RBSE Solutions Class 5 Maths Chapter 4 Vedic Mathematics Exercise 4.1

Subtract

Question (1). Subtract:
\( \begin{array}{r} 82 \\ - 54 \\ \hline \end{array} \)
Answer:
\( \begin{array}{r} 82 \\ - 54 \\ \hline 28 \end{array} \)
To perform this subtraction using the Vedic Mathematics methods of Ekanyunena Purvena and Param Mitra Digit Sutra:
(i) First, look at the units column: 2 minus 4. Since 4 cannot be directly subtracted from 2 (because 4 is larger), we use the 'param mitra' (complementary) digit of 4. The param mitra of 4 is 6 (because \(4 + 6 = 10\)). We add this param mitra digit (6) to the top digit in the units place (2), so \(6 + 2 = 8\). Write this 8 below in the units place of the answer.
(ii) Next, we need to adjust the digit in the tens place of the top number, which is 8. This is where 'Ekanyunena Purvena' comes in, meaning "one less than the previous". So, we put an Ekanyunena mark (a dot below) on the digit 8, making it \( \underset{\bullet}{8} \). This means its value effectively becomes 7.
(iii) Now, for the tens column: subtract 5 from the modified 8 (which is now 7). So, \(7 - 5 = 2\). Write this 2 below in the tens place of the answer. The final answer is 28.
In simple words: When the bottom digit is bigger than the top, we use its 'friend' digit and add it to the top one. Then, we make the digit to the left on the top row one less.

🎯 Exam Tip: Always remember that the 'Ekanyunena' mark affects the digit's value in the next column's subtraction, making it one less than its original value.

Question (2). Subtract:
\( \begin{array}{r} 66 \\ - 48 \\ \hline \end{array} \)
Answer:
\( \begin{array}{r} 66 \\ - 48 \\ \hline 18 \end{array} \)
To subtract using the Vedic Mathematics method:
(i) Look at the units column: 6 minus 8. Since 8 cannot be subtracted from 6, find the 'param mitra' digit of 8. The param mitra of 8 is 2 (because \(8 + 2 = 10\)). Add this 2 to the top digit in the units place (6), so \(2 + 6 = 8\). Write 8 in the units place of the result.
(ii) Now, apply 'Ekanyunena Purvena' to the tens digit of the top number, which is 6. Place a dot below it, making it \( \underset{\bullet}{6} \). This means its value effectively becomes 5. This method streamlines the borrowing process.
(iii) For the tens column: subtract 4 from the modified 6 (which is now 5). So, \(5 - 4 = 1\). Write 1 in the tens place of the answer. The final answer is 18.
In simple words: If the top digit is smaller than the bottom, use the bottom digit's 'friend' to help subtract. Make sure to reduce the digit on the left by one afterward.

🎯 Exam Tip: The 'param mitra' digit is always the number that, when added to the original digit, makes 10.

Question (3). Subtract:
\( \begin{array}{r} 74 \\ - 69 \\ \hline \end{array} \)
Answer:
\( \begin{array}{r} 74 \\ - 69 \\ \hline 05 \end{array} \)
To solve this subtraction problem using Vedic methods:
(i) Start with the units column: 4 minus 9. Since 9 is larger than 4, we find the 'param mitra' digit of 9, which is 1 (as \(9 + 1 = 10\)). Add this 1 to the top digit 4, so \(1 + 4 = 5\). Write 5 in the units place of the answer.
(ii) Next, apply 'Ekanyunena Purvena' to the digit in the tens place of the top number, which is 7. Put a dot below it, so it becomes \( \underset{\bullet}{7} \). This changes its value to 6. This consistent step simplifies subtraction across columns.
(iii) Now, for the tens column: subtract 6 from the modified 7 (which is 6). So, \(6 - 6 = 0\). Write 0 in the tens place of the answer. The final answer is 05, or simply 5.
In simple words: When the bottom number is bigger, we use its 'friend' to subtract and then reduce the digit to the left on the top row by one.

🎯 Exam Tip: For single-digit answers like 5, it's often represented as 05 if the original numbers had two digits, to maintain place value context.

Question (4). Subtract:
\( \begin{array}{r} 342 \\ - 143 \\ \hline \end{array} \)
Answer:
\( \begin{array}{r} 342 \\ - 143 \\ \hline 199 \end{array} \)
Using the Vedic Mathematics subtraction method:
(i) In the units column, we need to subtract 3 from 2. Since 3 > 2, we use the 'param mitra' digit of 3, which is 7. Add 7 to 2: \(7 + 2 = 9\). Write 9 in the units place.
(ii) Apply 'Ekanyunena Purvena' to the tens digit of the top number, which is 4. Mark it as \( \underset{\bullet}{4} \), so its value becomes 3. This is essential for correct column adjustment.
(iii) Now for the tens column: subtract 4 from the modified 4 (which is 3). Since 4 > 3, we again use the 'param mitra' digit of 4, which is 6. Add 6 to 3: \(6 + 3 = 9\). Write 9 in the tens place.
(iv) Apply 'Ekanyunena Purvena' to the hundreds digit of the top number, which is 3. Mark it as \( \underset{\bullet}{3} \), so its value becomes 2.
(v) Finally, for the hundreds column: subtract 1 from the modified 3 (which is 2). So, \(2 - 1 = 1\). Write 1 in the hundreds place. The final answer is 199.
In simple words: This method works by repeatedly using 'friend numbers' for subtraction and reducing the digit on the left. This way, we avoid complicated borrowing steps.

