8 Vedic Math Tricks for Unbelievably Fast Calculations
6 min read · Aug 12, 2024
Table of contents
Hi there!
Welcome to the ninth chapter in my mental math series.
Today, we're going to learn about some fascinating Vedic math tricks.
We've explained Vedic math and its sutras before, but now let's focus on some specific tricks from a higher level.
Basic Vedic Math Tricks
Squaring Numbers Ending in 5
Let me share with you a nifty little trick for squaring numbers that end in 5. I've mentioned it previously, and I'll mention it again because I love it.
Here's how it works:
- Take the tens digit of your number.
- Add 1 to it.
- Multiply these two numbers.
- Slap a 25 on the end of that result.
Let's say we're squaring 25.
- The tens digit is 2.
- We add 1 to get 3.
- Then multiply 2 and 3 to get 6.
- Put 25 at the end, and voila!
Therefore, 25² = 625
It works for any two-digit number ending in 5. For example:
- 35² = 1225 (3 × 4 = 12, append 25)
- 75² = 5625 (7 × 8 = 56, append 25)
- 95² = 9025 (9 × 10 = 90, append 25)
I love it!
Multiplying by 5
Now, here's another trick that'll come in handy - multiplying by 5. It's a bit different for even and odd numbers, but both are straightforward once you get the hang of it.
For even numbers:
- Cut the number in half.
- Add a zero at the end.
Let's say we're multiplying 2244 by 5:
- Half of 2244 is 1122
- Add a zero: 11220
Therefore, 2244 x 5 = 11220
For odd numbers:
- Subtract 1 from the number.
- Cut it in half.
- Add a zero at the end.
- Add 5 to the result.
Let's try 2245 x 5:
- 2245–1 = 2244
- Half of 2244 is 1122
- Add a zero: 11220
- Add 5: 11225
So, 2245 x 5 = 11225
Subtracting from Powers of 10
This one is perfect for subtracting from powers of 10.
Here's how it goes:
- Identify the nearest power of 10 you're subtracting from.
- For each digit except the last, subtract from 9.
- For the last digit, subtract from 10.
Let's work through an example: 1000–423
- Our power of 10 is 1000.
- Now, we apply the rule "All from 9 and the last from 10":
- 4 from 9: 9–4 = 5
- 2 from 9: 9–2 = 7
- 3 from 10: 10–3 = 7
Put it all together: 577
So, 1000–423 = 577!
This works for any power of 10. Let me give you a couple more examples:
- 10000–8675 = 1325
- 100000–875 = 99125
Try for yourself!
Advanced Vedic Math Techniques
Multiplication of Two-Digit Numbers
This next technique is a gem for multiplying two-digit numbers in your head. It's called the Urdhva Tiryagbhyam sutra, which means "vertically and crosswise." Don't let the fancy name scare you off - it's simpler than it sounds.
Let's say we're multiplying 13 x 15. Here's how it goes:
- Multiply the ones digits: 3 x 5 = 15
- Write down the 5, carry the 1
- Now, cross-multiply and add: (1 x 5) + (3 x 1) = 5 + 3 = 8
- Add the 1 we carried: 8 + 1 = 9
- Multiply the tens digits: 1 x 1 = 1
- Put it all together: 195
So, 13 x 15 = 195
This method is faster than the old-school way, and you can start from either end of the numbers.
Division by 5
Now, here's a slick trick for dividing by 5.
Here's how it works:
- Double the number you're dividing
- Move the decimal point one place to the left
Let's try it with 245 / 5:
- Double 245: 245 × 2 = 490
- Move the decimal: 49.0
That's it! 245 / 5 = 49
It works for any number. Try these:
- 680 / 5 = 1360 / 10 = 136
- 1275 / 5 = 2550 / 10 = 255
Multiplying by 11
Here is another of my favorite tricks. It's for multiplying any two-digit number by 11. It's so simple, you'll be doing it in your sleep.
