So here I go. This is regarding the name of the website - QuickerMaths.com. It is inspired by the name of the best mathematics books I have ever come across. This book helped me a lot in clearing CAT and reaching to IIM. The inspiration of creating an interactive platform (QuickerMaths.com) came from this book. As a token of appreciation and to do my bit today I will tell you about this book named -

Magical Book on Quicker Maths

Author: M. Tyra

About the book: The book will be a boon for the aspirants of today’s competitive exams irrespective of their background – whether they come from arts, science or commerce stream. Concepts have been clarified so well, that even if one is vaguely familiar with them as in the case of non-mathematics students, understanding will not be a problem. Direct formulae are beneficial for one and all. They save time and time is precious for everyone.

Must for Competitive Preparation

The book is profusely illustrated. Avoiding the temptation for haste and ending up with a cookbook, the author has put in two years of intensive effort and research. Ideas have been taken from available study material, number theory, readers’ suggestions and, finally Vedic mathematics.

Recently I purchased the latest edition of this book from an online book store Flipkart.com

Purchase Online - The list Price is Rs. 250; you get a Discount of 25% (Rs. 62) on Flipkart.com.

So you get it for: Rs. 188 (incl. of all taxes)

Those who have already read this book please give your feedback to help others

Author: Vineet Patawari

Related posts:

1. Vedic Maths Workshop
2. Squaring number ending in five : Vedic Maths Trick

Before going further on the method to find the cube root, please make a note of the following points –

1) Cube of a 2-digit number will have at max 6 digits (99^3 = 970,299). That implies if you are given with a 6 digit number, its cube root will have 2 digits.

2) This trick works only for perfect cubes, it will not work for any arbitrary 6-digit

3) It works only for integers

Now let us start with the trick to find cube root of a 5 or 6 digit number in vedic mathematic way.

Say you have to find the cube root of 54872. It is known that it’s a perfect cube.

Now divide this number into two parts. The right hand side should always have 3 digits. Remaining digits will come in left hand side. Do it as shown below.

54            |             872

You know the answer will have 2 digits. Digit at tens place and digit at units place. We will get the digit at tens place using the left hand side of the original number (54) and digit at units place using right hand side of the number (872)

Step 1.

Memorize these tables (very soon you will know why) –

Table 1: Cube of 1 to 10

Table 2: Unit’s digit of Cube Roots

Step 2.

For left hand side we need to use table 1. We have to see between which 2 numbers in the 2^nd column do 54 lies. In this case it lies between 27 and 64. So we will take the cube root of the smaller number i.e. 27 which is 3.

So 3 is the tens digit of the answer.

Step 3.

For right hand side we need to use table 2. Since our original number (the perfect cube) ends in 2 (see 54872), its cube root will ends in 8.

Thus the units digit will be 8.

Combining the results we get the answer as 38.

Thus (54872)^1/3  =  38

Try for perfect cubes like 185193, 42875, 1728.

You might also be interested in the trick of finding square root of any number

I hope you liked the simple trick to find the cube root. Leave your comments below -

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2. Shortcut to find the Cube of a number
3. Speed Multiplication by 111 : Vedic Maths

I have got a mail from some QuickerMaths follower, to illustrate usage of Vedic Mathematics in branches of mathematics other than arithmetic. This post is for that purpose only. Here I am highlighting the usage of Vedic Mathematics in finding out the remainder when an algebraic expression is divided by another.

Finding out the remainder becomes extremely easy using Vedic Maths.

So lets begin with a simple example -

Find the remainder when

x³ + 4x² + 6x - 7 is divided by (x + 5)

Solution:

Step I: Put divisor equal to 0 .i.e.

x + 5 = 0

x = -5

Step II: The remainder will be f(x).

f (-5) = (-5)³ + 4(-5)² + 6(-5) - 7

= -125 + 100 - 30 – 7

= -62

Example 2: (Mx³ + 3x² -3) and (2x³ – 5x +M) leaves the same remainder when divided by (x -4) Find the value of M.

Solution:

Let R1 and R2 be remainder for 1^st and 2^nd equation simultaneously

Rl = f (4) = M (4)³ + 3(4)² - 3 = 64M+ 45

R2 = f (4) = 2(4)³ - 5(4) + M = M + 108

They leave the same remainder. So,

Since, Rl = R2. We have

64 M + 45= M +108

Or, 63 M = 63

M = 1

Example 4: (Mx³ + x² - 2x – N) is exactly divisible by (x - 1) and (x + 1). Find the value of M and N.

Soln: When the expression is exactly divisible by any divisor, the remainder will be zero.

Now, the remainder, when the divisor is x-1, is

f (l) = M + 1 - 2 - N = 0          .

\M - N = 1                 ………….(1)

And the remainder, when the divisor is x + 1, is

f( -1) = M( -1)³ + (-1)² - 2(-1) - N = 0

-M + 1 + 2 - N = 0

M + N = 3                     …..(2)

Solving (1) & (2), we have,

M = 2, N = 1

Thanks to Nehul from Nagpur for asking this question. If you have any similar question, go to Contact Page and post your queries/suggestions.

