the rest.

So the 44 was already done.

This was correct.

Quote:
So I'm trying to divide 16 into 129, to give me 028 into the Quotient.
I am using Pencil and paper and don't want to use a Calculator - I want to solve it.

I rounded 16 to 20 and 129 to 30, to give me an Estimate of 6. - But I know 6 is wrong because the answer is 8 in the Book.
Here is a little tip.

Forget the rounding etc. That's trying to be too clever.

Start with a 'guess' for 16 into 129
You can see it's a higher number, so start with 10; 10x16 = 160 easy but too much.
So try 9 x16 = 144 - still too much
So try 8 x 16 = 128.

This must be correct since it is the first one down the chain from 10 that works (is less than 129).

It is usually easy to see whether we work up from 1 × or down from 10×

Note I was constructing my own table as I went along by taking off 16 each time.
This was probably why you tried to do the unsuccessful subtraction.

Last edited by skipjack; May 13th, 2019 at 07:45 AM.
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May 13th, 2019, 10:53 PM   #6
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Thanks everyone for the help!

I overlooked it - to put it simple. - I completely missed the 129.
I got the correct quotient in the end

I'm so happy now! Thank you all!
I really do Appreciate it.
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