Question

Fill in the following blanks
1. There are only ________ symbols in Roman Numerals.
2. _____, __________, and _________ are never subtracted.
3. The symbol I can be subtracted from _______ and ______ only once.
4. The symbol _______ can be subtracted from D and M only once.
5. LXVII stands for _________.
6. CCC = 3X
7. Symbol I, X, L and M are repeated whereas ______, ______ and ____ are never repeated.

Answer 1

Hint:We will solve this question by using the concept of Roman numerals. In Roman numerals, I is for 1, V is for 5, X is for 10, L is for 50, C is for 100, D is for 500 and M is for 1000. If we keep on adding LL or any numerals, we get, \[LL=50+50=100.\] So, in this way, we will proceed with our calculation to get our result. Also, in Roman Numerals, if the smaller value is written to the right of a symbol of greater value, its values get subtracted to the greater symbol.

Complete step by step answer:
Let us consider each part one by one.
1. There are seven basic symbols I, V, X, L, C, D, and M in Roman Numerals.
So the answer to 1 is 7.
2. In Roman Numerals, if a smaller value is written in the right of a symbol of greater value, its value gets subtracted to the value of the greater symbol. Now, because the symbols V, L, and D are never written to the left of a symbol of the greater value, so V, L, and D are never subtracted.
So, the answer of 2 is V, L, and D.
3. The symbol I can be subtracted from V and X only once.
So, the answer to 3 is V and X.
4. The symbol C can be subtracted from D and M only once.
So, the answer to 4 is C.
5. Now, because the symbol,
\[I\to 1\]
\[V\to 5\]
\[X\to 10\]
\[L\to 50\]
\[C\to 100\]
\[D\to 500\]
\[M\to 1000\]
Therefore for LXVII, we can write it as,
L we have as 50, X, we have as 10, so,
\[\Rightarrow LX=50+10=60\]
Now, finally from VII,
V we have as 5, I we have as 1.
\[\Rightarrow VII=5+1+1=7\]
Therefore,
\[\Rightarrow LXVII=60+7=67\]
Hence, LXVII is represented as 67.
So, the answer for 5 is 67.
6. CCC = 3X
Now because C represents 100. CCC stands for 300.
\[\Rightarrow CCC=100+100+100=300\]
\[300=CCC=3\times 100\]
So, the answer for 6 is 100.
7. Symbol I, X, C, and M are repeated whereas V, L, and D are never repeated.
So, the answer of 7 is V, L, and D.

Note:
We have I, II, III, IV, V, VI, VII, VIII, IX, and X as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Observe that here for \[IV\to 4\] I is subtracted from V only once, there is no symbol as IIV. Similarly, for IX, observe only once I is subtracted from X to get \[9\to IX.\] A numeral IIX does not exist. So, the confusion of part 3 can be avoided by using these.