RBSE Solutions Class 6 Maths Chapter 7 Vedic Mathematics Exercise 7.1

Rajasthan Board RBSE Class 6 Maths Chapter 7 Vedic Mathematics Ex 7.1

Question 1. Find out the addition by formula of Ekadhiken poorven.
(i) \( \begin{array}{r} 96 \\ +68 \\ \hline \end{array} \)
(ii) \( \begin{array}{r} 98 \\ 49 \\ +35 \\ \hline \end{array} \)
(iii) \( \begin{array}{r} 327 \\ 496 \\ +528 \\ \hline \end{array} \)
(iv) \( \begin{array}{rr} \text{Rs} & \text{P} \\ 418 & 75 \\ +395 & 36 \\ \hline \end{array} \)
(v) \( \begin{array}{rr} \text{km} & \text{m} \\ 86 & 786 \\ +75 & 345 \\ \hline \end{array} \)
(vi) \( \begin{array}{rr} \text{kg} & \text{gm} \\ 139 & 65 \\ +87 & 83 \\ \hline \end{array} \)
Answer:
(i) To find the sum of 96 and 68 using the Ekadhiken poorven formula:
1. Add the units digits: 6 + 8 = 14. Write 4 in the units column. Since there is a carry of 1 (from 14), place an `ekadhik` dot over the tens digit of the second number (6), making it \( \overset{\bullet}{6} \) (which is 7).
2. Add the tens digits: 9 + \( \overset{\bullet}{6} \) (which is 7) = 16. Write 6 in the tens column. Since there is a carry of 1, place an `ekadhik` dot over the imaginary zero to the left of 9, making it \( \overset{\bullet}{0} \) (which is 1).
3. Write down the value of \( \overset{\bullet}{0} \), which is 1, in the hundreds column.
So, \( 96 + 68 = 164 \).
(ii) To find the sum of 98, 49, and 35:
1. Add the units digits: 8 + 9 + 5 = 22. Write 2 in the units column. Carry over 2 to the tens column.
2. Add the tens digits along with the carry: 9 + 4 + 3 + 2 (carry) = 18. Write 8 in the tens column. Carry over 1 to the hundreds column.
3. Write down the carry of 1 in the hundreds column.
So, \( 98 + 49 + 35 = 182 \).
(iii) To find the sum of 327, 496, and 528:
1. Add the units digits sequentially: 7 + 6 = 13. Write 3 as the unit and place an `ekadhik` dot over 9 (from 496), making it \( \overset{\bullet}{9} \). Then, add this 3 to 8 (from 528): 3 + 8 = 11. Write 1 as the final unit digit and place an `ekadhik` dot over 2 (from 528), making it \( \overset{\bullet}{2} \). The units digit of the sum is 1.
2. Add the tens digits: 2 + \( \overset{\bullet}{9} \) (which is 10) = 12. Write 2 as the tens digit for this step and place an `ekadhik` dot over 4 (from 496), making it \( \overset{\bullet}{4} \). Then, add this 2 to \( \overset{\bullet}{2} \) (which is 3): 2 + 3 = 5. The tens digit of the sum is 5.
3. Add the hundreds digits: 3 + \( \overset{\bullet}{4} \) (which is 5) = 8. Then, add this 8 to 5 (from 528): 8 + 5 = 13. Write 3 as the hundreds digit and place an `ekadhik` dot over the imaginary zero before the numbers, making it \( \overset{\bullet}{0} \).
4. Write down the value of \( \overset{\bullet}{0} \), which is 1, in the thousands column.
So, \( 327 + 496 + 528 = 1351 \).
(iv) To find the sum of Rs 418 P 75 and Rs 395 P 36:
1. Add the units digits of the Paise column: 5 + 6 = 11. Write 1 in the units place of the Paise result. Place an `ekadhik` dot over 3 (from 36 P), making it \( \overset{\bullet}{3} \).
2. Add the tens digits of the Paise column: 7 + \( \overset{\bullet}{3} \) (which is 4) = 11. Write 1 in the tens place of the Paise result. The carry of 1 (from 11 tens of Paise) is passed to the units place of the Rupees column, assuming 100 Paise make 1 Rupee. So, the Paise sum is 11.
3. Now, add the Rupees column, starting with the units digits and including the carry from Paise: 8 + 5 + 1 (carry from Paise) = 14. Write 4 in the units place of the Rupees result. Place an `ekadhik` dot over 9 (from 395 Rs), making it \( \overset{\bullet}{9} \).
