Write a multiplication table of 9 using Vinculum Method and identify the number at fifth place. (a) 36 (b) 45 (c) 54 (d) 90

To create the multiplication table of 9 using the Vinculum Method, we first need to understand how the Vinculum method works. In this method, a vinculum (a horizontal line) is used to represent subtraction from a base number (usually 10, 100, etc.). For multiplication of numbers by 9, we use the base 10 subtraction method.

Steps to Create the Multiplication Table of 9 Using the Vinculum Method:
9 × 1 = 9: This is straightforward, and the result is 9.
9 × 2 = 18: For the result 18, we rewrite it as 1̅8. The 1̅ means 10 - 1 = 9, so 1̅8 is read as 8.
9 × 3 = 27: Similarly, we rewrite 27 as 2̅7, where 2̅ represents 10 - 2 = 8, so it’s 8.
9 × 4 = 36: Rewrite 36 as 3̅6, where 3̅ represents 10 - 3 = 7, so it’s 7.
9 × 5 = 45: Rewrite 45 as 4̅5, where 4̅ represents 10 - 4 = 6, so it’s 6.
9 × 6 = 54: Rewrite 54 as 5̅4, where 5̅ represents 10 - 5 = 5, so it’s 5.
9 × 7 = 63: Rewrite 63 as 6̅3, where 6̅ represents 10 - 6 = 4, so it’s 4.
9 × 8 = 72: Rewrite 72 as 7̅2, where 7̅ represents 10 - 7 = 3, so it’s 3.
9 × 9 = 81: Rewrite 81 as 8̅1, where 8̅ represents 10 - 8 = 2, so it’s 2.
9 × 10 = 90: This is straightforward, and the result is 90.
Multiplication Table of 9 Using the Vinculum Method:
9 × 1 = 9
9 × 2 = 1̅8 (8)
9 × 3 = 2̅7 (8)
9 × 4 = 3̅6 (7)
9 × 5 = 4̅5 (6)
9 × 6 = 5̅4 (5)
9 × 7 = 6̅3 (4)
9 × 8 = 7̅2 (3)
9 × 9 = 8̅1 (2)
9 × 10 = 90
Identifying the Number at the Fifth Place:
Looking at the table, the number at the fifth place is the result of 9 × 5, which is 4̅5 (6).

Answer:
The number at the fifth place is 6, which corresponds to option (b) 45.