## The Criss-Cross Method: An Alternative Form of Multiplication

Traditionally, multiplication of multiple digit numbers is done as a series of multiplications that are eventually added together to form a final answer. The criss-cross method is a variation on this technique that allows for much quicker processing of the problem without the need for a calculator or extensive use of paper space. There are many situations, such as trips to the grocery store, where you will find a need to perform multiplication of odd numbers in order to stay within a budget as you shop.

This system of multiplication is adopted from Vedic Mathematics’ URDHVA-TIRYAK SUTRA, which means vertically and cross-wise.

To start with, we will look at a simple example just to get a grasp on the steps involved in the method. Later we will apply it to a slightly more advanced problem to show how to handle carrying numbers from one digit to the next. For now, we will multiply 111 by 111. Read More

## How to Find Square of Numbers Ending in 9

Squaring any number ending in 9

We can easily calculate the square of any number ending in 9 using the method described in this post. Let us understand this method with the help of an example –

Finding the square of 39

Firstly add 1 to the number. The number now ends in zero and is easy to square.
40^2 = (4*4*10*10) = 1600. This is our subtotal.

In the next step, add 40 plus 39 (the number we squared plus the number we want to square) Read More

## Origin of Vedic Mathematics

Origin of Vedic Maths or Vedic Ganit

At the beginning of the twentieth century, when there was a great interest in the Sanskrit texts in Europe, Bharati Krsna Swamiji tells us some scholars ridiculed certain texts which were headed ‘Ganita Sutras’- which means mathematics. They could find no mathematics in the translation and dismissed the texts as rubbish. Bharati Krsna Swamiji, who was himself a scholar of Sanskrit, Mathematics, History and Philosophy, studied these texts and after lengthy and careful investigation was able to reconstruct the mathematics of the Vedas. According to his research all of mathematics is based on sixteen Sutras, or word-formulae.

Bharati Krsna wrote sixteen volumes expounding the Vedic system, which you can find in the book named Vedic Mathematics by Bharati Krsna Tirthaji. These sutras were unaccountably lost and when the loss was confirmed in his final years he wrote a single book: Vedic Mathematics, currently available. It was published in 1965, five years after his death. The term Vedic Mathematics now refers to a set of sixteen mathematical formulae or sutras and their corollaries derived from the Vedas.

You can find more details about Origin of Vedic Maths here at wikipedia – http://en.wikipedia.org/wiki/Bharati_Krishna_Tirtha’s_Vedic_mathematics

## Base Method of Multiplication

Base method of multiplication derived from Vedic Mathematics can be applied for multiplication of two numbers close to 100.

This post in is in continuation of an earlier post named “Vedic Multiplication of two numbers close to hundred“. Though you can understand this post stand alone, yet I’ll recommend you to read the linked post before reading this one.

In this post I’ll explain how to multiply two numbers lesser than the base (in this case 100). In the earlier post it was about both numbers more than 100.

## Trick to Find Square of Numbers from 51 to 59

I’ll share with you one simple method of finding the square of numbers between 50 and 60. Like many other Vedic Mathematics methods, in this method also, we will get the answer in two parts. Since the numbers are in 50s and square of 50 is 2500, we will just use 25 in our calculations, ignoring the zeros.

1. To get the first part of the answer, add the digit at the units place to 25 and write the sum
2. To get the second part, calculate the square of units place digit and write it

It’ll be easier to understand this with an example. Read More

## Vedic Multiplication Trick for 2 Numbers Starting with Same Digits

Multiplication Method – multiplying 2 numbers starting with same digit(s)

This vedic maths trick will help you in multiplying two numbers when these numbers start with the same digit. For example 34 x 37; see their ten’s digit (starting digit) is same. Another example can be 234 x 232, see their hundred’s and ten’s digits (starting two digits) are same.

In one of the earlier post a similar method was described. In that like this trick the starting digit(s) should be same but at the same time the sum of digit at unit’s place should be 10 – please check that out – Vedic multiplication

Learn Multiplication

34 x 37

To multiply 34×37, we know they are in the base 30. Hence the reference point (base) will be 30.

Step 1.

Determine how much more is 34 from 30. The answer is 4

Determine how much more is 37 from 30. The answer is 7

Step 2.

Either add 4 to 37 = 41 or 7 to 34 = 41.

The result will be same always.

Step 3.

Multiply the resultant number from step 2 by the base, which is in this case 30

41×30 = 41x3x10 = 123×10 = 1230

Step 4.

Add to the resultant of step 3 the product of the numbers obtained from step 1. This will give you the answer.

1230+ (4×7) = 1230 + 28 = 1258

Another example,

23 x 29

From step 1 and step 2 above, 23 + 9 = 32 or 29 + 3 = 32

From step 3 : 32 x 20 = 640

From step 4 : 640 + (3×9) = 667

One more example,

234 x 232

From step 1 and step 2 above, 234 +2 = 236 or 232 + 4 = 236

From step 3 : 236 x 230 = 54280

From step 4 : 54280 + (4×2) = 54288

using the above method can also be used for multiplying two numbers close to humdred

## Vedic Division by Nine

Friends, this time it has been a long time I have written a post. I badly wanted to write one but because of very busy schedule I couldn’t.

This post is one of the many areas where Vedic Mathematics really surpasses traditional methods as you shall soon see. This post is about dividing any number by 9.

We will start by taking an example

Divide 200103002 by 9

## Division in Vedic Mathematics

There are so many shortcuts for multiplication but hardly any shortcuts for division. Nandeesh has translated a Sanskrit Sutra to reduce long division to one line short-cut. Join me in thanking him for his great efforts.

Long Division reduced to one-line shortcut

Example 1:  716769 ÷ 54.

Reduce the divisor 54 to 5 pushing the remaining digit 4 “on top of the flag” (Dhvajanka so to say).

Corresponding to the number of digits flagged on top (in this case, one), the rightmost part of the number to be divided is split to mark the placeholder of the decimal point or the remainder portion.

Let us walk through the steps of this example:
716769 ÷ 54 = 13273.5 Read More

## Finding Cube Root – Vedic Maths Way

This is an amazing trick which was always appreciated by the audience I have addressed in various workshops. This awe inspiring technique helps you find out the cube root of a  4 or 5 or 6 digits number mentally.

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 Read More

## Find the remainder – Vedic Algebra

### Vedic Algebra

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)