Here's how it works:
- Write down the first digit
- Add the two digits and put the answer in the middle
- Write down the last digit
Let's try it with 32 x 11:
- Write down 3
- Add 3 + 2 = 5
- Write down 2
So, 32 x 11 = 352
It works for any two-digit number. Let's try a few more:
- 45 x 11 = 495 (4, 4+5=9, 5)
- 67 x 11 = 737 (6, 6+7=13 so write 3 and carry 1, 7)
- 89 x 11 = 979 (8, 8+9=17 so write 7 and carry 1, 9)
Finding Square Values
Now, here's a real gem for squaring numbers near 100. This one's a bit trickier, but it's worth mastering.
Let's square 99:
- Find the difference from 100: 100–99 = 1
- Subtract this from 99: 99–1 = 98
- Multiply by 100: 98 × 100 = 9800
- Square the difference: 1² = 1
- Add these together: 9800 + 1 = 9801
So, 99² = 9801
This works for any number close to 100. Try these:
- 98² = 96 × 100 + 2² = 9604
- 95² = 90 × 100 + 5² = 9025
Memory Techniques in Vedic Math
Memorizing Pi Digits
Now, let's talk about something really impressive - memorizing digits of pi.
You might be wondering why on earth you'd need to do this. Well, it's not about pi itself. It's about training your mind to remember complex information.
The Vedic folks had a clever system called Katapayadi. It's like a secret code for numbers. Each digit gets assigned a consonant sound. For example:
3 - no sound
1 - ka
4 - gha
1 - ka
5 - ṅa
9 - jha
So, 3.14159 becomes something like "ka-gha-ka-ṅa-jha". Basically they turned these sounds into words or phrases that are easier to remember.
Real-Life Applications of Vedic Math Tricks
Quick Mental Math for Shopping
Alright, now we're getting to the good stuff - how to use these tricks in real life?
Let's start with shopping. These skills will come in handy when you're negotiating deals or just trying to save a buck at the store.
Here's a slick trick for calculating discounts:
- Subtract the discount percentage from 100
- Move the decimal point one place left
- Multiply the original price by this number and divide by 10
Let's say you're looking at a $50 item with a 20% discount:
- 100–20 = 80
- 80 becomes 8
- $50 x 8 = $400, then $400 ÷ 10 = $40
So, the discounted price is $40, and you're saving $10.
For estimating totals before you hit the cashier, try this:
- Round each price to the nearest whole number
- Add these numbers in your head
- Adjust based on whether you rounded up or down more
Financial Calculations
Now, let's talk money. These Vedic tricks can help you make smart financial decisions on the fly.
For calculating interest quickly, try the "Base Method". Let's say you want to know 8% interest on $1200 for a year:
- Find 1% of $1200: $1200 × 0.01 = $12
- Multiply by 8: $12 × 8 = $96
So, you're looking at $96 interest, for a total of $1296 after a year.
Here's another gem - the "Rule of 72". It tells you how long it'll take for an investment to double. Just divide 72 by the interest rate.
For example, if you're getting 6% interest: 72 ÷ 6 = 12 years
That means your money will double in about 12 years.
Exam Strategies Using Vedic Tricks
If you're in school, these tricks can help you in any situation where you need to think fast under pressure.
They're particularly valuable in standardized tests like the SAT, CAT, and GMAT, where speed and precision are crucial.
Here are some time-savers:
- Use the "Vertically and Crosswise" method for quick multiplication
- For dividing by 9, just add the digits until you get a single number. That's your remainder, and the number of additions is your quotient.
- For squaring numbers ending in 5, like 85², multiply the first digit by its successor (8 x 9 = 72) and add 25 to the end (7225).
To check your work quickly, try the digital root method. It's a lifesaver when you need to double-check your calculations in a hurry.
Conclusion
Well, we've covered a lot of ground here. Hopefully you enjoyed it!
But here's a tip, don't just file these Vedic math tricks away as just another post you read. Take even just one of these techniques, and run with it.
See you in the next chapter 🙂 Be well.
About the author
Richard Reis
Founder of Mental Math Pro! Also currently doing a fun little "25 AI Startups in 50 Weeks" challenge.