Take Care. God Bless!!

Vineet Patawari

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1. Divisibility Rules including 7 and 13
2. Origin of Vedic Mathematics
3. Vedic Maths Subtraction

To appreciate the Vedic Maths process of finding the HCF you first need to know the other methods taught in school. I am giving you two other methods to compare with.

Example 1: Find the H.C.F. of x^2 + 5x + 4 and x^2 + 7x + 6.

Example 1: Find the H.C.F. of x^2 + 5x + 4 and x^2 + 7x + 6.

1. Factorization method:x^2 + 5x + 4 = (x + 4) (x + 1)

x^2 + 7x + 6 = (x + 6) (x + 1)

H.C.F. is ( x + 1 ).

2. Continuous division process.

x^2 + 5x + 4 ) x^2 + 7x + 6 ( 1

x^2 + 5x + 4___________2x + 2 ) x^2 + 5x + 4 ( ½x

x^2 + x__________4x + 4 ) 2x + 2 ( ½2x + 2______0
Thus 4x + 4 i.e., ( x + 1 ) is H.C.F.

Now see Vedic Maths way of finding HCF of 2 algebraic expressions.

i.e. x+1 is the HCF

Isn't it much simpler than the above 2 methods.

Now see some more examples -

Related posts:

1. Finding Cube Root – Vedic Maths Way
2. Origin of Vedic Mathematics
3. Vedic Mathematics Course Outline

Vedic Sutra: Vedic Mathematics Technique

Beejank: The Sum of the digits of a number is called Beejank. If the addition is a two digit number, then these two digits are also to be added up to get a single digit.

Find the Beejank of 632174.

As above we have to follow

632174  --> 6 + 3 + 2 + 1 + 7 + 4 --> 23 --> 2 + 3 --> 5

But a quick look gives 6 & 3 ; 2 & 7 are to be ignored because 6+3=9,2+7=9.

Hence remaining 1 + 4 --> 5 is the beejank of 632174.

Checking of Addition

Thumb Rule: Whatever we do to the number, we also do to their digit sum: then the result                 we get from the digit sum of the number must be equal to the digit sum of the answer.

For example: The number: 12+45+96+75+25 =253

The digit sum = 3+9+6+3+7 =28=10=1

Answer’s digit sum: 2+5+3 =10=1 (verified)

Another example:  3.5+23.4+17.5 = 44.4

The digit sum: 8+9+13=8+9+4=21=3

Answer’s digit sum: 12=3 (verified)

Casting Out Nines

This method is also known as "casting-out-nines". The method involves converting each number into its "casting-out-nines" equivalent, and then redoing the arithmetic. The casting-out-nines answer should equal the casting-out-nines version of the original answer. Below are examples for using casting out nines to check addition.

We get the casting-out-nines equivalent of a number by adding up its digits, and then adding up those digits, until you get a one digit number. If our answer is 9, then that becomes 0. As a short cut, we don't have to add in any of the 9's in our work, as these are the equivalent of 0. We can just "cast out" those 9's. For example, 19 becomes 1, without even adding 1 and 9 and getting 10, and then adding 1 and 0 and getting 1. As a further short cut, we can group numbers together which add up to 9, and replace them with 0. 2974 becomes 4, because we can cast out the 9 and the 2+7 (which is also 9 or 0). Well, let's try an arithmetic problem:

137892     3

+ 92743   + 7

------    --

230635     1

3+7=10, casting out 9 we get 1.

This rule is also applicable to subtraction, multiplication and up to some extent to division also

In the next post I will explain the use of this method for all of them.

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2. Speed Multiplication by 111 : Vedic Maths
3. Vedic Multiplication by 11

This fast calculation trick or vedic maths trick will teach you how to multiply any number by 5. The concept can be divided in two parts as shown-

MULTIPLYING 5 TIMES AN EVEN NUMBER

Memory Trick: Halve the number you are multiplying by and place a zero after the number.

Example:

i. 5 × 136, half of 136 is 68, add a zero for an answer of 680.

ii. 5 × 874, half of 874 is 437; add a zero for an answer of 4370.

MULTIPLYING 5 TIMES AN ODD NUMBER: subtract one from the number you are multiplying, then halve that number and place a 5 after the resulting number.

Example:

343 x 5 = (343-1)/2 | 5 =  1715

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3. Vedic Multiplication by 11

Application: Multiplication of two numbers close to Hundred

Case 1: Both numbers greater than 100.

Example of vedic multiplication using above method

• 103 x 104 = 10712

The answer is in two parts: 107 and 12,

107 is just 103 + 4 (or 104 + 3), and 12 is just 3 x 4.

• Similarly 107 x 106 = 11342

107 + 6 = 113 and 7 x 6 = 42

123 x 103 = 12669

(123 + 3) | (23 x 3) = 126 | 69 =12669 .

If the multiplication of the offsets is more than 100 then this method won’t work. For example 123 x 105. Here offsets are 23 and 5.

Multiplication of 23 and 5 is 115 which are more than 100. So this method won’t work.

