In our 30 MATH-Inic Specials for Christmas series, which is sponsored by Palawan Pawnshop Express Pera Padala, we will publish one Vedic Math technique daily for 30 days. Each of this post, which shows a different approach to common problems, is taken from our book “30 Master Strategies of Computing”. which, we finally decided, to release in e-book format, one master strategy at a time.
An abridged e-book version of the first 10 “master strategies” will be given FREE to those who will purchase a set of books – 25 Math Short Cuts, Algebra Made Easy as Arithmetic and Inspirational Maths from India. See details at https://www.facebook.com/MATHInicPhils.
MSC #1 – By One More than the One Before
“By One More Than the One Before” is the first Vedic Math Sutra or word formula. It is applied in various ways: counting, arithmetic sequences, squaring numbers ending in 5, multiplying complementary numbers, division, divisibility tests, recurring decimals and other applications.
When a number ending in 9 is a divisor or a denominator of a fraction, it would be easier to use its Ekadhika instead. The Ekadhika is “one more than the number before 9”. 2 is the Ekadhika for 19, 3 for 29, 4 for 39 and so on.
If we want to divide a number by 19, for example, we can use its Ekadhika, 2, instead. If we want to convert 3/29 into its decimal equivalent, it is simpler to use 3, as divisor. Similarly, if we wish to determine if a number is divisible by 49, we can use an “osculator” of 5.
In our example, we want to get the result when 2367 is divided by 19. We will use the 2, the Ekadhila of 19 as the divisor using the following steps:
- Separate the last digit of the dividend 7 by a remainder bar. Only one digit is separated because the working base of 19 is 20 which has only 1 zero. (We will explain base division in a later post).
- Divide the first digit of the dividend by our Ekahika, 2 to get 1 with no remainder. 1 is the first quotient digit.
- Add this 1 to the next figure of the dividend 3 to get 4.
- Divide 4 by 2 to get the next answer digit 2. Again, there is no remainder.
- Repeat steps 3 and 4: add 2 to the next dividend digit 6 to get 8; 8 divided by 2 will give 4 with no remainder..
- Write down 4 as the 3rd answer digit.
- Add this 4 to 7 the last digit of the dividend to get 11, the remainder of the division.
Therefore 2367 ÷ 19 = 124 rem 11. Watch out for the release of Master Strategy in Computing #1 – “By One More Than the One Before” with problems and solutions from national and international Vedic Math competitions this Christmas Season!