Flag Method (Direct Division Method )- Division in Vedic Mathematics
Direct Flag Method is a General Method of Vedic Mathematics is used to carry division of ANY types of numbers.
In this post you will see Flag Method Division of Vedic mathematics. Before starting, It is very important to know Vinculum & playing with Quotients & Remainders.
Also Read More Division Sutras in Vedic Mathematics
Single Digit Flag
#1. 1234/12 Dividend = 1234 and Divisor = 12. Split divisor (12) in 2 parts (1 and 2) where division will be carried using ONLY 1(new divisor) and 2 is called as flag. As flag is single digit, Split dividend in 2 parts such that 2nd part will have same number as that of flag i.e. 1 digit.
Process (see the example for each step):
- Division of 1 by 1 (Q=1 and R= 0). Write Q=1 and carry forward the R=0(written in white under and between 1&2).
- Multiply the new Q(1) with the flag(2) and subtract this product from 02 = 0 and divide this subtraction by 1. It gives Q= 0 and R= 0(Carry forward R=0). (i.e. Multiply, Subtract, Divide)
- Follow same above process, So multiply new Q(0) with flag(2) and subtract this product from 03 = 3 and divide this subtraction by 1. It gives Q= 3 and R= 0(Carry forward R=0).
- For remainder we carry same process EXCEPT we don’t divide. (i.e. Multiply, Subtract) So multiply new Q(3) with flag(2) and subtract this product from 04 = -2. As we get negative subtraction, we reduce the quotient by 1 and increase the remainder by the 1st multiplier of new multiplier (1X1 =1). So new Q = 2 and new R =1. (Refer Topic How to Play with Quotient and Remainder). We carry this method till we don’t have negative subtraction.
- Now Multiply the new Q(2) with the flag(2) and subtract this product from 14 = 10(positive) and put it down as it is.
- So final answer: Quotient = 102 and Remainder = 10 (Remainder should always < Divisor| (How to Play with Quotient and Remainder).
# 15623/123 Dividend = 15623 and Divisor = 123. Split divisor (123) in 2 parts (1 and 23) where division will be carried using ONLY 1(new divisor) and 23 is called as flag. As flag is double digit, Split dividend in 2 parts such that 2nd part will have same digits as that of flag i.e.2 digits.
- We carry out the same process except 1 change. As flag is of 2 digit, whenever we need to do subtraction, we subtract the CROSS multiplication of 2 latest quotient digits with the flag.i.e. if Flag=ab and new Q = cd then subtract (ad+bc).
- If we have only 1 digit in the Quotient which happens only in starting step then we do multiplication with the 1st digit of flag.
- It has different way of calculating Remainder. Remainder: Subtract [10(cross multiplication of flag(ab) and latest Q(cd))+ Last digit multiplication of ab and cd i.e. bd]… See examples to get more cleared.
Process (see the example for each step):
- Division of 1 by 1 gives Q=1 and R = 0. (Carry Forward R=0).
- Multiply the new Q(1) with the 1st part of flag(2)(See above 2nd rule) and subtract this product from 05 = 3 and divide this subtraction by 1. It gives Q= 3 and R= 0(Carry Forward R=0).
- Now Cross Multiply (see above 1st Rule) new Q(13) with flag(23) and subtract this product(9) from 06 = -3(negative). Since its negative, reduce the quotient by 1 and and increase the remainder by the 1st multiplier of new multiplier (1X1 =1). So new Q = 2 and new R =1. (See Basic Requisites page).
- Cross multiply new Q(12) with flag(23) and subtract the product(7) from 16=9 and divide this by 1 giving Q= 9 and R = 0.
- Carry out similar process to get till you reach calculation for Remainder.
- Remainder: 223 – [10(6+14) + 21] = 223 – [200 + 21] = 2 (See above 3rd rule).
- Final Answer: Quotient: 127 and Remainder: 2.
More Examples on Shortcut Tricks for dividing large numbers in Vedic Mathematics.
Answer in Decimal format: We can answer in terms of decimal as well. We append zeroes and carry same process which we used to carry Quotient only difference the step which we had used for calculating remainder will be omitted and even after the vertical line (decimal point) process remains same. Decimal point comes at same place where the Remainder would have come.
1452563 / 1234: Remainder part FINALLY will go as 4563 – [100(7×2+7×3+1×4) + 10(3×7+4×7) + 4×7] = 145 (Same problem can be solved by considering flag as 34 and divisor as 12 but for that table of 12 will be required to be known.)
What You Think ????
How the following examples should be solved using Flag Method !!!
|1) 473/34 2) 93489/29 3) 783458/112 4) 8274/189 5) 783458/118 6) 1452563/1234||Subscribe us for regular updates