4. Add the tens digits of the Rupees column: 1 + \( \overset{\bullet}{9} \) (which is 10) = 11. Write 1 in the tens place of the Rupees result. Place an `ekadhik` dot over 3 (from 395 Rs), making it \( \overset{\bullet}{3} \).
5. Add the hundreds digits of the Rupees column: 4 + \( \overset{\bullet}{3} \) (which is 4) = 8. Write 8 in the hundreds place of the Rupees result.
So, the total sum is Rs \( 814 \) P \( 11 \).
(v) To find the sum of 86 km 786 m and 75 km 345 m:
1. Add the units digits of the meters column: 6 + 5 = 11. Write 1 in the units place of the meters result. Place an `ekadhik` dot over 4 (from 345 m), making it \( \overset{\bullet}{4} \).
2. Add the tens digits of the meters column: 8 + \( \overset{\bullet}{4} \) (which is 5) = 13. Write 3 in the tens place of the meters result. Place an `ekadhik` dot over 3 (from 345 m), making it \( \overset{\bullet}{3} \).
3. Add the hundreds digits of the meters column: 7 + \( \overset{\bullet}{3} \) (which is 4) = 11. Write 1 in the hundreds place of the meters result. This implies 11 hundred meters, which is 1 km and 131 m (since 1000m = 1km). A carry of 1 km is passed to the units place of the kilometers column. So, the meters sum is 131.
4. Now, add the kilometers column, starting with the units digits and including the carry from meters: 6 + 5 + 1 (carry from meters) = 12. Write 2 in the units place of the kilometers result. Place an `ekadhik` dot over 7 (from 75 km), making it \( \overset{\bullet}{7} \).
5. Add the tens digits of the kilometers column: 8 + \( \overset{\bullet}{7} \) (which is 8) = 16. Write 6 in the tens place of the kilometers result. Place an `ekadhik` dot over the imaginary zero to the left of the kilometers numbers, making it \( \overset{\bullet}{0} \).
6. Write down the value of \( \overset{\bullet}{0} \), which is 1, in the hundreds column of kilometers.
So, the total sum is 162 km 131 m.
(vi) To find the sum of 139 kg 65 gm and 87 kg 83 gm:
1. Add the units digits of the grams column: 5 + 3 = 8. Write 8 in the units place of the grams result.
2. Add the tens digits of the grams column: 6 + 8 = 14. Write 4 in the tens place of the grams result. A carry of 1 (from 14 tens of grams, assuming 100 gm = 1 kg for this problem) is passed to the units place of the kilograms column. So, the grams sum is 48.
3. Now, add the kilograms column, starting with the units digits and including the carry from grams: 9 + 7 + 1 (carry from grams) = 17. Write 7 in the units place of the kilograms result. Place an `ekadhik` dot over 8 (from 87 kg), making it \( \overset{\bullet}{8} \).
4. Add the tens digits of the kilograms column: 3 + \( \overset{\bullet}{8} \) (which is 9) = 12. Write 2 in the tens place of the kilograms result. Place an `ekadhik` dot over the imaginary zero to the left of 8 (from 87 kg), making it \( \overset{\bullet}{0} \).
5. Add the hundreds digits of the kilograms column: 1 + \( \overset{\bullet}{0} \) (which is 1) = 2. Write 2 in the hundreds place of the kilograms result.
So, the total sum is 227 kg 48 gm.
In simple words: The Ekadhiken Poorven method involves adding digits column by column, from right to left. When a sum in a column exceeds 9, instead of carrying over a number, an 'ekadhik' dot is placed on the *previous* digit of the next number to the left, which effectively increases that digit by one. This simplifies the carry operation, making calculations quicker.

🎯 Exam Tip: When using the Ekadhiken poorven method, remember to place the 'ekadhik' dot correctly on the *previous* digit for each carry, and always count a dotted digit as one higher than its face value.