Multiply Eight Digit Numbers by 11, 111, 1111 – Vedic Math, Solved Example

Vedic Math is a system of mathematics that has its roots in ancient Indian texts known as the Vedas. The term “Vedic mathematics” was inscribed in the early 20th century by Bharati Krishna Tirtha, a Hindu scholar and mathematician. Vedic mathematics is based on a set of 16 mathematical sutras, or aphorisms, which are essentially short, easy-to-remember rules and techniques for solving a wide range of mathematical problems.

Features of Vedic Math

There are certain features of Vedic Math for solving complex mathematical problems in very little time. Some of the most important benefits of Vedic maths are described as follows.

• Simplicity: Vedic mathematics makes mathematical problems simple and takes less time in mathematical calculations. The sutras offer alternative methods for performing arithmetic operations like addition, subtraction, multiplication, and division.

• Mental math: Vedic mathematics helps us in solving mental calculations, making it particularly useful for rapid mental math calculations. The techniques taught in Vedic mathematics can be helpful for students and individuals who want to improve their mental math skills.

• Versatility: The Vedic mathematical techniques are versatile and can be applied to various mathematical problems. They can be especially useful for simplifying complex calculations and reducing the number of steps required to solve problems.

• Cross-multiplication: Vedic mathematics often uses cross-multiplication and other techniques to simplify multiplication and division, making these operations more intuitive and efficient.

• Algebra and geometry: Vedic mathematics also includes methods for solving algebraic equations and geometric problems.

In this article, we will understand in detail about particular Vedic Numerical procedure that arrangements with duplicating eight-digit numbers by 11111111, a grouping of ones. This strategy is a subset of Vedic Science and grandstands the straightforwardness and style of Vedic Math in taking care of duplication errands that could somehow be bulky with traditional techniques. Below is the step-wise process to multiply any digit by 11111111.

Steps of Multiplying 8 digit no by 11111111 using Vedic Math

Here is the step-wise process to calculate the multiplication of 8 digit no by 11111111 using Vedit Math.

Stage 1: Begin with the eight-digit number you need to duplicate by 11111111.

Step 1

Stage 2: Separate the eight-digit number into two four-digit gatherings. Embed an upward bar “|” between them. For instance, in the event that you have the number 12345678, separate it into 1234|5678.

Step 2

Stage 3: Work out the amount of the digits in the left four-digit bunch (1234 in this model). The amount of 1 + 2 + 3 + 4 is 10. Place this total in the center between the two gatherings, similar to this: 1(0)|234.

Step 3

Stage 4: On the off chance that there is an extend from stage 3 (in this model, there is a 1 continued), add this persist to the right four-digit bunch. In this way, 5678 + 1 = 5679.

Step 4

Stage 5: Occupy the spaces encompassing the center digit with a similar number as the center digit. For this situation, you encompass every digit with 0s in the left gathering and 5s in the right gathering. In this way, it becomes 1555555|067955.

Step 5

Stage 6: Presently, you add the left and right gatherings. 1555555 (left) + 067955 (right) approaches 1555555|6835105.

Stage 7: That is all there is to it! The outcome is 15555556835105.

Trick to multiply eight digit numbers by 11111111:

This Vedic Math technique works on the augmentation of eight-digit numbers by 11111111 by breaking it down into more modest, more sensible advances, which makes it simpler for mental computations.

Separate the Number: Take the eight-digit number you need to duplicate by 11111111 and split it into two equivalent four-digit gatherings, with an upward bar in the middle between.

Compute the Center Digit: Track down the amount of the digits in each gathering. Place the total in the center, between the two gatherings. On the off chance that the aggregate is a two-digit number, record the last digit in the center, and extend the primary digit to the left gathering.

Continue: In the event that there is a persist from the main gathering’s aggregate, add it to the left gathering’s total. This guarantees you represent the continue while adding the left and right gatherings later.

Fill the Encompassing Digits: Fill in the digits to the left and right of the center digit with a similar number as the center digit. This really makes an example around the center digit.

Add the Gatherings: At long last, add the passed on bunch and the right gathering to obtain your end-product. The passed on gathering might have an extra digit because of the continue from stage 3.

Tricks to Multiply any number by 11, 111, 1111 and so on – Vedic Math

For multiplying any numbers with 11,111,1111 and so on using Vedic Math, we have to choose an instance first. We’ll call it ABCDEFGH.

Stage 1: Record the eight-digit number, with spaces between the digits:

A B C D E F G H

Stage 2: Begin from the furthest right digit (H) and compose it for all intents and purposes.

Stage 3: Add the furthest right digit (H) to the digit to its left side (G) and compose the outcome underneath the line:

A B C D E F G

H

I (H + G)

Stage 4: Add the following digit (G) to the digit to its left side (F) and compose the outcome underneath the line:

A B C D E F G

G H

I

Proceed with this cycle, adding every digit to the one to its left side, and composing the outcome beneath the line.

