# Left to Right method for large numbers | Carrying problem

Hi everyone!!'m approaching the subject of mental calculation and I would like to take very good care of the bases. So I’m practicing the left to right method of addition and I have found a little problem doing addition with 4+ figures.

For what I know with LtoR you go at every step you look forward one step to take care of the carrying. Let’s say we have 57 + 64, while you are doing the step 5+6 you look forward and see 4+7 is greater than 9 so you add the carrying while you are stating the result.

Now, when you have bigger numbers you have just to repeat this “looking forward” for the number of figures. Let’s say 1234+5678, while I’m doing 1+5 I look forward to 2+6, while I’m doing 2+6 I look forward to 7+3 etc.

So the routine should be adding the first number, look forward to see if there’s any carrying, stating the first result number, adding the second number, look forward to see if there’s any carrying, stating the second result number etc.

However let’ say I have 3444+1557. If I do my usual routine I would state the first number as a 4 because looking forward till the second figure would suggest me that I have no carrying. In reality the result is clearly wrong because the last carrying (7+4) will affect the result.

How do people solve this problem for 4+ figures numbers in order not to risk to make mistakes in their performances?

Thx!!

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If you start writing down the answer while still calculating it, you could be writing down the answer completely wrong without realizing it. That is why you need to do the problem mentally first and as soon as you have the full and correct answer in your head, you can write it down or say it out loud.

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To improve the impression to a general audience keeping track of the current number and the next means that you can always be writing down 1 number as you go. It is a fairly easy way to game the system.

That said, for everyone but albinoblanke, applying the major system with a simple body journey, memory palace or story should carry you through the first 20 digits ( with 1 metric tonne of practice ).
60 in theory but I think you need a better organized system to be fast enough past 20 but these are just my initial impressions.

I am close to 18 digits in 180 seconds currently. You probably need to get the process down under 3 seconds for it to be practical and 1 second to be smooth.

There are people here with 30 second card deck memorization times. So it is doable ( with 10 metric tonnes of practice and some talent). There is a recorded run of 12.39 seconds for a 52 card deck as well.

In performance obviously the first way is a lot less stressful and some people here might be able to chat while they did it which really boggles my mind but I keep practicing.

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Thanks for your answer, doesn’t this increase drastically the time necessary to give the result to an audience thus depriving the performance of much of its “shock value”? With ten figures addition for example it would start to become quite a large amount of time…

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Not necessarily. With large numbers, the chances that the last few digits will affect the first few digits gets smaller and smalller so you often can go ahead and say the first parts of the answer that you know is correct while calculating.

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When adding two numbers together the process is easy.
If the lookahead number ends in 8 or less, you are done.
If the lookahead number ends in 9, you need to look ahead at the next digit.

In the case of 3444 + 1557 you go ‘4’, ‘49’, ‘499’, ‘499 | 11’.
The ‘|’ in this case is a tens separator. It means 4,990 + 11.
In your mind - when you are at the last digit and just for a second, separate the tens from the ones in the addition:
499 | 11. Now work out the carry 499+1 = 500 or
499 + 1 | 1 = 500 | 1 = 5,000 + 1.

Two digits together added together are never more than 18.
That is why if you look ahead and the look ahead number ends in an eight, you are done.
If you get a 9, like you pointed out in your example of 3444 + 1557, then you could get a carry from the next digit. So you just continue.

When adding three numbers together the process is easy too
If the lookahead number ends in 7 or less, you are done.
If the lookahead number ends in 8 or 9, you need to look ahead at the next digit.

Three digits together added together are never more than 27.
That is why you can stop at 7.

So this is a slight misconception. The very fact that the look ahead digit is 9 suggests that a carry from the next digit could carry into this one and it does.

Excellent! There are 2 ways of doing this and you need to find a way that works best for you:
1: start by adding 3 to 1 and think 4. Your intermediate steps are 4, 49, 499, 5,001. So after each step you multiply the result by 10.
2: start by guessing the amount of digits the answer will have and call out the intermediate result accordingly. What I mean is instead of adding 3 to 1, you think ‘3,000 + 1,000 equals 4,000’. So while adding the intermediate staps are: 4,000, 4,900, 4990, 5001.

Choose what works best for you.

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So, before stating/writing any digit, I should look forward till the end see if there’s any two digits that adds up to 9. Is that right?

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No, that is not right.