But it can still work with a little modification. Consider the following examples:

Example 1

122 x 123 = 15006

Step 1: 22 x 23 = 506 (as done earlier)

Step 2: 122 + 23 (as done earlier)

Step 3: Add the 5 (digit at 100s place) of 506 to step 2

Answer: (122 + 23 + 5) | (22 x 23) = 150 | 06 = 10506

Example 2

123 x 105 (Different representation but same method)

123 + 5 = 128

23 x 5 = 115

128 | 115

= 12915

In the next post we will tell you about vedic multiplication, i.e.,  how to multiply two numbers lesser than the base (in this case 100)

If you liked this method of vedic multiplication included in ancient Vedic Maths, Please leave a comment to let us know.

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3. Multiply 2 numbers, sum of whose unit places is 10

Cubes of all the single digits should be memorized. Find below the table of cubes of first ten natural numbers -

1³ = 1,              2³ = 8,              3³ = 27,            4³ = 64,            5³ = 125,

6³ = 216,          7³ = 343,          8³ = 512,          9³ = 729,          10³ = 1000

To find the cube of any 2 digit number, we have to take the following steps

First Step: The first thing we have to do is to put down the cube of the tens-digit in a row of 4 figures. The other three numbers in the row of answer should be written in a geometrical ratio in the exact proportion which is there between the digits of the given number.

Second Step: The second step is to put down, under the second and third numbers, just two times of second and third number. Then add up the two rows.

Finding the cube of 12

Or, 12³ = ?

First Step: Digit in ten’s place is 1, so we write the cube of 1. And also as the ratio between 1 and 2 is 1:2, the next digits will be double the previous one. So, the first row is

1 2 4 8

Step II: In the above row our 2^nd and 3^rd digits (from right) are 4 and 2 respectively. So, we write down 8 and 4 below 4 and 2 respectively. Then add up the two rows.

Ex 2: 16³ = ?

Soln:

Explanations: 1³ (from 16) = 1. So, 1 is our first digit in the first row. Digits of 16 are in the ratio 1:6, hence our other digits should be 1×6 = 6, 6×6 = 36, 36×6 = 216. In the second row, double the 2^nd and 3^rd number is written. In the third row, we have to write down only one digit below each column (except under the last column which may have more than one digit). So, after putting down the unit-digit, we carry over the rest to add up with the left-hand column. Here,

i) Write down 6 of 216 and carry over 21.

ii) 36 + 72 + 21 (carried) = 129, write down 9 and carry over 12.

iii) 6 + 12 + 12 (carried) = 30, write down 0 and carry over 3.

iv) 1 + 3 (carried) = 4, write down 4.

Related posts:

1. Finding Cube Root – Vedic Maths Way
2. Speed Multiplication by 111 : Vedic Maths
3. Vedic Multiplication by 11

Multiplication with 9/ 99 / 999 and so on.

we know, 789 × 999 = 788,211

You will get the answers in two parts,

• The left hand side of the answer: subtract 1 from 789, which is 788
• The right hand side of the answer subtract 789 from 1000 = 1000-789= 211

Thus, 999 x 789 = 789-1   |  1000-789 = 788, 211 (answer)

{for the right hand side of the answer, 789 should be subtracted from (999+1)}

or,  99999 x 78 = 78-1   | 100000 - 78

= 7799922

{78 should be subtracted from (99999+1)}

Another example:

1203579 × 9999999 = 1203579-1   | 10000000- 1203579

=120357887964 21

Number in red is 1 less than 1203579. Number in blue is (10000000-1203579). Hence the answer.

This method has to be altered a little bit when number of 9s are lessers than the number of digit in the divisor.

1432  x 9 = 1432 (10 – 1) = 14320 – 1432 = 12888

So for multiplication with 9, put a zero after that number and subtract the number itself from that.

Likewise for 99 put two zeroes after that number .

3256 x 99 = 325600 – 3256 =  322344

Related posts:

1. Fast Multiplication Tricks
2. Vedic Multiplication of two numbers close to Hundred
3. Vedic Multiplication by 11

Multiplying 5 Times an Odd Number: Subtract one from the number you are multiplying, then halve that number and place a 5 after the resulting number.

Example: 343 * 5 = (343-1)/2 | 5 = 1715

Critical reasoning Concepts:

Basic Orientation of Critical Reasoning:

Intellectual Responsibility:

Adults are responsible for the things they do, and this includes thinking clearly and carefully about things that matter. This is hard work and no one succeeds at it completely, but it is part of the price for being in charge of your life.

In addition to thinking for ourselves, it is important to think well. This means basing our reasoning on how things are, rather than how we wish they were. It means being open to the possibility that we are mistaken, not allowing blind emotion to cloud our thought, and putting in that extra bit of energy to try to get to the bottom of things.

This doesn't mean that we should constantly be questioning everything. Life is too short and busy for that. But in many cases successful action requires planning and thought. It is also desirable to reflect on our most basic beliefs from time to time, and the college years are an ideal time for this. In the end you may wind up with exactly the same views that you began with. But if you have thought about them carefully, they will be your own views, rather than someone else's.

For more Tricks on Vedic Maths

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