A B C D E F G

F G H

I I

A B C D E F G

E F G H

I I

A B C D E F G

C D E F G H

I I I

Stage 5: Repeat this cycle until you have added every one of the digits, and you’ll have your response. The eventual outcome will be a 16-digit number:

A B C D E F G

A B C D E F G

B C D E F G H

Thus, the result of the eight-digit number ABCDEFGH and 11,111,111 is ABCCDEFGHIJKLMNOP.

In this technique, you are basically adding successive digits from right to left and extending any overabundance to the following segment depending on the situation.

Example with Solutions

Following are the solved example of Multiplying any eight digit numbers by 11, 111, 1111 and so on.

Example 1: Multiply 3456 by 11

Solution:

Step 1. Record the number with spaces:

3 4 5 6

Step 2. Begin with the furthest right digit (6) and get it on paper:

3 4 5 6

Step 3. Add 6 and 5 and compose the outcome underneath:

3 4 5 6

1 (6 + 5)

Step 4. Add 5 and 4 and compose the outcome beneath:

3 4 5 6

9 1 (5 + 4)

Step 5. Add 4 and 3 and compose the outcome beneath:

3 4 5 6

7 9 1 (4 + 3)

Step 6. Add 3 and 0 (you can expect 0 for any missing digits):

3 4 5 6

0 7 9 1 (3 + 0)

Answer: Multiplication of 3456 by 11 is 38016.

Example 2: Multiply 6789 by 11

Solutions:

Step 1: Record the number with spaces:

6 7 8 9

Step 2: Begin with the furthest right digit (9) and record it on paper:

6 7 8 9

Step 3: Add 9 and 8 and compose the outcome beneath:

6 7 8 9

7 (9 + 8)

Step 4: Add 8 and 7 and compose the outcome beneath:

6 7 8 9

5 7 (8 + 7)

Step 5: Add 7 and 6 and compose the outcome beneath:

6 7 8 9

3 5 7 (7 + 6)

Step 6: Add 6 and 0 (accepting 0 for missing digits):

6 7 8 9

0 3 5 7 (6 + 0)

Answer: Multiplication of 6789 by 11 is 74679.

You can correspondingly apply this strategy to different numbers.

Problem 3: Multiply 12345 by 11.

Solution:

Step 1: Record the number with spaces:

1 2 3 4 5

Step 2: Begin with the furthest right digit (5) and record it on paper:

1 2 3 4 5

Step 3: Add 5 and 4 and compose the outcome beneath:

1 2 3 4 5

9 (5 + 4)

Step 4: Add 4 and 3 and compose the outcome underneath:

1 2 3 4 5

7 9 (4 + 3)

Step 5: Add 3 and 2 and compose the outcome beneath:

1 2 3 4 5

5 7 9 (3 + 2)

Step 6: Add 2 and 1 and compose the outcome beneath:

1 2 3 4 5

3 5 7 9 (2 + 1)

Answer: Multiplication of 12345 by 11 is 135795

Example 4: Multiply 7890 by 11

Solution:

Step 1: Record the number with spaces:

7 8 9 0

Step 2: Begin with the furthest right digit (0) and record it on paper:

7 8 9 0

Step 4: Add 0 and 9 and compose the outcome beneath:

7 8 9 0

9 (0 + 9)

Step 5: Add 9 and 8 and compose the outcome underneath:

7 8 9 0

7 9 (9 + 8)

Step 6: Add 8 and 7 and compose the outcome underneath:

7 8 9 0

6 7 9 (8 + 7)

Step 7: Add 7 and 0 and compose the outcome underneath:

7 8 9 0

7 6 7 9 (7 + 0)

Answer: Multiplication of 7890 by 11 is 86790.

Example 5: Multiply 987654 by 11

Solution:

Step 1: Record the number with spaces:

9 8 7 6 5 4

Step 2: Begin with the furthest right digit (4) and record it on paper:

9 8 7 6 5 4

Step 3: Add 4 and 5 and compose the outcome beneath:

9 8 7 6 5 4

9 (4 + 5)

Step 4: Add 5 and 6 and compose the outcome beneath:

9 8 7 6 5 4

1 9 (5 + 6)

Step 5: Add 6 and 7 and compose the outcome beneath:

9 8 7 6 5 4

4 1 9 (6 + 7)

Step 6: Add 7 and 8 and compose the outcome underneath:

9 8 7 6 5 4

6 4 1 9 (7 + 8)

Step 7: Add 8 and 9 and compose the outcome underneath:

9 8 7 6 5 4

8 6 4 1 9 (8 + 9)

Answer: Multiplication of 987654 by 11 is 10861994.

You can use these Vedic Math tricks to solve any complex multiplication in very less time. It is advised to solve more and more problems in order to gain proficiency in using these Vedic Math tricks.