Mathematics is a fundamental skill that influences various aspects of our daily lives, from managing finances to solving complex problems in different fields. Vedic Mathematics offers a unique approach to calculations, emphasizing mental math techniques that are both efficient and fascinating.
In this blog, we will explore ten incredible Vedic Math tricks that can help you enhance your calculation speed and accuracy. Whether you’re a student looking to improve your math skills or someone interested in learning more about the ancient mathematical wisdom, these tricks will surely pique your interest and expand your mathematical knowledge.
Significance of Vedic Mathematics
Vedic Math, an ancient Indian system with roots dating back thousands of years, offers a treasure trove of tricks to transform you into a calculation master.
Unlike traditional math methods that often rely on memorization and lengthy procedures, Vedic Math emphasizes a more intuitive and visual approach. This blog post delves into 10 incredible Vedic Math tricks that will not only make solving problems faster and easier, but may even spark a newfound appreciation for the beauty and elegance of mathematics.
Squaring a Number Ending in 5 (Last Digit Squaring)
This trick comes in handy when you need to square a two-digit number ending with 5. Here’s how it works:
Steps:
- Identify the first digit (excluding the 5). Let’s use the example of 25^2. The first digit here is 2.
- Step 2: Square the first digit and add 1. In our example, 2^2 = 4 + 1 = 5.
- Step 3: Multiply the first digit by the number formed in step 2. So, 2 x 5 = 10.
- Step 4: Append a 25 to the end of the product from step 3. This gives us 1025.
Explanation: This trick utilizes the property (a + b)^2 = a^2 + b^2 + 2ab. In this case, a represents the first digit (2) and b represents 5. By squaring a and b separately, we essentially avoid the need for a lengthy multiplication process.
Multiplying by 5 (Shortcut Multiplication)
This trick simplifies multiplying any number by 5. Here’s the magic:
Steps:
- Write down the original number. Let’s multiply 347 by 5.
- Step 2: Simply add a 0 to the end of the number. This gives us 3470.
Explanation: This trick leverages the fact that multiplying by 5 is essentially the same as shifting the decimal point one place to the left. Since decimals might not be prevalent in all situations using Vedic Math, adding a 0 achieves the same effect of multiplying by 10 and then dividing by 2 (which is the same as multiplying by 5).
Subtracting from Multiples of 10 (Complementary Subtraction)
This trick streamlines subtracting any number from a multiple of 10 (100, 1000, 10000, and so on). Here’s the process:
Steps:
- Break down the number you want to subtract into its place values. For example, to subtract 372 from 1000, we have 3 hundreds, 7 tens, and 2 units.
- Subtract each place value digit from 9. So, we get 6 hundreds (9 – 3), 3 tens (9 – 7), and 8 units (9 – 2).
- Combine the subtracted digits to form the answer. Therefore, 1000 – 372 = 638.
Explanation: This trick utilizes the concept of complements – the difference between a number and the next multiple of 10. Subtracting from 9 (one less than the next multiple of 10) in each place value position becomes easier than directly subtracting a potentially larger number from each place value. This can significantly reduce the mental strain involved in complex subtraction problems.
Multiplying Two-Digit Numbers (11 - 19) (Vertically Neighbouring Numbers)
This trick offers a quick way to multiply two-digit numbers between 11 and 19.
- Steps:
- Identify the units digits of each number. (Example: Multiply 13 by 17)
- Multiply the units digits and write down the last digit of the product in the units place of the answer. (3 x 7 = 21, so write down 1)
- Add the tens digits of both numbers and add 1 to the sum if there’s a carryover. (1 + 1 + 1 = 3)
- Write down the sum from step 3 in the tens place of the answer. (The answer is 211)
Explanation: This trick utilizes distributive property and properties of vertically numbers for a faster solution.
