Question

The product obtained when 13 is multiplied by 7 (in roman numbers) is
 (a) XXCI
 (b) LXI
 (c) XCI
 (d) CI

Answer 1

Hint: Here, we need to write the product of 13 and 7 in roman numerals. First, we will find the product of 13 and 7 by repeated addition. Then, we will use roman numerals to represent the product in roman numbers.

Complete step by step solution:
Multiplication is the repeated addition of equal groups. It helps in adding multiple equal groups quickly. It is denoted by the symbol \[ \times \]. Brackets may also be used to denote multiplication.
For example: Suppose that the number 2 is added repeatedly 15 times, that is \[2 + 2 + \ldots \ldots + 2\] 15 times. This can be represented using multiplication as \[2 \times 15\].
Here, we will first multiply 13 by 7.
We can write 13 multiplied by 7 as
\[13 \times 7 = 13 + 13 + 13 + 13 + 13 + 13 + 13\]
Adding the terms in the expression, we get
\[13 \times 7 = 91\]
In roman numerals, I represents 1, V represents 5, X represents 10, L represents 50, C represents 100, D represents 500, and finally, M represents 1000.
When a symbol comes after a larger symbol, the values are added.
For example: In LV, V comes after the larger symbol L. Thus, LV \[ = 50 + 5 = 55\].
When a symbol comes before a larger symbol, the values are subtracted.
For example: In XL, X comes before the larger symbol L. Thus, XL \[ = 50 - 10 = 40\].
Now, we will rewrite 91 in roman numerals.
The number 91 can be written as \[100 - 10 + 1\].
To subtract 10 from 100, that is X from C, we would write X before C to get XC (number 90).
To add 1 to 90, that is I to XC, we would write I after XC to get XCI.
The roman numerals XCI represent the number 91.
Thus, the correct option is option (c).

Note: The product of 13 and 9, that is 91 can be written as \[50 + 10 + 10 + 10 + 10 + 1\]. However, in roman numerals, no symbol is written more than three times in a row. If we use the sum \[50 + 10 + 10 + 10 + 10 + 1\] to represent 91, we would have to use X four times in a row. Hence, we did not use this sum to represent 91 as roman numerals.