Multiplying a number with 11,111 or with more ones

Multiplication by 11

To multiply any 2-figure number by 11 we just put the total of the two figures between the 2 figures.

• 26 x 11 = 286

Notice that the outer figures in 286 are the 26 being multiplied. And the middle figure is just 2 and 6 added up.

• So 72 x 11 = 792

For bigger numbers

234 x 11 = 2574

We put the 2 and the 4 at the ends.
We add the first pair 2 + 3 = 5.
And we add the last pair: 3 + 4 = 7.

To multiply a two-digit number by 111, add the two digits and if the sum is a single digit, write this digit Two Times in between the original digits of the number. Some examples:

• 36 x 111= 3996
• 54 x 111= 5994

The same idea works if the sum of the two digits is not a single digit, but you should write down the last digit of the sum twice, but remember to carry if needed as illusrated in example below

• 57 x 111= 6327

Because 5+7=12, but then you have to carry the one twice.

For 3 digit numbers
Carry if any of these sums is more than one digit.
Thus 123x111 = 1 | 3 (=1+2) | 6 (=1+2+3) | 5 (=2+3) | 3

Similarly,

• 241 x 111= 26751

For an example where carrying is needed

• 352 x 111= 39072

3 | 8 (=3+5) | 10 (=3+5+2)| 7 (=5+2)| 2
= 3 | 8 | 10 | 7 | 2 = 3 | 9 | 0 | 7 | 2
= 39072

Vedic Mathematics - Introduction

Vedic Mathematics is based on Atharvaveda which was rediscovered from the Vedas between 1911 and 1918 by Sri Bharati Krsna Tirthaji (1884-1960). Vedic Mathematics is based on sixteen sutras which are called as formulas or techniques that are easy to learn and apply. These principles are general in nature and can be applied in many ways. In practice many applications of the sutras may be learned and combined to solve actual problems. Research shows that application of Vedic mathematics uses both the part of the brain and this helps in improving the mental memory. It’s also useful for senior executives from the corporate sector who have to deal with numbers a lot and to be strong in this area is considered as an important asset.

Albeit the techniques from Vedic mathematics aids quick calculations in the all the scenarios, however, the techniques are highly relevant for pattern based calculations and increases the speed by manifold. 

Multiplication of numbers near the base

Vedic techniques for multiplying  the number close to the base is atleast 10 times faster than the normal method. The techniques can be used to multiply large numbers such as 999999 x 999998, 10003 x 10004.   We have show the examples along with the steps below

Multiply 88 by 98.

88     12

98     02

86     24

Both 88 and 98 are close to 100. 88 is 12 below 100 and 98 is 2 below 100. (100- 88 = 12 & 100-98 = 02)

As before the 86 comes from subtracting crosswise: 88 - 2 = 86 (or 98 - 12 = 86): you can subtract either way, you will always get the same answer. And the 24 in the answer is just 12 x 2: you multiply vertically. Since our base is 100, so the figure at the right hand side should consist of only two digits.

So 88 x 98 = 8624

Let see how this works in case of bigger numbers (9999 X 9997 ) through examples below

 9999   0001

 9997  0003

  9996 0003

The steps are as follows

1. Write the two numbers to be multiplied above and below.
2. Take a base for the calculation. The base should be that power of 10, which is nearest to the number to be multiplied.
3. Subtract each number from the base and write the remainder with respective plus (+) or minus (-) sign.
4. The product will have two parts left and right.
5. The left hand product is obtained by cross operation of the numbers written diagonally.
6. The right hand product is obtained by multiplying the two digits written at right hand portion.