RBSE Solutions Class 6 Maths Chapter 7 Vedic Mathematics Exercise 7.3

Question 1. Convert the general numbers into its vinkulum.
(i) 8
(ii) 27
(iii) 82
(iv) 78
(v) 96
Answer:
Vinkulum numbers use negative digits (shown with a bar over them) to simplify calculations. A dot over a digit means it increases by one.

(i) **Converting 8 to Vinkulum:**
The digit 8 is 5 or more. We find its complement from 10, which is 2. So, we write \( \overline{2} \).
Now, put a dot on the imaginary digit '0' to the left of 8. This makes it \( \dot{0}\overline{2} \).
The \( \dot{0} \) becomes 1.
So, 8 in vinkulum is \( 1\overline{2} \). This form, \( 1\overline{2} \), literally means \( 10 - 2 = 8 \).

(ii) **Converting 27 to Vinkulum:**
The rightmost digit, 7, is 5 or more. Its complement from 10 is 3. So, we write \( \overline{3} \).
Put a dot on the digit 2 to its left. This gives us \( \dot{2}\overline{3} \).
The \( \dot{2} \) becomes 3.
So, 27 in vinkulum is \( 3\overline{3} \). This form means \( 30 - 3 = 27 \).

(iii) **Converting 82 to Vinkulum:**
The rightmost digit, 2, is less than 5, so it remains as 2.
Move to the left. The digit 8 is 5 or more. Its complement from 10 is 2. So, we write \( \overline{2} \).
Put a dot on the imaginary digit '0' to the left of 8. This becomes \( \dot{0}\overline{2}2 \).
The \( \dot{0} \) becomes 1.
So, 82 in vinkulum is \( 1\overline{2}2 \). This form means \( 100 - 20 + 2 = 82 \).

(iv) **Converting 78 to Vinkulum:**
The leftmost digit, 7, is 5 or more. Its complement from 10 is 3. So, we write \( \overline{3} \).
Put a dot on the imaginary digit '0' to the left of 7. This makes it \( \dot{0}\overline{3}8 \). The 8 remains as it is.
The \( \dot{0} \) becomes 1.
So, 78 in vinkulum is \( 1\overline{3}8 \). This form means \( 100 - 30 + 8 = 78 \).

(v) **Converting 96 to Vinkulum:**
The leftmost digit, 9, is 5 or more. Its complement from 10 is 1. So, we write \( \overline{1} \).
Put a dot on the imaginary digit '0' to the left of 9. This becomes \( \dot{0}\overline{1}6 \). The 6 remains as it is.
The \( \dot{0} \) becomes 1.
So, 96 in vinkulum is \( 1\overline{1}6 \). This form means \( 100 - 10 + 6 = 96 \).
In simple words: To convert a number to its vinkulum form, change any digit 5 or higher into its negative (bar) form and add one to the digit on its left. If a digit is less than 5, it stays the same.

🎯 Exam Tip: Remember that a number can have multiple valid vinkulum forms depending on the conversion method used. Always ensure your chosen method is consistent and leads to the correct value.