Vedic multiplication

Author: Roger Morrison
Date Of Creation: 23 September 2021
Update Date: 21 June 2024
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Fast Vedic Mental Math Tricks - Multiplication 01 | Fast Math | Don’t Memorise
Video: Fast Vedic Mental Math Tricks - Multiplication 01 | Fast Math | Don’t Memorise

Content

Vedic math is a form of mental arithmetic designed to help you solve arithmetic equations in an easier and faster way. Using just a few simple techniques, Vedic Math helps you break down complex multiplications into simple multiplication, subtraction, and addition steps. With a little practice, you can use Vedic multiplication to solve both large and small problems easily and in just a few seconds.

To step

Method 1 of 3: Vedic multiplication of numbers by one digit

  1. Use Vedic Math to multiply numbers greater than 5. If any of the numbers you are multiplying is greater than 5, Vedic Math can help you solve the multiplication faster and easier. However, if any of the numbers is less than 6, it is likely that it will be faster to recall the answer from memory.
    • Vedic multiplication has been developed for larger numbers. Therefore, when multiplying by 1, 2, 3, 4 or 5, it is usually much faster and easier to solve the problem without using Vedic math.
  2. Write down the numbers you want to multiply. Write the first number of the problem and the second number directly below it on a piece of paper. Draw a line below the second number (you will write down the solution to the problem below this line).
    • For example, if you want to multiply 6 x 7, write down 6 and write the 7 directly below it. Draw the line just below 7.
    • Although Vedic math is a form of mental arithmetic that can be used without a pen and paper, it can be helpful for those who are starting to write down a problem and thus better visualize the steps.
    • However, if you are more adept at solving math problems in your head, you can just visualize this markup instead of writing it down.
  3. Subtract both the top and bottom number from the Vedic base of 10. If you are doing the calculations one by one, first subtract the top number from 10 and write the result to the right of the original number. Then you subtract the bottom number from 10 and write it to the right of the original number and directly below the top number recalculation. You now have two columns of numbers, with the original numbers in a column on the left and your new numbers in a column on the right.
    • For example, to multiply 6 x 7, first do 10 - 6 = 4. Write the 4 to the right of the 6. Then calculate 10 - 7 = 3. Write the 3 to the right of the 7, just below the 4.
    • Subtracting from 10 takes the "base" of the numbers. The term "base" refers to the base 10 number system used in Vedic math, as well as the fact that the "base number" or base is taken as the basis for the calculations.
    • The bases in Vedic mathematics are 10, 100, 1000 and 100,000. For single-digit numbers, use the base of 10, because this is the base closest to single-digit numbers.
  4. Multiply the numbers in the right column. In the usual way, multiply the top number in the right column by the bottom number in the right column. If the answer to the multiplication is greater than 10, write the right-most digit below the line and transfer the left-most digit to the next step. If the answer is one digit, just write the one digit answer below the line below the right column.
    • For example: for the original problem 6 x 7 you now have, for example, 4 and 3 in the right column. Calculate 4 x 3 = 12. Write the 2, the right-most digit, below the line. Take the 1, the left number, to the next step.
    • To help you remember the number on the far left, you can write the numbers next to each other. However, write the left number a little way away from the sum so you don't get confused.
  5. Subtract a number in the right column from the number in the diagonal left column. Choose the top or bottom number from the left column (it doesn't matter which one you choose - the solution will always be the same). Then subtract the number that is diagonal in the right column.
    • For example, if the original problem is 6 x 7, the 6 is written above 7 in the left column, and 4 above 3 in the right column. So you can perform either 6 - 3 or 7 - 4, both of which are equal to 3.
  6. Add the number you memorized (if applicable) to the result. If the solution to the multiplication of the numbers in the right column was more than 10, write the number on the far right under the line of the right column and transfer the number on the far left. At this point, add the memorized digit to the solution of the diagonal subtraction in the previous step, and write the sum below the line of the left column.
    • For the original problem, the 6 of 6 x 7 will be noted above the 7 in the left column, and 4 above the 3 in the right column. Then you calculate 4 x 3 = 12, and you write the 2, the number on the far right, under the line of the right column, and remember 1, the number on the far left. Then add the memorized 1 to the 3 that arose from 6 - 3 or 7 - 4 in the previous step, resulting in 4. Write the 4 in the left column below the line of the problem.
  7. Read the number below the problem line to answer the original problem. You have now written two numbers below the line. These numbers together represent a single number, which is the solution to your original equation.
    • In the example of the problem 6 x 7 you now have a 4 in the left column and a 2 in the right column below the line of the problem. So the answer to your original problem, 6 x 7, is 42.

