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 we will use parentheses to indicate negative digits)
Hence, 19 can be written as 2(1) as 98 as 10(2) and 997 as 100(3). They can be evaluated as 20 – 1, 100 – 2 and 1000 – 3 respectively.
Yesterday, we showed that with number splitting we can easily multiply 997 x 7. This can be easier done using bar numbers. The multiplication 100(3)x 7 will easily give 70(21). In normal notation, this is equivalent to 7000 – 21 or 6979.
Similarly, while the multiplication 197 x 27 can not be easily computed mentally, by using bar numbers, the problem can be rewritten as 20(3) x 27. The product is, with the help of number splitting, 54(81) or 5319.
The use Bar numbers will be explained fully on the opening session of the Inspirational Math from India (year 4) on Dec 4 2021 by Ms. Cris Jeanel H. Sanchez, Math Subject Area Head of Stonyhurst Southville International School – Malarayat Campus and coach of Michael Tongson, top scorer in the 1st Philippine National Vedic Mathematics Olympiad.
In today’s MATH Special for Christmas, we will apply bar numbers in subtraction:
Using the conventional right to left method taught in schools, this subtraction will require 4 regroupings. With the use of bar numbers 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.
The difference, 2 (5) and 2(562) can be 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.