RBSE Solutions Class 5 Maths Chapter 4 Vedic Mathematics Exercise 4.2

Subtract the following

(Sutra - Ekadhikena purvena + param mitra digit)

Question 1. (1) Subtract \( \begin{array}{r} 200 \\ -132 \end{array} \) using the Ekadhikena Purvena and Param Mitra Digit methods.
Answer: The result of the subtraction is \( \begin{array}{r} 200 \\ -132 \\ \hline 068 \end{array} \). Here are the steps using the Vedic Mathematics methods:
(i) To subtract 2 from 0, we consider 0 as 10. We take the 'param mitra digit' of 2, which is 8, and add it to the 0, getting 8. This 8 is written below. An 'Ekadhik mark' is then placed on the digit 3 below, making it \( \overset { . }{3} \). This process is part of Vedic subtraction to handle borrowing.
(ii) Now, \( \overset { . }{3} \) acts as 4. To subtract 4 from the next 0 (which is also treated as 10), we use the param mitra digit of 4, which is 6. We add this 6 to 0, which gives 6. This 6 is written below.
(iii) Next, an 'Ekadhik mark' is placed on the 1 (which is the digit above the 3), making it \( \overset { . }{1} \), effectively 2.
(iv) Finally, we subtract 2 from 2, which leaves 0. This gives the final answer as 068. The Ekadhik mark simplifies borrowing by increasing the next subtrahend.
In simple words: When a number on top is smaller, we use a special 'friend number' (param mitra digit) and a 'dot mark' (Ekadhik mark) to help subtract. This makes sure we get the correct difference, just like regular borrowing.

🎯 Exam Tip: Always clearly identify the 'param mitra digit' for the number being subtracted and remember to add the 'Ekadhik mark' to the previous digit of the subtrahend.

Question 2. (2) Subtract \( \begin{array}{r} 500 \\ -309 \end{array} \) using the Ekadhikena Purvena and Param Mitra Digit methods.
Answer: The result of the subtraction is \( \begin{array}{r} 500 \\ -309 \\ \hline 191 \end{array} \). Here are the steps using the Vedic Mathematics methods:
(i) To subtract 9 from 0, we add the param mitra digit of 9 (which is 1) to 0, writing 1 below. We place an Ekadhik mark on the 0 in the subtrahend, making it \( \overset { . }{0} \).
(ii) Now, \( \overset { . }{0} \) becomes 1. To subtract 1 from the next 0, we add the param mitra digit of 1 (which is 9) to 0, writing 9 below. We place an Ekadhik mark on the 3 in the subtrahend, making it \( \overset { . }{3} \).
(iii) Now, \( \overset { . }{3} \) becomes 4. We subtract 4 from 5, writing 1 below. This completes the subtraction. This Vedic method provides a quick way to perform subtractions by adjusting digits.
In simple words: We use 'friend numbers' and 'dot marks' (Ekadhik marks) when we cannot subtract directly. This helps us borrow from the next column easily and find the correct answer.

🎯 Exam Tip: When using the param mitra digit, ensure you apply the Ekadhik mark to the correct digit in the subtrahend to account for the 'borrowing'.

Question 3. (3) Subtract \( \begin{array}{r} 805 \\ -608 \end{array} \) using the Ekadhikena Purvena and Param Mitra Digit methods.
Answer: The result of the subtraction is \( \begin{array}{r} 805 \\ -608 \\ \hline 197 \end{array} \). Here are the steps using the Vedic Mathematics methods:
(i) To subtract 8 from 5, we add the param mitra digit of 8 (which is 2) to 5, writing 7 below. We then put an Ekadhik mark on the 0 in the subtrahend, making it \( \overset { . }{0} \). This is a core step for borrowing.
(ii) Now, \( \overset { . }{0} \) becomes 1. To subtract 1 from the next 0, we add the param mitra digit of 1 (which is 9) to 0, writing 9 below. We then put an Ekadhik mark on the 6 in the subtrahend, making it \( \overset { . }{6} \).
(iii) Now, \( \overset { . }{6} \) becomes 7. We subtract 7 from 8, writing 1 below. This process ensures accurate calculation even with multiple 'borrows'.
In simple words: When the top number is smaller than the bottom number, we use a special 'friend number' and add a 'dot' to the next bottom number. This helps us subtract step-by-step from right to left.

🎯 Exam Tip: Practice identifying the param mitra digit quickly for each number (e.g., for 1 it's 9, for 2 it's 8, for 3 it's 7, etc.) as this speeds up the calculation process.

