Speedy and accurate addition (Part IV)


Let us see another procedure for carrying out additions speedily and accurately. The idea here is to "divide and rule." We shall break our task into smaller activities to have better control on them to gain speed and accuracy.

Let us consider some examples. Suppose we start adding the column by the conventional method. With the only change that when the running total becomes greater than 10, we reduce it by 10 and go ahead with the reduced answer. As we do so, we keep track of the number of times our total was higher than 10. Also, we keep a note of the final reduced answer for the column.

With the help of the number of times we encountered the total higher than 10 and the final reduced answer (i.e. after subtracting 10), we can calculate the total for the column. The advantage of doing addition in measure of tens is obvious. Multiplication by ten is very easy, as we have to just add a zero to the right of the number we multiply.

Let us add the column here, applying the procedure explained above (see figure on the left).

Let us now do this with an example having multi-digit numbers to add (see figure on the left). Can we use any other number beyond which we continue to count? Yes! We can use any number we like! However, the number we choose should have some facility with respect to multiplication. The other number whose multiples can be found easily is 11. Multiplying this number by any number from 1 to 9 is very easy, and as you know whatever number we are multiplying 11 with is to be written twice. Hence, we can add the column till the running total becomes 11 instead of 10. We reduce the answer by 11 and go ahead with the reduced answer.

Let us add the earlier column again, but this time we will add in groups of 11. See the figure here.

Let us add the earlier multi-digit numbers as well in groups of 11 (see the figure on the left).


This method, in which we never count higher than 11, is also proposed by Trachtenberg in his famous book The Trachtenberg Speed system of Basic Mathematics1. In this system you can start adding from the leftmost column as well.

Now, try the following additions by either counting in tens or elevens.

The copyright of the article Speedy and accurate addition (Part IV) in Math for Kids is owned by Vidya Narayan Wadadekar . Permission to republish Speedy and accurate addition (Part IV) in print or online must be granted by the author in writing.

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