#### Let's learn by an example:

## CIX + CV + CCCXL = ?

#### 109 + 105 + 340 = ? The Romans did not have the Hindu-Arabic numbers

### 1. Substitute for subtractives.

#### Substitute for any subtractives in the roman numerals; that is, "uncompact" them using only the additive notation.

#### Subtractive notation = a group of two numerals, one of a lower value preceding another larger one, the only allowed ones are: IV, IX, XL, XC, CD, CM, M(V), M(X), (X)(L), (X)(C), (C)(D), (C)(M) - to calculate the value subtract the first symbol from the second.

#### Additive notation = a group of two or more numerals, equal or sorted in descending order from high to low, largest symbol on the left, down to the smallest on the right - to calculate the value add up the symbols.

#### CIX:

#### IX = X - I = V IIIII - I = V IIII = VIIII

#### CIX = CVIIII

#### CCCXL:

#### XL = L - X = XXXXX - X = XXXX

#### CCCXL = CCCXXXX

### 2. Put the Roman numerals of the same sign together.

#### CVIIII +

#### CV +

#### CCCXXXX =

#### CVIIIICVCCCXXXX

### 3. Sort the symbols in order.

#### Sort the symbols in order from left-to-right with the largest symbol on the left, down to the smallest on the right.

#### CVIIIICVCCCXXXX =

#### CCCCCXXXXVVIIII

### 4. Combine groups of the same symbols together.

#### Starting on the right end (smaller values), combine groups of the same symbols into larger ones.

#### CCCCCXXXXVVIIII =

#### CCCCCXXXXXIIII

#### CCCCCXXXXXIIII =

#### CCCCCLIIII

#### CCCCCLIIII =

#### DLIIII

### 5. Rewrite the repetitive symbols.

#### Rewrite the symbols written in excessive additive notation by using the substractive notation.

#### The numeral I should not repeat itself more than 3 times in a row, rewrite:

#### DLIIII =

#### DLIV

## Final answer: