Multiplication Trick for Multiples of 11

If you know how to quickly multiply any number by 11 (click on the link to read further), the short cut multiplication method for 22, 33, etc. becomes easy to grasp. It’s an extension to the earlier method and you’ve seen earlier that there is no need to remember multiplication tables.

Multiplication by 11 is easy. Start from the right, add the two adjacent digits and keep on moving left. Since you can write only one digit in each step, if there is a carryover add it to the number obtained in the next step. So let’s begin to learn multiplication by multiples of 11.

Multiplication Trick for 22

For multiplication with 22, the rule is (number +next number)*2

Let us look at it step by step –
Step 1: For sake of simplicity, assume that there are two invisible 0 (zeroes) on both ends of the given number.
Say if the number is 786, assume it to be 0 7 8 6 0

Step 2:Start from the right, add the two adjacent digits and multiply by 2. Keep on moving left.
Add the last zero to the digit in the ones column (6), and multiply by 2. Write the answer below the ones column.
Then add this 6 with digit on the left i.e. 8 and multiply by 2.
Next add 8 with 7 and multiply with 2.
Next add 7 with 0 and multiply by 2.
(0+7)*2     |    (7+8)*2  |    (8+6)*2   |   (6+0)*2
=   14   |   30   |  28   |  12

Step 3: Start from right most digit. Keep only the unit’s digit. Carryover and add the ten’s digit to the next number to the left. Doing this we get the answer as 17292.
Yes, job done. Quite simple, isn’t it?

Multiplication with Other Multiples Of 11

For multiplication with 33, the rule is (number +next number)*3
For multiplication with 44, the rule is (number +next number)*4
and so on….till
For multiplication with 99, the rule is (number +next number)*9. However, their is a simpler way of multiplication trick for 99

Multiplication Examples:
56789*22 = 0567890*22= (0+5)*2  |   (5+6)*2  |   (6+7)*2  |   (7+8)*2  |   (8+9)*2  |   (9+0)*2=1249358
123678*88 = 01236780*88 = (0+1)*8  |   (1+2)*8  |   (2+3)*8  |   (3+6)*8  |   (6+7)*8  |   (7+8)*8  |   (8+0)*8=10883664

Try it yourself. Share your experience with all by posting a comment below.

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Shortcut to Find Square of 2-Digit Numbers with Unit Digit as 1

Special shortcut methods of squaring 2 digit numbers

In previous articles we’ve discussed special shortcut Vedic Math Techniques to find the square of any number ending in 5 and square of 2 digit numbers ending in 9.  In this article we will discuss –

Square of 2-digit numbers whose unit digit is 1

Let us take a 2 digit number in its generic form. Any two digit number whose unit digit is 1, say a1 can be expressed as 10a+1, where a is the digit in ten’s place

Square of a1= a2 | 2xa | 1

Here, ‘|’ is used as separator.

That means for the left most part of the answer, a is squared, hence first part will be a2. The middle part will be twice of a and the last or the right most part will always be 1.

Let us see a few examples.

(21)2= 2 squared | 2 . 2 |1 = 441
(31)2= 3 squared | 2 . 3 |1 = 961
(41)2= 4 squared | 2 . 4 |1 = 1681
(51)2= 5 squared | 2 . 5 |1 = 2601 (Here the square of 5 is 25 but since the product of 2.5 is 10 we write down 0 and add 1 to 25). Similarly,
(91)2= 9 squared | 2 . 9 |1 = 8281

Square of 3-digit numbers ending in 1

Now let us try to extend the above shortcut method to 3 digit numbers as well. Let us straight away start with an example 131.

Like earlier separate the given number in 2 halves, left hand side will have digits other than 1 and right hand side will have 1 as usual.

Hence, the answer is

(131)2= 13 squared | 2 . 13 | 1 =

= 169 | 26 | 1

= 17161

Let’s take another example of squaring a three digit number ending in 1.

261 = 26 squared | 2×26 | 1

= 676 | 52 | 1

= 68121

From the above illustrations you must have noticed that higher the initial number to be squared higher is the square in first part. Hence to extend this method to large 3 digit numbers one should be proficient in squaring any 2 digit number.

Try it yourself

21, 71, 91, 161, 231 and 321

Answers: 441, 5041, 8281, 25921, 53361 and 103041

This article is based on a suggestion given by a reader Vishal Mishra. If you also have some suggestions you can email it to me or post it here as comment. 

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Vedic Maths Tricks for Multiplication

Both the videos given below cover Vedic Maths Multiplication Trick i.e. The Criss-Cross Method or Urdhva Tiryak Sutra.

Each video is made using different tools and aids. I would request you to share your opinion on which format of the recording did you like more. Please share your views by posting a comment below. I intend to make more such videos after getting your feedback.

 Vedic Maths Multiplication Tutorial: Video 1


Vedic Maths Multiplication Tutorial: Video 2

The videos are posted without any sort of editing. Kindly ignore all kind of disturbances and aberrations. Your feedback will help me in improving the quality of future video tutorials, which will be posted for free on  

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Find Value of Sin and Cos using Fingers

Today I am going to share with you a special memory trick for trigonometry, mailed to me by Debasis Basak – a young Class IX follower of

By this method we can find out Sines and Cosines of different angles. It just requires your left hand. Let’s understand this trick step by step –

Step 1:-
First mark the angles of 0, 30, 45, 60, and 90 on little, ring, middle and pointer finger and thumb of your left hand.