Vertically Neighboring Numbers (Last Digit Trick)
This trick tackles multiplication involving a one-digit number and a two-digit number ending in either 1 or 9. Here’s how it works:
- Steps:
- Identify the units digit of the two-digit number. (Example: Multiply 7 x 21)
- If the units digit is 1, subtract it from the one-digit number and write down the result in the tens place of the answer. If the units digit is 9, add the one-digit number and 1 (carryover) and write down the result in the tens place. (Here, 7 – 1 = 6)
- Multiply the tens digit of the two-digit number with the one-digit number and write down the product in the units place of the answer. (2 x 7 = 14, so write down 4)
Explanation: This trick leverages the properties of vertically neighbouring numbers (differing by 1) to simplify multiplication.
Digit Sum Subtraction (Special Cases)
This trick streamlines subtraction problems where the digits in the minuend (number being subtracted from) add up to a multiple of 10 (10, 20, 30, etc.).
- Steps:
- If the digits in the minuend add up to a multiple of 10, subtract that multiple of 10 from the minuend.
- Subtract the subtrahend (number being subtracted) from the remaining tens digit of the minuend.
Example: Subtract 43 from 77 (7 + 7 = 14, a multiple of 10)
- Solution: (77 – 70) – 3 = 7 – 3 = 4
Explanation: This trick simplifies subtraction by separating the tens and units digits and leveraging the fact that subtracting a multiple of 10 is easier.
Multiplication by 11 (Special Case)
Vedic Math offers a unique approach to multiplying by 11. Here’s the process:
- Steps:
- Write down the digits of the number you want to multiply by 11.
- Insert a 0 between each digit.
- Add the original digits and the inserted 0s.
Example: Multiply 32 by 11
- Solution: 3 (original) + 0 (inserted) + 2 (original) + 3 (inserted) = 8 (answer)
Explanation: This trick utilizes the distributive property and the fact that 11 can be represented as 10 (place holder for the 0s) + 1 (added to the original digits).
Alternate Multiplication (Ubhayamadhyam)
This trick tackles multiplication involving two-digit numbers. It offers an alternative and sometimes faster approach compared to traditional multiplication.
- Steps:
- Identify the tens digits of both numbers. (Example: Multiply 42 by 37)
- Add the tens digits and multiply the sum by 10. (4 + 3 = 7, so 7 x 10 = 70)
- Find the product of the units digits and add it to the result from step 2. (2 x 7 = 14, so 70 + 14 = 84)
- Subtract the product of the tens digits from the result in step 3. (4 x 3 = 12, so 84 – 12 = 72)
Explanation: This trick utilizes the distributive property and strategically manipulates the tens and units digits for a potentially quicker solution.
Squares of Numbers Near Multiples of 5 (Special Cases)
This trick simplifies squaring a number close to a multiple of 5 (either 5 less or 5 more).
- Steps:
- For a number ending in a digit 5 less than a multiple of 5 (e.g., 25):
- Square the tens digit and subtract 25 from the result. (Square of 2 = 4, so 4 – 25 = -21)
- For a number ending in a digit 5 more than a multiple of 5 (e.g., 35):
- Square the tens digit and add 25 to the result. (Square of 3 = 9, so 9 + 25 = 34)
Explanation: This trick leverages the properties of squares near multiples of 5 to reduce the number of calculations needed.
Division by 4 (Repeated Halving)
This trick offers a quick way to divide a number by 4 through repeated halving.
- Steps:
- Divide the number by 2 (halving).
- Continue halving the result until you reach a number divisible by 2 without a remainder.
- The final halved number is the quotient (result of the division).
Example: Divide 48 by 4
- Solution: 48 / 2 = 24, 24 / 2 = 12, 12 / 2 = 6 (divisible by 2 without a remainder). The answer is 6.
Explanation: This trick simplifies division by 4 by leveraging the fact that dividing by 4 is essentially the same as halving the number twice (or repeatedly dividing by 2).
Remember, consistent practice is key to mastering Vedic Math. Experiment with these tricks, explore other techniques, and have fun unlocking the fascinating world of Vedic mathematics!
Final Thoughts
In conclusion, the journey through the realm of Vedic Mathematics has been nothing short of enlightening. The ten amazing tricks we’ve explored in this blog represent just a glimpse of the vast treasure trove of mathematical knowledge preserved in ancient Indian texts.