Question 4. (4) Subtract \( \begin{array}{r} 1700 \\ -973 \end{array} \) using the Ekadhikena Purvena and Param Mitra Digit methods.
Answer: The result of the subtraction is \( \begin{array}{r} 1700 \\ -973 \\ \hline 0727 \end{array} \). Here are the steps using the Vedic Mathematics methods:
(i) To subtract 3 from 0, we add the param mitra digit of 3 (which is 7) to 0, writing 7 below. We then put an Ekadhik mark on the 7 in the subtrahend, making it \( \overset { . }{7} \). This is the first step in adjusting for borrowing.
(ii) Now, \( \overset { . }{7} \) becomes 8. To subtract 8 from the next 0, we add the param mitra digit of 8 (which is 2) to 0, writing 2 below. We then put an Ekadhik mark on the 9 in the subtrahend, making it \( \overset { . }{9} \).
(iii) Now, \( \overset { . }{9} \) becomes 10. To subtract 10 from 7, we consider 7 as 17. We add the param mitra digit of 10 (which is 0) to 7, writing 7 below. We then put an Ekadhik mark on the implied 0 before the 9 in the subtrahend, making it \( \overset { . }{0} \).
(iv) Now, \( \overset { . }{0} \) becomes 1. We subtract 1 from 1, writing 0 below. This systematic approach simplifies complex subtractions.
In simple words: This method makes subtraction easier by using 'complementary' digits and adding a 'dot' to the next digit down. This helps avoid traditional borrowing when the top number is smaller.

🎯 Exam Tip: Pay close attention when subtracting a larger digit from a smaller one; the 'param mitra digit' is key here, and remember to apply the Ekadhik mark accurately.

Question 5. (5) Subtract \( \begin{array}{r} 8305 \\ -5281 \end{array} \) using the Ekadhikena Purvena and Param Mitra Digit methods.
Answer: The result of the subtraction is \( \begin{array}{r} 8305 \\ -5281 \\ \hline 3024 \end{array} \). Here are the steps using the Vedic Mathematics methods:
(i) Subtract 1 from 5, which gives 4. Write 4 below.
(ii) To subtract 8 from 0, we add the param mitra digit of 8 (which is 2) to 0, writing 2 below. We then place an Ekadhik mark on the 2 in the subtrahend, making it \( \overset { . }{2} \).
(iii) Now, \( \overset { . }{2} \) becomes 3. Subtract 3 from 3, writing 0 below.
(iv) Subtract 5 from 8, writing 3 below. This method is effective for subtractions involving digits that are directly subtractable and those that require using param mitra digits. The Ekadhik mark helps keep track of these adjustments clearly.
In simple words: We subtract digits from right to left. If a top number is too small, we use its 'friend' number and put a dot on the next bottom number, then subtract normally.

🎯 Exam Tip: When a digit can be directly subtracted without needing a param mitra digit, proceed normally and only apply the Ekadhik mark when a 'borrow' is implicitly required.

Question 6. (6) Subtract \( \begin{array}{r} 4000 \\ -2736 \end{array} \) using the Ekadhikena Purvena and Param Mitra Digit methods.
Answer: The result of the subtraction is \( \begin{array}{r} 4000 \\ -2736 \\ \hline 1264 \end{array} \). Here are the steps using the Vedic Mathematics methods:
(i) To subtract 6 from 0, we add the param mitra digit of 6 (which is 4) to 0, writing 4 below. We then place an Ekadhik mark on the 3 in the subtrahend, making it \( \overset { . }{3} \). This is the initial step for handling a borrow.
(ii) Now, \( \overset { . }{3} \) becomes 4. To subtract 4 from the next 0, we add the param mitra digit of 4 (which is 6) to 0, writing 6 below. We then place an Ekadhik mark on the 7 in the subtrahend, making it \( \overset { . }{7} \).
(iii) Now, \( \overset { . }{7} \) becomes 8. To subtract 8 from the next 0, we add the param mitra digit of 8 (which is 2) to 0, writing 2 below. We then place an Ekadhik mark on the 2 in the subtrahend, making it \( \overset { . }{2} \).
(iv) Now, \( \overset { . }{2} \) becomes 3. We subtract 3 from 4, writing 1 below. This systematic application of Ekadhik mark and param mitra digit helps in complex multi-digit subtractions.
In simple words: This Vedic method helps subtract by using 'friend numbers' for digits that are too large on the bottom and marking the next digit with a 'dot' to carry over the 'borrowing' effect.

🎯 Exam Tip: When multiple zeros are involved in the minuend, apply the Ekadhik mark sequentially to the subtrahend digits, as this ensures each 'borrow' is correctly propagated.

