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Partial Sums Method

of Addition

The Partial Sums method is a two-stage process. In the first stage one looks at each column (working left to right) and adds up the place-values represented by the digits in that column. In the second stage those partial sums are added together. In the first example at right the process is applied to 148 + 67 + 266. The student reference does not recommend a specific algorithm for the addition problem in the second stage. Frequently the second stage problem will be "easy" in that it can be done one column at a time without any carries, as is the case in the first example. Perhaps the student is expected to use the Partial Sums method in cases where the second stage addition problem involves carrying.

So, let us explore the Partial Sums algorithm in a case where the second stage and even the logical third stage involve carrying. Try 148 + 855 or, for an example that is a bit harder for mental arithmetic, see the problem at right, 678 + 67 + 266. The mathematically inclined reader will note that the Partial Sums method (iterated so long as carrying is required) terminates, because every application of the basic step will reduce, from the right, the range of columns for which carrying is required.