Operations on Roman Numerals

The four basic operations on Roman numerals are addition; subtraction; multiplication and division. 

The Roman numerals satisfy the commutative, associative and distributive laws for addition, subtraction, multiplication and division. If we add, subtract, multiply or divide (except by zero) with two Roman numerals, we will get a Roman numerals. Therefore, the Roman numerals are ‘closed’ with respect to addition, subtraction, multiplication and division)

We will learn about the basic operations on Roman numerals in more detailed explanations along with the examples.

I. Addition of Roman Numerals:

1. Find the sum of LXXX and VI. Give the answer is Roman Numerals.

Solution:

LXXX = 50 + 10 + 10 + 10 = 80 and VI = 5 + 1 = 6

Now, LXXX + VI

     = 80 + 6

     = 86

We write 86 in Roman numerals as LXXXVI.

Therefore, LXXX + VI = LXXXVI

2. Add DCIX + MCII. Give the answer is Roman Numerals.

Solution:

DCIX = 500 + 100 + 10 - 1 = 609 and MCII = 1000 + 100 + 2 = 1102

Now, DCIX + MCII

     = 609 + 1102

     = 1711

We write 1711 in Roman numerals as MDCCXI.

Therefore, DCIX + MCII = MDCCXI

II. Subtraction of Roman Numerals:

3. Subtract LI from XCV. Write the answer in Roman numerals.

Solution:

LI = 50 + 1 = 51 and XCV = 100 - 10 + 5 = 95

Now, XCV – LI

     = 95 – 51

     = 44

We write 44 in Roman numerals as XLIV.

Therefore, XCV - LI = XLIV

4. Subtract LXIII from CLVII. Write the answer in Roman numerals.

Solution:

LXIII = 50 + 10 + 1 + 1 + 1 = 63 and CLVII = 100 + 50 + 5 + 1 + 1 = 157

Now, CLVII - LXIII

     = 157 - 63

     = 94

     = XCIV

Therefore, CLVII - LXIII = XCIV

III. Multiplication of Roman Numerals:

5. Find the product of the Roman numerals IX and XC.

Solution:

IX = 10 - 1 = 9 and XC = 100 - 10 = 90

Now, IX × XC

     = 9 × 90

     = 810

     = DCCCX

Therefore, IX × XC = DCCCX

6. Find the product of the Roman numerals LIX and XIV.

Solution:

LIX = 50 + 10 - 1 = 59 and XIV = 10 + 5 - 1 = 14

Now, LIX × XIV

     = 59 × 14

     = 826

     = DCCCXXVI

Therefore, LIX × XIV = DCCCXXVI

IV. Division of Roman Numerals:

7. Divide CXXV by XXV.

Solution:

CXXV = 100 + 10 + 10 + 5 = 125 and XXV = 10 + 10 + 5 = 25

Now, CXXV ÷ XXV

    = 125 ÷ 25

    = 5

    = V

Therefore, CXXV ÷ XXV = V

8. Find the quotient of MCXI and XI.

Solution:

MCXI = 1000 + 100 + 10 + 1 = 1111 and XI = 10 + 1 = 11

Now, MCXI ÷ XI

    = 1111 ÷ 11

    = 101

    = CI

Therefore, MCXI ÷ XI = CI.

5th Grade Math Problems

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