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division of fractional number

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 Fractional number convert in to decimal in one line

Vulgar fractional number whose denominator ending by 9 like, 1/19, 1/29, 4/39 etc. will be convert in to decimal number in one line by using Ekadhikena purvena sutra of Vedic Mathematics.

There are two method in Vedic Mathematic to solve this fraction number.

1)Multiplication Method

2)Division Method

We will learn both the methods, you can apply any one which will be easy to understand.

 

1)Multiplication Method:

Beauty of this method is that we get our answer without doing any division.

In this method we get our answer from right to left, means we get our last digit first & then we move towards left side. The number of digits we will get after decimal point is depends upon the fractional number, but we can stop when series is getting repeated.

 

Ex. i) 1/19

For 1/19, denominator ending by 9, so we can apply our sutra Ekadhikena Purvena. Ekadhikena purvena means one more than previous. In denominator 19 previous number is 1 & one more than previous is 1 + 1 =2.

So, here 2 is the constant multiplier for whole conversion of the fraction.

 

Step 1: As we start from right to left so first, we find right most digit.

Numerator = 1 is our right most digit.

1/19 = 0.                           1

 

Step 2: As 2 is our multiplier, multiply rightmost digit 1 x 2 =2. Write down 2 to the left side of 1.

1/19 = 0.                         21

 

Step 3: Now multiply this 2 by multiplier 2, 2 x 2 = 4, Write down 4 to the left side of 2.

1/19 = 0.                       421

 

Step 4: Multiply 4 X 2 = 8, write down 4 to the left-hand side of 4

  1/19 = 0.                  8421

 

Step 5: Multiply 8 X 2 =16, so now we write down 6 to the left-hand side of 8 & carry over 1 in our next digit

1/19 = 0.                  168421

 

Step 6: Multiply 6 X 2 = 12 + 1 (carry over) = 13, So we write down 3 & carryover 1

1/19 = 0.                 1368421

 

Step 7: Multiply 3 X 2 =6 + 1(Carryover) = 7, so we write down to the 7 left-hand side of 3

1/19 = 0.                  7368421

 

Do continue till step 18

1/19 = 0.                 147368421   —(8)

1/19 = 0.                947368421   —(9)

1/19 = 0.             18947368421   —(10)

1/19 = 0.            178947368421   —(11)

1/19 = 0.           1578947368421   —(12)

1/19 = 0.          11578947368421   —(13)

1/19 = 0.          31578947368421   —(14)

1/19 = 0.    631578947368421   —(15)

1/19 = 0.  12631578947368421   —(16)

1/19 = 0.  52631578947368421   —(17)

1/19 = 0.1052631578947368421   —(18)

Now from step 18 onwards same series of the number start to repeat, so we stop here,

 

fractional to decimal using easy & fast way

 

Note: The maximum number of decimal places before repetition start is,

     Denominator – Numerator

     19 -1 = 18 places

Number series may repeat before (Denominator – numerator) obtained number also, so we must stop when number series gets repeated.

 

Ex 2) 4 / 39

 

 If we check denominator, it ends by 9 so we can apply our trick here.

In 39, previous digit is 3, one more than previous is 3+1 = 4

 So, here 4 is our constant multiplier. And numerator 4 is our last digit of decimal

 Now steps are already explained in above sum, so we directly write down answers,

 

4/39 = 0.          4 (Numerator as last digit)

4/39 = 0.        164 (4 X 4 =16)

4/39 = 0.       2564 (6 X 4 =24 + 1=25)

4/39 = 0.      22564 (5 X 4 =20 + 2=22)

4/39 = 0.     102564 (2 X 4 =8 + 2=10)

4/39 = 0.     102564 (0 X 4 =0 + 1=1)

4/39 = 0.  4102564

We can observe that series is started to repeat from here, so we stop

 

fractional to decimal by fast & easy method

 

Ex 3) 5/23

Denominator is not ending by 9, but we can convert it in that form, by multiplying 3 to both denominator as well as numerator.

 

 

Now, denominator ends by 9, so we can solve by Vedic method.

In 15/69, previous digit is 6, one more than previous is 6 + 1 =7 so, our constant multiplier is 7 & numerator is 15, which is our last digit.

 

15/69 = 0.                15( we write down 5 as a last digit & carry over 1)

15/69 = 0.               365( 5×7 = 35 + 1(carry)=36)

Similar way we continue.

 

15/69 = 0.2173913043478260869565

After that series is started to repeat.

 

fractional to decimal using vedic method

 

                          

2) Division Method

In division method we get our solution from left to right.

We will solve same example that we solve by multiplication method.

 

Ex i) 1/19

Here also in 19 previous digit is 1, so one more than previous is 1 + 1 =2

So, 2 is our constant divisor

 

Step 1: Numerator is 1 so we divide it by divisor 2.

1/2, (Q = 0 & R = 1)

1/19 = 0.10  (Q = 0 is our first digit & R = 1 we write down to the left-hand side of 0)

As our divisor is fixed i.e. 2, & dividend is the number generated by Reminder & quotient.(RQ)

So here dividend is 10

 

Step 2: Divide 10 by 2 (Q = 5, R =0)

1/19 = 0.005 (As above step we write down Q = 5 as our second digit & R = 0 at left hand side of 5)

So, our new dividend is 05(RQ)

 

Step 3: Divide 5 by 2 (Q = 2, R =1)

1/19 = 0.0512

 

We will repeat the step till the number series is not repeated

 

Step 4: Divide 12 by 2 (Q = 6, R =0)

1/19 = 0.05206

 

Step 5: Divide 6 by 2 (Q = 3, R =0)

1/19 = 0.052603

 

Step 6: Divide 3 by 2 (Q = 1, R =1)

1/19 = 0.0526311

 

Step 7: Divide 11 by 2 (Q = 5, R =1)

1/19 = 0.05263115

 

Step 8: Divide 15 by 2 (Q = 7, R =1)

1/19 = 0.052631517

 

Step 9: Divide 17 by 2 (Q = 8, R =1)

1/19 = 0.0526315718

Similarly, we repeat the step up to step 18,

After step 18 our answer will be,

1/19 = 0.0526315789473684201

Now after step 18, divide 1 by 2 so our step 1 will be repeated so we stop here,

 

vedic method of division

 

Find this links to study more:

1. Criss-Cross method of multiplication

2. Division in one line when divisor is 9

3. Square of number ends by 5 in 2-3 seconds

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i love vedic math !!!!!!!

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i love vedic math

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