What is Ekadhikena Purvena? | Simple Explanation for Class 5

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What is the Ekadhikena Purvena (Vedic Maths)?

Grade Level:

Class 5

Maths, India-specific, History of Maths

Definition

What is it?

Ekadhikena Purvena is a special trick from Vedic Maths that helps you multiply numbers quickly. It means 'by one more than the previous one'. This method is super useful for multiplying numbers that end in 5 or numbers where the sum of the last digits is 10 and the remaining digits are the same.

Simple Example

Quick Example

Imagine you want to quickly calculate the area of a square playground where each side is 25 meters. Using Ekadhikena Purvena, you can find 25 x 25 very fast. You just take the first digit (2), multiply it by 'one more than it' (3), and then put 25 at the end. So, 2 x 3 = 6, and add 25, giving you 625.

Worked Example

Step-by-Step

Let's multiply 35 by 35 using Ekadhikena Purvena.

Step 1: Identify the last digits. Both numbers end in 5. This method works well for numbers ending in 5.
---Step 2: Take the first digit of the number, which is 3.
---Step 3: Find 'one more than the previous one' for this digit. One more than 3 is 4.
---Step 4: Multiply these two numbers: 3 x 4 = 12.
---Step 5: Now, take the last digits (5 and 5) and multiply them: 5 x 5 = 25.
---Step 6: Combine the results from Step 4 and Step 5. Place the result of Step 5 (25) after the result of Step 4 (12).
---Answer: So, 35 x 35 = 1225.

Why It Matters

Vedic Maths, including Ekadhikena Purvena, is a part of India's rich mathematical heritage, showing how ancient Indians developed clever ways to solve problems. Learning these tricks helps you do calculations faster and improves your mental math skills, which is great for competitive exams like Olympiads or even for jobs in finance or engineering where quick calculations are needed.

Common Mistakes

MISTAKE: Applying this method to any multiplication problem | CORRECTION: Remember, Ekadhikena Purvena is best for specific types of multiplications, especially numbers ending in 5 or where the last digits add up to 10 and the remaining digits are identical.

MISTAKE: Forgetting to multiply the last digits (e.g., 5x5=25) and just writing 5 | CORRECTION: Always remember the last part of the rule: multiply the units digits (e.g., 5 x 5 = 25) and place this product at the end of your answer.

MISTAKE: Adding 'one more' to the wrong part of the number (e.g., adding to the whole number) | CORRECTION: The 'one more than the previous one' rule applies only to the digit(s) before the last digit (the units digit). For 35, it applies to 3.

Practice Questions

Try It Yourself

QUESTION: Use Ekadhikena Purvena to find 15 x 15. | ANSWER: 225

QUESTION: A small square photo frame has sides of 45 cm. What is its area? (Hint: 45 x 45) | ANSWER: 2025 square cm

QUESTION: Try multiplying 75 by 75 using this method. What do you get? | ANSWER: 5625

MCQ

Quick Quiz

Which multiplication problem can be solved easily using Ekadhikena Purvena?

23 x 27

45 x 45

12 x 34

61 x 69

The Correct Answer Is:

Ekadhikena Purvena is ideal for numbers ending in 5, like 45 x 45. While it can also work for numbers where the last digits sum to 10 and the remaining digits are the same (like 23x27 or 61x69), 45x45 is the most straightforward application of the 'numbers ending in 5' rule.

Real World Connection

In the Real World

Imagine you're helping your parents calculate the total cost if they buy 25 kilograms of rice at 25 rupees per kilogram. Instead of using a calculator, you can quickly find 25 x 25 = 625 rupees using this Vedic Maths trick. This is super useful in small businesses, local shops, or even for managing your pocket money!

Key Vocabulary

Key Terms

VEDIC MATHS: Ancient Indian system of mathematics with quick calculation tricks | EKADHIKENA PURVENA: 'By one more than the previous one' rule for multiplication | DIGIT: A single number (0-9) | MULTIPLICATION: The process of finding the product of two or more numbers | UNITS DIGIT: The rightmost digit in a number (e.g., 5 in 35)

What's Next

What to Learn Next

Great job learning Ekadhikena Purvena! Next, you can explore other Vedic Maths sutras like 'Nikhilam Sutra' for multiplication near base numbers. These tricks will make you even faster at calculations and show you more wonders of Indian mathematics.