Vedic Math: Easy Tricks and Tips
Vedic Math is a collection of ancient techniques that make solving mathematical problems faster and easier. Below are some of the most useful Vedic Math tricks, along with examples, tips, and practice questions to help you master them.
1. Ekadhikena Purvena (By one more than the previous one)
This trick is useful for squaring numbers ending with 5.
Formula: (a5)2 = a × (a + 1) | 25
Example: 252 = 2 × (2 + 1) | 25 = 6 | 25 = 625
Tip: Always remember to add 1 to the first part and append 25 at the end.
Practice Questions:
- 352 = ?
- 752 = ?
- 1052 = ?
2. Nikhilam Navatashcaramam Dashatah (All from 9 and the last from 10)
This trick is used for subtraction from numbers like 100, 1000, etc.
Formula: Subtract each digit from 9 and the last digit from 10.
Example: 1000 - 357 = (9-3) (9-5) (10-7) = 643
Tip: This method is especially useful for quick mental calculations.
Practice Questions:
- 1000 - 482 = ?
- 100 - 67 = ?
- 10000 - 1234 = ?
3. Urdhva-Tiryagbhyam (Vertically and Crosswise)
This method is used for multiplication of two numbers.
Formula: Multiply vertically and crosswise, then add the results.
Example: 12 × 13 = (1×1) | (1×3 + 2×1) | (2×3) = 1 | 5 | 6 = 156
Tip: Practice this method with two-digit numbers first to get comfortable.
Practice Questions:
- 23 × 24 = ?
- 34 × 12 = ?
- 45 × 67 = ?
4. Paravartya Yojayet (Transpose and Apply)
This trick is used for division, especially when dividing by numbers close to a base.
Formula: Adjust the divisor to a base and apply the division.
Example: 123 ÷ 9 = 13 with a remainder of 6.
Tip: This method is useful for quick division without long calculations.
Practice Questions:
- 234 ÷ 9 = ?
- 456 ÷ 8 = ?
- 789 ÷ 11 = ?
5. Anurupyena (Proportionality)
This method is used for solving equations and proportions.
Formula: Use ratios and proportions to find the unknown.
Example: If 2x = 10, then x = 5.
Tip: This method is great for solving algebraic equations quickly.
Practice Questions:
- If 3x = 21, find x.
- If 5y = 45, find y.
- If 4z = 36, find z.
6. Yavadunam (Whatever the extent of its deficiency)
This trick is used for squaring numbers close to a base.
Formula: (a - b)2 = a2 - 2ab + b2
Example: 962 = (100 - 4)2 = 1002 - 2×100×4 + 42 = 10000 - 800 + 16 = 9216
Tip: Use this method for numbers close to 100, 1000, etc.
Practice Questions:
- 982 = ?
- 1022 = ?
- 9952 = ?
7. Gunitasamuchyah (The product of the sum is equal to the sum of the product)
This method is used for verifying the correctness of multiplication.
Formula: Cross-check the multiplication by summing the digits.
Example: 12 × 13 = 156 → 1+2=3, 1+3=4, 3×4=12 → 1+5+6=12
Tip: This is a quick way to verify your multiplication results.
Practice Questions:
- Verify 14 × 15 = 210.
- Verify 23 × 24 = 552.
- Verify 34 × 12 = 408.
8. Antyayor Dasakepi (The sum of the last digits is 10)
This trick is used for multiplying numbers where the last digits add up to 10.
Formula: Multiply the first part by (first part + 1) and append the product of the last digits.
Example: 32 × 38 = (3 × 4) | (2 × 8) = 12 | 16 = 1216
Tip: This method is perfect for numbers like 23 × 27, 45 × 45, etc.
Practice Questions:
- 23 × 27 = ?
- 45 × 45 = ?
- 56 × 54 = ?
9. Lopana Sthapanabhyam (By alternate elimination and retention)
This method is used for solving equations by eliminating variables.
Formula: Eliminate one variable and solve for the other.
Example: Solve 2x + 3y = 12 and 4x - y = 10.
Tip: This method is useful for solving simultaneous equations quickly.
Practice Questions:
- Solve: 3x + 2y = 16 and 2x - y = 5.
- Solve: 5x + 4y = 32 and 3x - 2y = 6.
- Solve: 4x + 3y = 18 and 2x - y = 4.
10. Vilokanam (By mere observation)
This trick is used for solving problems by simple observation.
Formula: Look for patterns or simplifications.
Example: 99 × 101 = (100 - 1) × (100 + 1) = 1002 - 12 = 9999
Tip: This method is great for spotting shortcuts in calculations.
Practice Questions:
- 98 × 102 = ?
- 97 × 103 = ?
- 999 × 1001 = ?
General Tips and Tricks
- Practice Regularly: The more you practice, the faster you'll get.
- Break Down Problems: Break complex problems into smaller, manageable parts.
- Use Mental Math: Try to solve problems in your head without writing them down.
- Memorize Key Formulas: Knowing key formulas by heart will save you time.
- Stay Calm: Keeping a calm mind will help you think clearly and solve problems faster.