done before all subtraction. Example: Partial differences The partial differences method is different from other vertical subtraction methods because no borrowing or carrying takes place. In their place, one places plus or minus signs depending on whether the minuend is greater or smaller than the subtrahend. The sum of the partial differences is the total difference. Example: Nonvertical methods Counting up Instead of finding the difference digit by digit, one can count up the numbers between the subtrahend and the minuend. Example: 1234 − 567 = can be found by the following steps: Add up the value from each step to get the total difference: . Breaking up the subtraction Another method that is useful for mental arithmetic is to split up the subtraction into small steps. Example: 1234 − 567 = can be solved in the following way: 1234 − 500 = 734 734 − 60 = 674 674 − 7 = 667 Same change The same change method uses the fact that adding or subtracting the same number from the minuend and subtrahend does not change the answer. One simply adds the amount needed to get zeros in the subtrahend. Example: "1234 − 567 =" can be solved as follows: See also Absolute difference Decrement Elementary arithmetic Method of complements Negative number Plus and minus signs Notes References Bibliography Brownell, W.A. (1939). Learning as reorganization: An experimental study in third-grade arithmetic, Duke University Press. Subtraction in the United States: An Historical Perspective, Susan Ross, Mary Pratt-Cotter, The Mathematics Educator, Vol. 8, No. 1 (original publication) and Vol. 10, No. 1 (reprint.) PDF External links Printable Worksheets: Subtraction Worksheets, One Digit Subtraction, Two Digit Subtraction, Four Digit Subtraction, and More Subtraction Worksheets Subtraction Game at cut-the-knot Subtraction on a Japanese abacus selected from Abacus: Mystery of the Bead Elementary arithmetic