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1492 = MCDXCII

14 = XIV

49 = XLIX

Sum: 1492 + 14 + 49 = MCDXCII + XIV + XLIX

Expected answer: 1555 = MDLV

Method 1

Similar to the decimal system. Work from the right and examine the unit portions of each value. Expand the individual values, cancel out the positive and negative values and sum the remainder. If the result is greater than or equal to X, carry the X(s) and leave the remainder (the units). Repeat for the tens portion, the hundreds and the thousands. Combine the answers.

Start with the units:

II + IV + IX =

I + I - I + V - I + X = (expanded)

I + I - I + V - I + X = (cancel out similar + and - values)

V + X =

XV =

V (carry X)

Now the tens (with carry):

XC + X + XL ( + X) =

- X + C + X - X + L + X = (expanded)

- X + C + X - X + L + X = (cancel out similar + and - values)

C + L =

CL =

L (carry C)

And the hundreds (with carry):

CD ( + C ) =

- C + D + C = (expanded)

- C + D + C = (cancel out similar + and - values)

D (no carry)

And finally the thousands (no carry):

M

Combine the results:

M + D + L + V =

MDLV

Method 2

Combine the numbers into a single number and expand the individual values. Cancel all similar positive and negative values. Then sort in descending order. Simplify if necessary.

MCDXCII + XIV + XLIX =

MCDXCIIXIVXLIX = (combined)

M - C + D - X + C + I + I + X - I + V - X + L - I + X = (expanded)

M - C + D - X + C + I + I + X - I + V - X + L - I + X = (cancel out similar + and - values)

M + D + V + L = (unsorted)

M + D + L + V = (sorted)

MDLV

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Q: How would you actually find the sum of 1492 14 and 49 in two different ways using only Roman numerals in step by step stages throughout both calculations giving reasons why?
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