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# Consider the following expression and evaluate it’s value - $IX+VI\times II=?$

Last updated date: 09th Aug 2024
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Hint: In this question, we are given an expression in roman numerals and we need to find its solution. For this, we will first convert roman numerals into Hindu Arabic numerals by understanding the concept. After that, we will solve the expression and then convert the solution obtained in Hindu Arabic numeral into Roman numeral.

Here, we are given an expression in Roman numeral.
Let us change individual Roman numerals to Hindu Arabic numerals.
For this, let us first understand the method of writing roman numerals.
There are a total seven alphabets which are used to write Roman numbers which are I(1), V(5), X(10), L(50), C(100), D(500) and M(1000).
Rule 1: The Roman digits I, X and C are repeated upto three times in succession to form a number. Example: XXX = 10+10+10 = 30. The digits V, L and D are not repeated.
Rule 2: When a digit of lower value is written to the right of highest value, the values of all digits are added. Example: III = 1+1+1 = 3.
Rule 3: When a digit of lower value is written to the left of higher value, then value of lower digit is subtracted from value of the digit of higher value. Example: XL = 50-10 = 40.
Now, we are given numerals as IX, VI and II. For IX: Since I is a smaller alphabet than X written on the left so, it will be subtracted from X. Hence, IX = 10-1 = 9. For VI: Since I is a smaller alphabet than X written on the right so it will be added to V. Hence, VI = 5+1 = 6.
For II: Since I can be repeated and it is written two times, so it can be added and we get II = 1+1 = 2.
Hence our expression $IX+VI\times II$ becomes $9+6\times 2$.
Let us solve this expression. Multiplying 6 and 2 first, we get: $9+12$.
Adding 9 and 12 we get: $21$.
Hence the value of $IX+VI\times II$ in Hindu Arabic numerals is 21.
Let us find it in Roman numerals.
As we can see, 21 can be written as 10+10+1. So we will add two tens and one 1. Hence we need to add X, X and I. For addition, I must be at the right of the higher value X, hence roman numeral will be $21=IX+VI\times II=XXI$.
Hence, the value of $IX+VI\times II$ becomes equal to XXI.

Note: Students should note that all rules should be followed carefully as there is a huge chance of making mistakes while adding or subtracting. Note that, V, L and D cannot be repeated. Also, I, X and C can be repeated only three times.