Question

Simplify the following in which the roman numbers are used.
 $ \dfrac{M}{L} \times \dfrac{{D - C}}{{XL}} $
(A) CC
(B) CL
(C) XC
(D) LL

Answer 1

Hint: The given problem revolves around the concepts of basic arithmetic and roman numbers. In the given question, we are required to evaluate the value of the expression given to us involving roman numerals. So, first we convert the expression given to us in roman numerals to simple mathematical numeral form. Then, we simplify the expression using the BODMAS rule and represent the answer as a roman number so as to match the options given. We break down the information given to us to try and identify what must be done in order to solve the problem.

Complete step by step solution:
So, the given roman number expression is $ \dfrac{M}{L} \times \dfrac{{D - C}}{{XL}} $ .
We know that M in roman numbers represent $ 1000 $ , L represents $ 50 $ , X represents $ 10 $ , C represents $ 100 $ and D represents $ 500 $ .
We also know the basic roman number rules like writing a number on the left of a number means to subtract the first number from the second one such as XL denotes $ 40 $ .
So, we write the given expression in normal mathematical numeral form.
 $ \Rightarrow \dfrac{{1000}}{{50}} \times \dfrac{{500 - 100}}{{40}} $
Now, we have to simplify the above mathematical expression using the BODMAS rule.
So, we first carry on the subtraction in the numerator and then cancel out the common factors in the numerator and denominator of both the fractions. So, we get,
 $ \Rightarrow \dfrac{{1000}}{{50}} \times \dfrac{{400}}{{40}} $
 $ \Rightarrow 20 \times 10 $
Evaluating the product of the numbers, we get,
 $ \Rightarrow 200 $
Now, we have to represent the result of the arithmetic expression as a roman number to match with the options given in the problem.
We know that the roman numeral for representing $ 100 $ is C. Also, writing a number to the right of a number means to add both the number.
So, the roman numeral for $ 200 $ is CC.
Hence, option (A) is the correct answer.
So, the correct answer is “Option A”.

Note: When we combine numbers and variables in a valid way, using operations such as addition, subtraction, multiplication, division, exponentiation, and other operations and functions as yet unlearned, the resulting combination of a mathematical symbol is called a mathematical expression. Roman numbers are just another system of numerical notation. One must remember the basic roman number notations like M, L, C, X and D so as to solve such questions.