Method 2 of 3: Multiply two-digit numbers

  1. Write down your multiplication. On a piece of paper, write the first number with two digits of the multiplication on top and the second number directly below it. Draw a line below the second number (you will write down the solution to the problem below this line).
    • For example, if you want to use Vedic math to multiply 20 x 21, write 20 and 21 right below it. Draw a line just below 21.
    • If you are particularly adept at solving math problems in your head, you can visualize this layout instead of writing it down. However, it may be helpful to write down the multiplications when you first start with the Vedic multiplication.
  2. Use traditional multiplication to multiply the numbers in the left column. First, multiply the top left digit of the first number by the bottom left digit of the second number. Write your answer below the multiplication line, in the leftmost column. This number is the first part of the solution.
    • For example, when multiplying 20 x 21, first multiply the 2 (the first, left digit in 20) by 2 (the first, left digit in 21), which is equal to 4. Write the 4 below the line of the multiplication in the left column.
  3. Multiply the diagonal numbers and add the solutions. First, multiply the number from the top left column by the number from the bottom right column. Then multiply the number in the left column by the number in the top right column. Add the solutions and write the answer below the multiplication line to the right of the solution in the previous step.
    • For example, when multiplying 20 x 21, you first multiply the 2 (the number from the top left column in the 20) by 1 (the number from the bottom right column in the 21), which is equal to 2. Then you multiply 2 (the number from the bottom left column in the 21) with 0 (the number from the top right column in the 20), which equals 0. Add the solutions (2 and 0) together, and you get 2 for the answer. Write the 2 below the multiplication line to the right of the 4 you already wrote below the multiplication line.
  4. Determine the final answer by multiplying the numbers in the right column. Multiply the top number in the right column by the number at the bottom right column. Write the solution below the multiplication line in the rightmost column. Then read the number below the multiplication line from left to right to get your final answer to the original problem.
    • For example, when multiplying 20 x 21, you would multiply 0 (the top number in the right column) by 1 (the bottom number in the right column), which equals 0. Write 0 below the multiplication line to the right of the 4 and the 2 you have already written down. Then you see that the answer to your original equation, 20 x 21, is 420.

Method 3 of 3: Vedic multiplication by three digit numbers

  1. Write down the numbers you are multiplying. First, write down the first three-digit number of the multiplication. Then write the second number directly below it. Draw a line below the second number (you will write down the solution to the problem below this line). You should now have three columns of numbers.
    • If you are using Vedic math to multiply 121 x 151, for example, write 121 and write 151 directly below it. Draw a line below 151.
    • While you may think that after some practice you will be able to memorize a Vedic multiplication, it can still be helpful to write out the multiplications when you first start out.
  2. Multiply the numbers in the left column. First, multiply the top left digit of the first number by the bottom left digit of the second number. Write your answer below the multiplication line, in the leftmost column. This number is the first part of the solution.
    • For example, when multiplying 121 x 151, you first multiply the 1 (the first, left digit in 121) by 1 (the first, left digit in 151), which is equal to 1. Write the 1 below the multiplication line in the left column.
  3. Multiply the numbers in the left column by the diagonal middle numbers. First multiply the top number of the left column by the bottom number of the middle column.Then multiply the bottom number of the left column by the top number of the middle column. Add the result of these two calculations together. The resulting number is the second part of the solution.
    • For example, when multiplying 121 x 151, you first multiply the 1 (the number from the top left column in 121) by 5 (the number from the bottom middle column in 151), which is equal to 5. Then you multiply 1 ( the number from the lower left column in the 151) by 2 (the number from the top middle column in the 121), which equals 2. Add the solutions, 5 and 2, and you get 7. Write 7 below the multiplication line to the right of the 1 you already wrote below the multiplication line.
  4. Multiply the leftmost and rightmost numbers. First multiply the number in the top left by the number in the bottom right. Then multiply the leftmost digit by the rightmost digit. Add these two solutions together and write the answer on the side so you don't forget.
    • For example, when multiplying 121 x 151, you would multiply 1 (the left-most digit) by 1 (the right-most digit), which is equal to 1. Then multiply 1 (the left-most digit at the bottom) by 1 (the right-most number at the top), which is equal to 1. Add these solutions together, and you get 2 for the answer.
  5. Add the multiplication of the middle numbers to the previous solution. Multiply the top number in the middle column by the bottom number in the middle column. Then add the solution to the number you found in the previous step. If the answer is less than 10, simply write the answer below the multiplication rule to the right of the numbers you have already written down. If the answer is greater than 9, write the rightmost digit below the multiplication line and add the next left digit to the number to its left.
    • For example, when multiplying 121 x 151, you would multiply 2 (the middle digit of 121) by 5 (the middle digit of 151), which is equal to 10. Add this 10 to the 2 you got in the previous step is found, which is equal to 12. Since 12 is greater than 9, write the 2 (the rightmost digit of 12) in third place below the multiplication line to the right of the 1 and 7 you already wrote down. Then add the 1 (the leftmost digit in 12) to 7 (the digit to the left below the multiplication line).
    • That's why you wrote 1, 8, and 2 below the multiplication line at this point.
  6. Go to the middle column to multiply the diagonals in the right column. First, multiply the top number of the middle column by the bottom number of the right column. Then multiply the top number of the right column by the bottom number of the middle column. Add these numbers together and write the solution to the right of the three numbers you have already written down.
    • For example, when multiplying 121 x 151, you would multiply 2 (the middle digit of 121) by 1 (the bottom right digit of 151), which equals 2. Then multiply 1 (the top right digit of 121) by 5 (the bottom right digit of 121). middle digit of 151), which equals 5. Add these together, which equals 7. Write the 7 next to the 1, 8, and 2 you already wrote down.
  7. Multiply the numbers in the right column to find the solution. Multiply the top number in the right column by the bottom number in the right column. Write the solution below the multiplication line to the right of the four numbers you have already written down. Then if you read from left to right, you have the solution of the original equation.
    • For example, when multiplying 121 x 151, you would multiply 1 (the right-most digit of 121) by 1 (the right-most digit of 151), which is equal to 1. Write the 1 to the right of the 1, 8, 2 and 7 that you have already written down. So the answer to your original problem of 121 x 151 is 18,271.