Worksheet Solutions: Eleven Check Method | Improve Your Calculations: Vedic Maths (English) - Class 6 PDF Download

Answer the following Questions.

Q1: What is the basic principle behind the Eleven Check Method?
Ans: The Eleven Check Method relies on calculating the alternating sum of the digits of a number, then taking the result modulo 11. This helps determine if the operation (addition, subtraction, multiplication) is performed correctly, as the results should be consistent when using this method.

Q2: How do you calculate the alternating sum for a number using the Eleven Check Method?
Ans: To calculate the alternating sum, start from the rightmost digit and alternately add and subtract each digit moving left. For example, for the number 2434, the calculation would be 4 − 3 + 4 − 2 = 3.

Q3: In the Eleven Check Method, how do you handle negative results in the alternating sum? 
Ans: If the alternating sum results in a negative number, add 11 to it until it becomes positive. For example, if the sum is -3, then − 3 + 11 = 8.

Q4: How do you verify a multiplication operation using the Eleven Check Method? 
Ans: First, find the alternating sum for each number being multiplied. Then multiply these sums. Finally, find the alternating sum for the product. If this matches the alternating sum of the multiplied sums (modulo 11), the multiplication is verified.

Q5: Explain how the Eleven Check Method can be used to verify a subtraction operation.
Ans: Calculate the alternating sum for both the minuend and the subtrahend. Subtract the alternating sum of the subtrahend from the alternating sum of the minuend. If the result is negative, add 11. This result should match the alternating sum of the difference.

Q6: What should you do if the alternating sum of a number exceeds 11?
Ans: If the alternating sum exceeds 11, take the sum modulo 11 to find the remainder. This remainder is the positive digit sum used for further calculations.

Q7: How do you handle two-digit alternating sums in the Eleven Check Method?
Ans: For two-digit sums, take the sum modulo 11. For example, if the sum is 13, then 13 mod 11 = 2.

Q8: How does the Eleven Check Method account for the difference between the alternating sums of two numbers?
Ans: When subtracting two numbers, if the alternating sum of the result is negative, add 11 to get a positive digit sum. For example, if the difference is -1, then − 1 + 11 = 10.

Q9: Why might the Eleven Check Method fail to catch certain errors?
Ans: The method might fail if the error does not affect the alternating sum modulo 11. For instance, swapping digits or similar errors that maintain the alternating sum might not be detected.

Q10: How can the Eleven Check Method be used as a teaching tool?
Ans: It provides an additional method for students to verify their work, enhancing their understanding of number properties and modulo arithmetic. It can also help students develop attention to detail and error-checking skills in arithmetic operations.