MSC #4 – Using Bar Numbers

A very creative Vedic Math device is the bar (or vinculum) number. It uses a vinculum or bar over a digit to indicate that it is negative. In this way, large digits can be replaced by their smaller complements leading to easier computations. (Note: here we will use parentheses to indicate negative digits) Hence, 19, which is 20 – 1, can be written as 2(1), 98 which is 100 -2 as 10(2) and 997 which is 1000 -3 as 100(3). Depending on the need, 789 may be expressed as 79(1), 8(11) or 1(211). In our illustrated example, while the multiplication 197 x 27 cannot be easily calculated mentally, by using bar numbers, the problem can be rewritten as 20(3) x 27. With the help of number splitting- MSC #3, which was the subject of our post yesterday, we can easily compute 2 x 27 = 54 and 03 x 27 = 81. Thus 2(03) x 27 = 54(81) or 5319. Another example of bar number application is in subtraction: 7 3 8, 2 3 4  –   5 8 6, 7 9 6              2(5)2, (562) Using the conventional right to left method taught in schools, this subtraction will require 4 regroupings. With the use of bar notation, we can do it digit by digit from left to right. Starting from the first column we have, 7 – 5 = 2. For the next column, we notice that the digit in the minuend, 3, is less that the digit of the subtrahend, 8 and so we can reverse the numbers so that we will have 8 – 3 = 5. However, since we reversed the numbers, we will write the answer as negative or bar 5. For the third column we have 8 – 6 = 2. For the last 3 columns, all the digits in the minuend are less than the corresponding digits in the subtrahend, so the difference will be negative and will be written as bar numbers, (5), (6) and (2) or (562) The difference, 2 (5) and 2(562) can easily be “devinculated or written in normal notation by using our MATH Special for Christmas #2, “All from 9 and the Last from 10”. 20 – 5 is 15 and 2000 – 562 is 1438. So the final answer is 151, 438.