Early in elementary school students are taught how to add single digit numbers. Then students progress to addition of two digit numbers, which is taught from right to left. But in many cases, it’s actually easier and quicker, particularly adding your head, to add from left to right. When figuring out an answer to an addition problem on paper using the right to left method, you are actually answering the problem backwards, which makes that method quite a bit more difficult to add mentally. After all, we read numbers from left to right, so why not calculate numbers from left to right?
For an example as to why this method makes more sense, consider the following. Suppose we add 56 and 37. Using the right to left method, we add the 6 and 7 to get 13, so we write a 3 under the one’s digit and carry the 1. So the first part that we see in the answer is 3. But if we use the left to right method, which I’ll discuss in the next paragraph, you will know quickly that the answer is 90-something. That answer is a lot more precise and significant to just knowing the the problem ends in 3. With two digit addition, the left to right method might not seem to be much of an advantage, but it will be clear that there is an advantage when progressing to three digit numbers.
The easiest two digit numbers to add are those that don’t require carrying. Let’s take the problem 37 plus 52. Using the left to right method we can think of the problem as 37 plus 50, then adding 2. Basically we are taking the 52 and changing it to 50 plus 2. You could add 52 to 30 and then add 7. By adding left to right you take 37 plus 50 (add the 3 and 5 to get 8 and drop down the 7 to get 87). Then add 2 to get 89. Notice this works also taking 37 plus 50 (3 plus 5 is 8 and drop the 7 to get 87). Then add 2 to get 89.
Let’s try another example, take 67 plus 55. In this example we have to carry, but the method is the same. We change the problem to 67 plus 50 plus 5. Adding left to right we get 6 plus 5 is 11 and drop down the 7 to get 117. Then add 5 to get 122.
Now we can try addition with three digit numbers. Suppose we want to add 553 and 327. Starting with 553, we add 300, then 20, then 7. Notice how we break down 327, into hundreds, tens and ones. Now add from left to right, 553 plus 300 is 853. Then add 20 from left to right (5 plus 2 is 7, then drop down the 3) to get 873. Now add 7 to get 880.
Let’s try another three digit addition. Suppose we want to add 736 and 235. Starting with 736, we add 200, then 30, then 5. Adding from left to right we get 736 plus 200 is 936. Add 30 to get 966 and then 5 to get 971.
Some three digit addition problems will be more complex, especially those in which there is carrying in each step. Let’s add 869 to 656. Starting with 869 we add 600, then add 60 and then add 9. Adding from left to right we get 14 and drop down the 69 to get 1469. Then add 50 to get 1519 and add 6 to get 1525. If it’s easier you could keep 656 and break down 869 to 800, 60 and 9. Adding in this fashion gives you 800 plus 656 equals 1456, add 60 to get 1516 and add 9 to get 1525.
Practice this alternative method which I have shown students and you may find it’s quicker, especially mentally, than the traditional method of adding from right to left. In my next article, I will address how to subtract from left to right.