Find the sum of the expression: IX + XV + XX = _________ (a) 45 (b) 35 (c) 44 (d) 40
Hint: Use the roman numerals knowledge to write IX as 9, XV as 15 and XX as 20. Then add these to find the desired result.
Complete step-by-step answer: We have been asked to find the value of the given expression, that is, IX + XV + XX. Actually the term whose sum we have been asked to find is called the Roman numerals. Roman numerals is a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe. Numbers in this system are represented by a combination of letters from present in English alphabet. Modern usage employs seven symbols each with a fixed integer value, as shown in the following table:
If ‘I’ is placed on the left hand side, then the value of the symbol is subtracted by ‘1’. For example: IV becomes 5 – 1 = 4 Similarly, if ‘I’ is placed on the right hand side, then the value of symbols is added by ‘1’. For example: VI becomes 5 + 1 = 6 This same procedure is followed for all the symbols. IX here ‘I’ is place on left of X, so we get IX = 10 – 1 = 9………..(i) Similarly, in XV, ‘V’ is placed on the right hand side of the ‘X’, so we add as shown below: XV = 10 + 5 = 15……(ii) Now, XX = 10 + 10 = 20………(iii) So, the given expression is, IX + XV + XX Substituting the values from equation (i), (ii) and (iii), we get IX + XV + XX = 9 + 15 + 20 = 44 Hence, the correct answer is option (c).
Note: Students should have knowledge about symbols, notations and other facts related to the roman numerals. They should also be careful about substituting the values otherwise the answer will be wrong.