Step 2:-
On the palm of your left hand write the equation √x /2

Find Value of Sin and Cos

Step 3:-
Suppose, you want to find Cos30. 

Fold the finger representing 30. i.e. ring finger of your left hand palm.  Count the numbers of fingers on the left of the ring finger. So since there are 3 fingers, x=3; put the value in the equation given in step 2

Step 4:-
Cos30 = √3/2

Finding Sine of the same angle is just a simple step away. Of the same left hand, if we count the fingers to the right of the folded finger, we will get value of sine.

Sin30 = √1 /2 = 1/2

Let’s take another example, sin60

60 is represented by pointer finger and there are 3 fingers to the right of this folded finger.

Hence, sin60 = √3/2

I appreciate the efforts of Debasis in sharing this trick with all of us. In case you want to share some quick calculation trick or technique, mail it to me at vineetpatawari [at] gmail [dot] com.

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Multiplying Whole Numbers Close to Each Other

These multiplication tricks will only work for you if you have memorized or can quickly calculate the square of numbers. Learn the trick of finding square of any two digit number.  Also master the shortcut to find the square of any number.

Multiplication of Two Numbers that Differ by 2

When two numbers differ by 2, their product is always the square of the number in between these numbers minus 1.

1. 18*20 = 19^2 – 1 = 361 – 1 = 360
2. 25*27 = 26^2 – 1 = 676 – 1 = 675
3. 49*51 = 50^2 – 1 = 2500 – 1 = 2499

Read More

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Best Tips for Modern Students for Vedic Mathematics

Vedic Mathematics is the name given to the ancient mathematics system. The “Bharati Krsna Tirthaji” from the Vedas rediscovered it and according to him, all the mathematics is based on the 16 sutras. These are also known as word formulas. Below are mentioned some of the tips for the students to learn easily and become a master of Vedic math.

It is all about the numbers

Whether numerical or word formulas both of them certainly employ the use of the numbers. Make yourself master of the numbers. Learn the general multiples of all the numbers and make a habit to spend your free time with numbers only. Practice as much as you can and you will be on the right track. You can also figure out something so that you come across these numbers repeatedly. You can paste wallpaper in your room, make some numerical figure as your desktop and subscribe to numerical magazines.

Try to Grip from the Fundamentals and then move forward

Have an approach, which will make youthe basics and fundamentals strong. Once you have a grip over the basics it means half of the work is done. Try to learn what it is all about the “Sutras” and the “Sub sutras” from the starting to the end. What does it all mean? Just solving the examples will not be sufficient but you have to make sure that you have the thorough knowledge of every aspect.

Practice as much as you can

Figures always need practice and you have to make them as your part and parcel. Try to practice every exercise you get your hand on and just solving the problems will not work check the answers also. If you get wrong answers, make sure you look for the right solution and method for a specific problem. There is no end to practice try as many problems as you can since Vedic math is meant to shorten your normal problem solving time pay special attention to any shortcuts you come across and learn them by heart.

Try to Get some Good References

It is always recommended to follow some trusted books. It is always true that right teaching and guidance can do wonders and you have to search both of these for you to get into the right direction. You can follow some good reference books and take some guidance in the form of internet, magazines, friends and family members. Here is a list of some popular vedic math and other quicker maths books

Some Mind and Brain Exercise can do wonders

Since Vedic math is all about the mind, you can learn a few exercises so that your brain is fresh while you start studying the Vedic math. Our brain needs regular exercise. In addition, you can learn how to refresh your mind after several intervals. Here are 7 resources available for exercising your brain

Keeping in mind the above tips will certainly give you an edge over the others in learning Vedic math and you can solve lengthy and complicated calculations beating the calculator after learning this math.

Author Bio
Claudia is a talented writer who has performed her duties well. She had taken up various assignments about IT Jobs training. She loves to share her knowledge and expertise with other people through her articles, follow me @ITdominus1.

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Quick Multiplication by 5

Tricks for fast calculation by 5

It is a simple trick which is very intuitive and easy to understand. Many followers might find it very simple. However, there are many who will enjoy this simple yet readily usable trick to multiply any number by five.

1. Multiplying 5 times an even number: halve the number you are multiplying by and place a zero after the number.


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. Read More

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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

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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

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Ratio of Area and Volume

Finding the ratio of areas or volumes given the length of a side of a 2 or 3 dimensional figure was always a time consuming task. With the help of the knowledge you are going to acquire now, this will be a simple and quick task.

In any two dimensional figure, if the corresponding sides are in the ratio a:b, then their areas are in the ratio a2:b2

Two dimensional figures can be any polygon like square, rectangle, rhombus, trapezium, hexagon, etc. It can also be a triangle or a circle. The sides, referred in the statement above, can be length, breadth or even diagonal in case of a polygon. In case of a circle the sides will be represented by radius or diameter or circumference. In triangle it can be sides or height of a triangle. Read More

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