Is adding numbers easier from right to left or left to right?

Question

It seems I think that the traditional way of adding numbers from right to left is kinda like using pliers for all the bolts.

Is there a way to add numbers from left to right?
We write numbers out left to right and say them also.

School? shows/teaches the basic method of adding columns working from right to left.

Which is mind torturing trying to remember the numbers to say them back to you if your doing the problem in your head.

Care to sample? Add your phone number to itself and then say the answer. Its a lot of numbers to remember and its hard to do.

Is there another way? Adding numbers from left to right?

Answer 1

Yes, you can add from left to right; you just have to keep an eye on the next place to see if there's going to be any overflow.

ex. 436782 + 132789
4 + 1 = 5, next digits are 3 and 3, no overflow -> 5.
3 + 3 = 6, next digits are 6 and 2, no overflow -> 6.
6 + 2 = 8, next digits are 7 and 7, overflow -> 9.
7 + 7 = 14, next digits are 8 and 8, overflow -> 5 (the 10 is the overflow we added to the previous digit)
8 + 8 = 16, next digits are 2 and 9, overflow -> 7
2 + 9 = 18 -> 8. So the answer is 569578.

The only difficulty is when the next two numbers add to 9; then you have to look at the following pair to determine if there is an overflow (and if they add to 9, the next pair, etc.) Alternatively, you can count it as a 9 and revise if you later have an overflow you haven't taken care of.

Like anything it sounds awfully complicated, but becomes easy enough with practice. Personally, I add from left to right most of the time, right to left some of the time, and use other shortcuts whenever possible. If the numbers are not similar in magnitude, it's often easier to add from left to right... but this is always a personal thing.

One point to note is that this doesn't work well for adding more than two numbers, because the overflow is too difficult to track.

Answer 2

Either method is equally valid. The right-to-left method was invented because in the event that some digit caused a carry, you would have to go back and overwrite the previous digit, which in pencil-and-paper arithmetic can mean a lot of erasing. However, if you're doing the problem in your head, overwriting previous numbers in the result is effortless, and in fact gives you fewer numbers that you have to remember. Thus, the left-to-right method is superior for mental arithmetic.

As an example, consider the mental process you might go through to add 143 to 317:

100+300 = 400
400+40+10=450
450+3+7=450+10=460

Much easier than doing it right-to-left, right?

Answer 3

When I add large numbers in my head, I usually do it the "wrong" way, starting from the left. Two reasons:
1) easier to say (I am auditive rather than visual: I hear numbers rather than see them) and we say numbers beginning from the left (however, the Germans have numbers that they say from the right, for example 43 is dreiundvierzig: three and forty).

2) the important part is usually the first few significant digits. If you are adding 2,467,148 + 2,366,224 it could be that you are trying to see if the project costs more of less than 5 million dollars.

The problem is doing the carry-overs after the fact.

In the above case, you'd go "four million, seven hundred and, no make that eight hundred and twenty... no, thirty three thousand, three hundred and sixty twelve." In English, you'd correct the last part to seventy two. In French, you'd leave it like that "soixante-douze".

So, if you do you mental calculations in blocks of two columns, it may be easier to go right to left in German, and left to right in French.

Answer 4

I suppose you mean when adding multidigit numbers in columns.
We usually do this right to left because of the need to carry over into the next place representing the next power of 10.
If you want to add left to right you can, but you'll have to back up sometimes to revise your partial sum if a carry occurred in the next place.
If you're doing the problem in your head, you've probably got your own method for doing this because this skill is very rare, especially with the popularity of calculators nowdays. So if you do multicolumn addition in your head and do it left to right, more power to you. Most of us need pencil and paper, whree the traditional right to left method works better because of place values, or grab the nearest calculator.

Answer 5

We hear ya !

The new math is confounding you? Slow and too broken down into tiny steps, ergo too annoying to perform ? How did the geniuses of the baby boomer generation live without the new math?

You ask about right to left vs left to right.

The Chinese have been trained to look at numbers and letters from right to left from birth, therefore write and do math that way.

The West have done basic math from top to bottom and algebra from left to right.

Whats the diff as long as the problem gets solved?

It all involves the teaching of math.
Rand Corporation which is a think tank proposed a math reform for the following reasons;
1. Math is changing because when we went to school we didn't learn enough, and our kids deserve to learn more math than we did. Today, we know better math, better ways to teach math, and better ways for students to learn. As a result, math is changing so that teaching and learning will work for everyone.
2. Math is changing because the world is changing. In the world today we do most of our work in groups, we use calculators and computers for computation and communication, and we rely on data and statistics when making decisions. School mathematics is changing so that today's students will be able to work today and in the future.
3. Math is changing because colleges and universities are changing. Throughout the United States, and especially at the nation's most prestigious universities, Calculus has been turned into an activity-oriented, problem-solving course. To prepare students for college, school math is changing to provide activities and problem solving for everyone.
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Answer 6

What format are the numbers in? If you have them in a text file, one to a line, then copy or rename that to have a .csv suffix ("comma-separated values" file) and open that with Excel. Don't worry about the lack of commas...those are only to separate values on a row. Each text file line is treated as a new row automatically. You should get a spreadsheet with 888 rows and just one column, and you can sum that easily.

Answer 7

I read somewhere that savants and mathematics prodigies typically add from left to right. They find it faster.
Why are they different? What is the method they use?
Wish I knew.
I think it was in a Discover magazine article if you wanted to do a journal search online.....

Answer 8

It doesn't matter. It may depend on the individual, some people might find 1 way easier, some will find the other easier & some won't notice a difference.

Answer 9

It seems like it would be easier right to left, because of the whole place values thing...

Answer 10

Right to left, for when you have to carry a 1 (or more). If you went left to right, those would be left out and you'd have to recalculate.