Multiplication by 99

 

Multiplication by 99 in Vedic Maths: A Simple Trick to Multiply Faster

Vedic Mathematics is a collection of ancient techniques and methods that simplify mathematical calculations. One of the most fascinating tricks in Vedic Math is multiplying by numbers like 99. While the traditional approach might seem tedious, Vedic Maths offers a swift and effective method to multiply by 99, saving time and reducing mistakes. Here's a breakdown of how to do it.

Step-by-Step Method for Multiplying by 99

The key idea behind multiplying by 99 is to use the concept of complementation. Instead of multiplying directly by 99, we’ll break it down into simpler operations that are easier to handle.

The Formula:

To multiply a number by 99, follow these steps:

  1. Subtract the number from the next base 100 number.
    Find the complement of the number by subtracting it from 100.
    For example, if the number is 47, then the complement is:
    100−47=53100 - 47 = 53

  2. Subtract the complement from 100
    This will give you the first part of the result. In our example, 47’s complement is 53.

  3. Attach the complement to the original number, subtracting 1 from it.
    This is where the trick happens. You subtract 1 from the original number and place the complement next to it.
    For 47, subtract 1 from 47:
    47−1=4647 - 1 = 46
    Now, combine 46 and 53 together to form the result:
    46 5346 \, 53

So,
47×99=465347 \times 99 = 4653

More Examples:

Example 1: 68 × 99

  1. Complement of 68: 100−68=32100 - 68 = 32

  2. Subtract 1 from 68: 68−1=6768 - 1 = 67

  3. Combine: 67 3267 \, 32
    So, 68×99=673268 \times 99 = 6732

Example 2: 125 × 99

  1. Complement of 125: 100−125=−25100 - 125 = -25

  2. Subtract 1 from 125: 125−1=124125 - 1 = 124

  3. Combine: 124 25124 \, 25
    So, 125×99=12375125 \times 99 = 12375

Why Does This Work?

This trick works because 99 is just one less than 100. When you multiply by 99, you're essentially multiplying by 100 and subtracting the original number. The process of finding the complement of the number, subtracting 1, and combining them works effectively because of how numbers scale in Vedic Maths.

The technique capitalizes on the distributive property of multiplication:

a×99=a×(100−1)=a×100−aa \times 99 = a \times (100 - 1) = a \times 100 - a

So, instead of dealing with large numbers directly, you simplify the problem by breaking it into smaller parts.

Advantages of Using this Trick:

  1. Speed: It’s much faster than the traditional multiplication method.

  2. Mental Calculation: You can do this mentally, which is great for improving your mental math skills.

  3. Error Reduction: Since you’re working with smaller numbers and simple steps, the chances of making a mistake are much lower.

Conclusion:

Multiplying by 99 using Vedic Maths is a fantastic way to simplify your calculations and speed up your math skills. By understanding the trick of complementing and subtracting, you can multiply any number by 99 in seconds. This method isn’t just about speed—it’s about mastering the art of quick mental calculations and applying simple yet powerful mathematical principles.

Try out this Vedic Maths trick the next time you need to multiply by 99 and see how easy it becomes!

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