Question 7. (7) Subtract \( \begin{array}{r} 9700 \\ -4904 \end{array} \) using the Ekadhikena Purvena and Param Mitra Digit methods.
Answer: The result of the subtraction is \( \begin{array}{r} 9700 \\ -4904 \\ \hline 4796 \end{array} \). Here are the steps using the Vedic Mathematics methods:
(i) To subtract 4 from 0, we add the param mitra digit of 4 (which is 6) to 0, writing 6 below. We then place an Ekadhik mark on the 0 in the subtrahend, making it \( \overset { . }{0} \). This is crucial for the first column.
(ii) Now, \( \overset { . }{0} \) becomes 1. To subtract 1 from the next 0, we add the param mitra digit of 1 (which is 9) to 0, writing 9 below. We then place an Ekadhik mark on the 9 in the subtrahend, making it \( \overset { . }{9} \).
(iii) Now, \( \overset { . }{9} \) becomes 10. To subtract 10 from 7, we consider 7 as 17. We add the param mitra digit of 10 (which is 0) to 7, writing 7 below. We then place an Ekadhik mark on the 4 in the subtrahend, making it \( \overset { . }{4} \).
(iv) Now, \( \overset { . }{4} \) becomes 5. We subtract 5 from 9, writing 4 below. This method effectively handles borrowing across multiple columns.
In simple words: When a digit on top is smaller, we use its 'friend number' and add a 'dot' to the digit below it in the next column. This way, we can subtract without traditional borrowing.

🎯 Exam Tip: Be careful with zero digits in the minuend; they require the consistent application of param mitra digits and Ekadhik marks to ensure accuracy in each column.

Question 8. (8) Subtract \( \begin{array}{r} 1000 \\ -854 \end{array} \) using the Ekadhikena Purvena and Param Mitra Digit methods.
Answer: The result of the subtraction is \( \begin{array}{r} 1000 \\ -854 \\ \hline 0146 \end{array} \). Here are the steps using the Vedic Mathematics methods:
(i) To subtract 4 from 0, we add the param mitra digit of 4 (which is 6) to 0, writing 6 below. We then place an Ekadhik mark on the 5 in the subtrahend, making it \( \overset { . }{5} \). This handles the first column's requirement for borrowing.
(ii) Now, \( \overset { . }{5} \) becomes 6. To subtract 6 from the next 0, we add the param mitra digit of 6 (which is 4) to 0, writing 4 below. We then place an Ekadhik mark on the 8 in the subtrahend, making it \( \overset { . }{8} \).
(iii) Now, \( \overset { . }{8} \) becomes 9. To subtract 9 from the next 0, we add the param mitra digit of 9 (which is 1) to 0, writing 1 below. We then place an Ekadhik mark on the implied 0 before the 8 in the subtrahend, making it \( \overset { . }{0} \).
(iv) Now, \( \overset { . }{0} \) becomes 1. We subtract 1 from 1, writing 0 below. This process ensures that borrowing is managed through a simple mark and digit replacement.
In simple words: When subtracting, if the top digit is smaller, we use its 'best friend' digit and add a 'dot' to the next digit below. This helps us get the answer step by step.

🎯 Exam Tip: For numbers like 1000 where multiple zeros are present, remember to apply the Ekadhik mark correctly across all preceding digits in the subtrahend until the borrowing is resolved.

Question 9. (9) Subtract \( \begin{array}{r} 9000 \\ -3896 \end{array} \) using the Ekadhikena Purvena and Param Mitra Digit methods.
Answer: The result of the subtraction is \( \begin{array}{r} 9000 \\ -3896 \\ \hline 5104 \end{array} \). Here are the steps using the Vedic Mathematics methods:
(i) To subtract 6 from 0, we add the param mitra digit of 6 (which is 4) to 0, writing 4 below. We then place an Ekadhik mark on the 9 in the subtrahend, making it \( \overset { . }{9} \). This sets up the first stage of borrowing.
(ii) Now, \( \overset { . }{9} \) becomes 10. To subtract 10 from the next 0, we add the param mitra digit of 10 (which is 0) to 0, writing 0 below. We then place an Ekadhik mark on the 8 in the subtrahend, making it \( \overset { . }{8} \).
(iii) Now, \( \overset { . }{8} \) becomes 9. To subtract 9 from the next 0, we add the param mitra digit of 9 (which is 1) to 0, writing 1 below. We then place an Ekadhik mark on the 3 in the subtrahend, making it \( \overset { . }{3} \).
(iv) Now, \( \overset { . }{3} \) becomes 4. We subtract 4 from 9, writing 5 below. This method provides a clear, step-by-step way to perform subtraction, especially useful for multi-digit numbers.
In simple words: We subtract starting from the right. If the bottom number is larger than the top, we use its 'complement' and put a dot on the next bottom number to adjust.

🎯 Exam Tip: When a param mitra digit calculation results in zero, ensure you still apply the Ekadhik mark to the next digit to maintain the correctness of the overall subtraction.