VEDIC MATHS-88

-

 

VEDIC MATHS

                           By OMKAR TENDOLKAR

Hello friends,

                      This is  post number 88 from the series of "Vedic maths" blogs. Here in this blog we will learn about "Auxilliary Fraction-V"

Reference:

We had already learn about "Types Of Decimals" in our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-83".

We had already learn about Reciprocals of Numbers Ending in 9 in "Auxilliary Fraction-I" in our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-84".

We had already learn about Reciprocals of Numbers Ending in 3 in "Auxilliary Fraction-II" in our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-85".

We had already learn about Reciprocals of Numbers Ending in 7 in "Auxilliary Fraction-III" in our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-86".

We had already learn about Reciprocals of Numbers Ending in 1 in "Auxilliary Fraction-IV" in our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-87".

Decimals:
Here in this post, we shall look at methods to convert fractions to decimals.

Vedic One-Line Method:

The conventional practice of converting a reciprocal or fraction into a decimal number involves the division of the numerator by the actual denominator. When the denominator is an odd prime number such as 19, 23, 29, 17 etc., the actual division process becomes too difficult; whereas, if we use the Vedic method, the whole division process becomes oral and the decimals of such fractions can be written directly.

We will now see additional techniques which can speed up the division of fractional numbers where :
  • the dividend is less than the divisor and
  • the divisor is small e.g. having 2 or 3 digits and
  • the last digit of the divisor ends with 1, 6, 7, 8 and 9 E.g. of such divisors are 19, 29, 27, 59, 41, 67, 121 etc.
Other divisors ending in 2, 3, 4, 5 and 7 can be converted to such divisors by multiplying by a suitable number.

We will see examples of divisors ending in each of the digits from 1 to 9 to get a good insight into the entire process.

Reciprocals of Numbers Ending in 8:

Let us consider cases where the divisor ends with 8.
E.g. 18, 28, 48, 88 etc.

General Steps:
  • Add 2 to the denominator and use that as the divisor
  • Remove the zero from the divisor and place a decimal point in the numerator at the appropriate position
  • Carry out a step-by-step division as explained before
  • Every division should return a quotient and a remainder and should not be
  • carried out as a decimal division
  • The quotient and the remainder is taken as the next base dividend as explained above
  • Since the last digit of the divisor is 8 which has a difference of 1 from 9, we multiply the quotient by 1 and add to the base dividend at each stage to compute the gross dividend.
Example :
1.Convert the fraction 5 / 28 to its decimal form.

Steps:
  • Add 2 to the divisor to get 30
  • The modified division is now 5 / 30
  • Remove the zero from the denominator by placing a decimal point in the numerator giving the modified division as 0.5 / 3
  • We will not write the final answer as 0.16666 but
  • We will carry out a step-by-step division as explained below
Steps for step-by-step division
Step 1:
5 / 28 = 0.5 / 3.

Step 2:
Here the starting point is 0.5 ÷ 2. As we can divide 5 by 2, we give a decimal point in the answer with 1 as quotient and remainder 1 to be written. This means our next dividend is .       

5 / 28  = 0. 1......
                2

Step 3:
Now, the base dividend is 21 Add the quotient digit (1) to the initial dividend to get 22.
The next number for division is 22 which on division by 3 gives q = 7 and r = 1. The result now looks as

5 / 28  = 0. 1 7......
                2 1

Step 4:
Now, the base dividend is 17 Add the quotient digit (7) to the base dividend to get 24
The next number for division is 24 which on division by 3 gives q = 8 and r = 0. The result now looks as

5 / 28  = 0. 1 7 8......
                2 1 0
Step 5:
The final result upto 5 digits of accuracy
 5 / 28  = 0. 1 7 8 5......
                2 1 0 1

Our answer becomes 0.1785.

Answer:
5 / 28 = 0.1785
.
NOTE: if this process of division is continued, the same set of digits will start repeating. We stop dividing once we get the required number of decimal places.

2. Convert the fraction 5 / 18 to its decimal form.

5 / 18 = 5 / 20 = 0.5 / 2

5 / 18  = 0. 2 7 7 7......
                1 0 0 0
Our answer becomes 0.27777.

Answer:
5 / 18 = 0.27777.

Solve the following example.
1. 1 / 28
Ans : 1 / 28 = 1 / 30 = 0.1 / 3 = 0.03571.

2. 1 / 48
Ans : 1 / 48 = 1 / 50 = 0.1 / 5 = 0.02083.

3. 5 / 58
Ans :  5 / 58 = 5 / 60 = 0.5 / 6 = 0.08620.

The simplicity of this method can be vouched from examples given above.

You may try following examples.
1. 7/68
2. 5/78
3. 1/48
4. 7/18
5. 3/48

In next blog we will discuss about "Auxilliary Fraction-VI".     

Are you excited for this?...
Then, please wait for it.
I will post my new blog in next week.

We will meet very soon through our next  blog. Till that stay connected, stay healthy and stay safe.

Thanks

for giving your valuable time.

Good day😊

Comments

Post a Comment

Popular posts from this blog

VEDIC MATHEMATICS

-
Image
  VEDIC MATHS                             By OMKAR TENDOLKAR Hello friends,                        I am Omkar Tendolkar from Kudal. I am studying in S.Y.B.Sc at SRM College, Kudal. I always enjoy sharing my knowledge. This is one of my attempts.            Some people find mathematics challenging to understand, while others struggle with calculations. Certainly, the comprehension of the subject depend on IQ (intelligent quotient), but equally crucial is one's perspective towards it. Because mastering calculation doesn't solely rely on a sharpe IQ; it also demands some basic tricks that can greatly assist in handling complex calculations.                  Starting today, I want to launch a "VEDIC MATHS" blog. Here, you will find a series of blog's explaining simple tricks that will...
Read more

VEDIC MATHS-1

-
Image
VEDIC MATHS                             By OMKAR TENDOLKAR Hello friends,                          This is our first blog in the series of 'Vedic Maths' blogs. Here, we will learn about the basic principles required in Vedic Maths. This blog will cover all the fundamental concepts necessary for understanding our next few blogs.   Base: It is the first number in the series. For a two-digit number: 10. Starting with 10, 100, 1000, 10000, etc. Complement: . Adding two numbers results in the next nearest base. 48 + 52 = 100. Then, We can say that 48 is the complement of 52 or 52 is the complement of 48. How to find: Subtract each digit from 9 and the last digit from 10. If... The last digit is 0, then take the second-to-last digit as the last one. For example: 60 is the complement of 40. All these examples, ranging from 2 digits to 6 digits, w...
Read more

VEDIC MATHS-15

-
Image
  VEDIC MATHS                             By OMKAR TENDOLKA R Hello friends,                       This is our 15th blog from the series of "Vedic maths" blogs. Here in this blog we will learn about   "Criss-Cross System of Multiplication " . Criss-Cross System of Multiplication :                In Vedic Mathematics , we have similar system as like traditional way of multiplication it helps us to get the answer much faster. This system is also universal system and can be used for any combination of numbers of any length.                      This system of Multiplication is given by the " Urdhva-Tiryak Sutra. " It means ' vertically and cross-wise '. The application of this system are manifold, but in this blog we shall confine our study only to it's utility in...
Read more