🎯 Exam Tip: Remember to apply 'Ekanyunena Purvena' to the digit immediately to the left every time you use a 'param mitra' digit for subtraction in a column.

Question (5). Subtract:
\( \begin{array}{r} 524 \\ - 267 \\ \hline \end{array} \)
Answer:
\( \begin{array}{r} 524 \\ - 267 \\ \hline 257 \end{array} \)
Let's perform this subtraction using Vedic Mathematics:
(i) In the units column, subtract 7 from 4. As 7 is greater than 4, find the 'param mitra' digit of 7, which is 3. Add 3 to 4: \(3 + 4 = 7\). Write 7 in the units place.
(ii) Apply 'Ekanyunena Purvena' to the tens digit of the top number, which is 2. Mark it as \( \underset{\bullet}{2} \), so its value becomes 1. This adjustment is key to the method.
(iii) In the tens column, subtract 6 from the modified 2 (which is 1). Since 6 > 1, find the 'param mitra' digit of 6, which is 4. Add 4 to 1: \(4 + 1 = 5\). Write 5 in the tens place.
(iv) Apply 'Ekanyunena Purvena' to the hundreds digit of the top number, which is 5. Mark it as \( \underset{\bullet}{5} \), so its value becomes 4.
(v) In the hundreds column, subtract 2 from the modified 5 (which is 4). So, \(4 - 2 = 2\). Write 2 in the hundreds place. The final answer is 257.
In simple words: The process is like a chain: if you can't subtract, use the 'friend' number, then make the next number to the left one less. Keep doing this for all columns.

🎯 Exam Tip: When applying 'Ekanyunena' multiple times, ensure you are marking the *original* digit in the higher place value before it is modified for the current column's subtraction.

Question (6). Subtract:
\( \begin{array}{r} 945 \\ - 876 \\ \hline \end{array} \)
Answer:
\( \begin{array}{r} 945 \\ - 876 \\ \hline 069 \end{array} \)
Let's subtract using the Ekanyunena Purvena and Param Mitra Digit Sutra:
(i) For the units column, subtract 6 from 5. Since 6 > 5, use the 'param mitra' digit of 6, which is 4. Add 4 to 5: \(4 + 5 = 9\). Write 9 in the units place.
(ii) Apply 'Ekanyunena Purvena' to the tens digit of the top number, which is 4. Mark it as \( \underset{\bullet}{4} \), so its value becomes 3. This keeps the calculation balanced.
(iii) For the tens column, subtract 7 from the modified 4 (which is 3). Since 7 > 3, use the 'param mitra' digit of 7, which is 3. Add 3 to 3: \(3 + 3 = 6\). Write 6 in the tens place.
(iv) Apply 'Ekanyunena Purvena' to the hundreds digit of the top number, which is 9. Mark it as \( \underset{\bullet}{9} \), so its value becomes 8.
(v) For the hundreds column, subtract 8 from the modified 9 (which is 8). So, \(8 - 8 = 0\). Write 0 in the hundreds place. The final answer is 069, or simply 69.
In simple words: This Vedic method helps solve subtractions quickly, especially when you need to borrow many times, by using 'friend numbers' and reducing the next digit.

🎯 Exam Tip: Always be careful with carrying the 'Ekanyunena' mark to the correct preceding digit to ensure accuracy in multi-digit subtractions.

Question (7). Subtract:
\( \begin{array}{r} 4162 \\ - 2536 \\ \hline \end{array} \)
Answer:
\( \begin{array}{r} 4162 \\ - 2536 \\ \hline 1626 \end{array} \)
Let's solve this using the Vedic Mathematics subtraction method:
(i) In the units column, subtract 6 from 2. Since 6 > 2, use the 'param mitra' digit of 6, which is 4. Add 4 to 2: \(4 + 2 = 6\). Write 6 in the units place.
(ii) Apply 'Ekanyunena Purvena' to the tens digit of the top number, which is 6. Mark it as \( \underset{\bullet}{6} \), so its value becomes 5. This prepares for the next step.
(iii) In the tens column, subtract 3 from the modified 6 (which is 5). So, \(5 - 3 = 2\). Write 2 in the tens place.
(iv) Now, for the hundreds column, subtract 5 from 1. Since 5 > 1, use the 'param mitra' digit of 5, which is 5. Add 5 to 1: \(5 + 1 = 6\). Write 6 in the hundreds place.
(v) Apply 'Ekanyunena Purvena' to the thousands digit of the top number, which is 4. Mark it as \( \underset{\bullet}{4} \), so its value becomes 3.
(vi) For the thousands column, subtract 2 from the modified 4 (which is 3). So, \(3 - 2 = 1\). Write 1 in the thousands place. The final answer is 1626.
In simple words: The 'friend number' method for subtraction, combined with making the next digit smaller, helps break down even big subtractions into easy steps.

