# The number obtained when 144 is divided by 16 in roman number

(a) \[\text{X}\]

(b) \[\text{VII}\]

(c) \[\text{VIII}\]

(d) \[\text{IX}\]

Answer

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**Hint:**In this type of question we have to use the concept of roman numerals conversion. In conversion of a number into Roman numeral 7 major letters are used they are \[\text{I,V,X,L,C,D }\!\!\And\!\!\text{ M}\] used to denote the numbers 1, 5, 10, 50, 100, 500 & 1000 respectively. Roman letters are usually written largest to smallest from left to right but not always. When we write Roman letters largest to smallest from left to right a letter to the right of another letter then it get added, for example when we write a Roman number \[\text{XVIII}\] then it will represent a number 18 as \[\text{XVIII = 10+5+3 = 18}\]. Also when we write Roman letters smallest to largest from left to right a letter to the left of another letter then it gets subtracted, for example \[\text{CD}\] then it will represent a number 400 as \[\text{CD = 500 - 100 = 400}\]. Now, here first we perform the division of 144 and 16 then the quotient obtained we write it in Roman numerals.

**Complete step-by-step solution:**

Now, we have to express the number obtained when 144 is divided by 16 in Roman numerals.

For this let us first perform division of 144 and 16

\[\Rightarrow 16\overset{9}{\overline{\left){\begin{align}

& 144 \\

& \underline {- 144} \\

&0 \\

\end{align}}\right.}}\]

Hence, when we divide 144 by 16 we get 9. Now we have to express 9 in Roman numerals.

Now, we know that we can express 9 as \[9=10-1\] and hence in roman numerals we can write the number 9 as \[\text{IX}\]

**Hence, option (d) is the correct option.**

**Note:**In this type of question we have to note that Roman numerals are special characters and alphabets that represent a number using lines and letters. Also students have to remember that in case of Roman numerals we cannot use the \[\text{IIII}\] instead of that we use the subtraction principle. A subtraction notation is used in the case of 400, 900, 40, 90, 9 and 4 to differentiate between the existing digits.

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