🎯 Exam Tip: Pay close attention to the sequence of operations, especially when using 'param mitra' digits for multiple columns in larger subtractions.

Question (8). Subtract:
\( \begin{array}{r} 7264 \\ - 3897 \\ \hline \end{array} \)
Answer:
\( \begin{array}{r} 7264 \\ - 3897 \\ \hline 3367 \end{array} \)
Let's perform this subtraction using the Vedic Mathematics method:
(i) In the units column, subtract 7 from 4. Since 7 > 4, use the 'param mitra' digit of 7, which is 3. Add 3 to 4: \(3 + 4 = 7\). Write 7 in the units place.
(ii) Apply 'Ekanyunena Purvena' to the tens digit of the top number, which is 6. Mark it as \( \underset{\bullet}{6} \), so its value becomes 5.
(iii) In the tens column, subtract 9 from the modified 6 (which is 5). Since 9 > 5, use the 'param mitra' digit of 9, which is 1. Add 1 to 5: \(1 + 5 = 6\). Write 6 in the tens place.
(iv) Apply 'Ekanyunena Purvena' to the hundreds digit of the top number, which is 2. Mark it as \( \underset{\bullet}{2} \), so its value becomes 1. This continuous adjustment is key.
(v) In the hundreds column, subtract 8 from the modified 2 (which is 1). Since 8 > 1, use the 'param mitra' digit of 8, which is 2. Add 2 to 1: \(2 + 1 = 3\). Write 3 in the hundreds place.
(vi) Apply 'Ekanyunena Purvena' to the thousands digit of the top number, which is 7. Mark it as \( \underset{\bullet}{7} \), so its value becomes 6.
(vii) In the thousands column, subtract 3 from the modified 7 (which is 6). So, \(6 - 3 = 3\). Write 3 in the thousands place. The final answer is 3367.
In simple words: This technique makes borrowing simpler by converting it into adding a 'friend number' and then reducing the digit to the left.

🎯 Exam Tip: When dealing with multiple applications of 'Ekanyunena Purvena', ensure each dot is placed correctly and its effect is carried forward to the next column's calculation.

Question (9). Subtract:
\( \begin{array}{r} 1245 \\ - 978 \\ \hline \end{array} \)
Answer:
\( \begin{array}{r} 1245 \\ - 978 \\ \hline 0267 \end{array} \)
Let's solve this subtraction using Vedic Mathematics principles:
(i) In the units column, subtract 8 from 5. Since 8 > 5, use the 'param mitra' digit of 8, which is 2. Add 2 to 5: \(2 + 5 = 7\). Write 7 in the units place.
(ii) Apply 'Ekanyunena Purvena' to the tens digit of the top number, which is 4. Mark it as \( \underset{\bullet}{4} \), so its value becomes 3. This adjusts the previous digit.
(iii) In the tens column, subtract 7 from the modified 4 (which is 3). Since 7 > 3, use the 'param mitra' digit of 7, which is 3. Add 3 to 3: \(3 + 3 = 6\). Write 6 in the tens place.
(iv) Apply 'Ekanyunena Purvena' to the hundreds digit of the top number, which is 2. Mark it as \( \underset{\bullet}{2} \), so its value becomes 1.
(v) In the hundreds column, subtract 9 from the modified 2 (which is 1). Since 9 > 1, use the 'param mitra' digit of 9, which is 1. Add 1 to 1: \(1 + 1 = 2\). Write 2 in the hundreds place.
(vi) Apply 'Ekanyunena Purvena' to the thousands digit of the top number, which is 1. Mark it as \( \underset{\bullet}{1} \), so its value becomes 0.
(vii) In the thousands column, subtract 0 (since 978 can be thought of as 0978) from the modified 1 (which is 0). So, \(0 - 0 = 0\). Write 0 in the thousands place. The final answer is 0267, or 267.
In simple words: This Vedic method simplifies subtraction with borrowing by using 'friend numbers' and making the next digit smaller. This makes calculations quicker and easier.

🎯 Exam Tip: When the subtrahend (bottom number) has fewer digits than the minuend (top number), imagine leading zeros for the subtrahend to correctly apply 'Ekanyunena Purvena' in the highest place values.