Brought to you by powerpointpros.com ROMAN NUMERALS

What are Roman Numerals? Basically, Roman numerals are letters that stand for numbers. Each letter used in Roman Numerals has a specific number value.

What are the letters’ values? Here are the most common letters and what number they stand for when using Roman Numerals. There are more letters for higher number values, but we’re just working with the basics. I=1 V=5 X=10 L=50 C=100 D=500 M=1000

How do I use Roman Numerals? When using Roman Numerals to represent a number value, you cannot just simply add the letters together to make numbers, and you certainly can’t use just the letter I, or else when you want to represent 50, you would get a long string of this: IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

How do I use Roman Numerals? Instead of using 50 of the letter “I” to represent the number 50, you can just use this: L

How do I use Roman Numerals? This leads us to our first rule: when representing a number that is the value of a Roman Numeral base letter, you ALWAYS use that base letter.

What does this rule mean? Just like in the first example of the 50 “I”s that could be replaced by a single “L,” if a number that you are representing using Roman Numerals happens to be the same value as a base letter, you always use that base letter.

What does this rule mean? So, if we look again at our list… …we can see that the value 1 will always be represented by an I; the value 5 will always be represented by a V; 10 will always be represented by an X; 50 will always be represented by an L, etc. I=1 V=5 X=10 L=50 C=100 D=500 M=1000

But what about other values? Although that rule may be true, you won’t always be so fortunate as to have to represent a value that is the same as the value of one of the base letters. This leads us to our second rule: you may use multiple letters to display one number value (unless of course the value is the same as that of a base letter.)

That rule doesn’t mean this: 49= IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

The Correct Usage Although the previous example makes sense in theory, it isn’t the correct way to represent the value “49.” Here’s why: Since there are Roman Numeral base letter values greater than 1 but less than 50, we can use those instead.

How do I use multiple letters? Let’s try with the value 31. To identify the letter(s) you are going to use, let’s pull up that chart again… I=1 V=5 X=10 L=50 C=100 D=500 M=1000

How do I use multiple letters? Are there any values on this chart that are greater than 1 but less than 32? I=1 V=5 X=10 L=50 C=100 D=500 M=1000 We can see that both the letters V and X are greater than 1 but less than 32.

How do I use multiple letters? When creating a Roman Numeral to represent a certain value, we start with the largest number possible. I=1 V=5 X=10 L=50 C=100 D=500 M=1000 We can see that both the letters V and X are greater than 1 but less than 32. Which of these two numbers is the greatest (largest) number? Now, we know that the first letter of our numeral is X.

How do I use multiple letters? Now subtract 10 from our value of = ? 21

How do I use multiple letters? Now our value is 21. Are there any letters that are greater than 1 but less than 22? I=1 V=5 X=10 L=50 C=100 D=500 M=1000 We can see that, again, both the letters V and X are greater than 1 but less than 22. This means that now, our Roman Numeral is XX. But we’re not done yet!

How do I use multiple letters? Our value now is 11. Can you identify letters on the chart whose values are greater than 1 but less than 12? I=1 V=5 X=10 L=50 C=100 D=500 M=1000 We can see that, for a third time, both the letters V and X are greater than 1 but less than 12. This means that now, our Roman Numeral is XXX. But there’s another step left!

How do I use multiple letters? Now our value is reduced to 1. But wait! One is a base letter: I! I=1 V=5 X=10 L=50 C=100 D=500 M=1000 As rule 1 implies, since the remaining value of “1” is a base letter already, so we can just use that! How convenient! This means that now, our Roman Numeral is XXXI. And since our remaining value is 0, we’re done!

Reviewing what we Previously Learned So, now we know that the value 31 can be written using the Roman Numerals XXXI! But, there’s one more thing that you need to know…

What about 4? There’s one more rule left: Only 3 of the same Roman Numeral may be used in a row. So how do we represent the number 4, then?

Letter Subtraction In Roman Numerals, for a value such as 31, the representation is XXXI. Notice that the numerals are ordered from the largest-valued numeral to the smallest- valued numeral. (The XXX portion is first, since the value of X (10) is greater than that of the I (1).) 31 cannot be represented as IXXX, or XXIX, XIXX, or any other way besides XXXI. The order of the numerals from greatest to least is always the case…unless you need to do “letter subtraction.”

What about 4? Since 4 is an easy demonstration of letter subtraction, we’ll demonstrate using that as our value.

What about 4? Our value is 4. Are there any values in the chart below that are greater than 1 but less than 5? I=1 V=5 X=10 L=50 C=100 D=500 M=1000 Looking at this chart, we can see that there are none. This means that the representation for the value of 4 is as simple as IIII, right? WRONG!

What about 4? Rule 3 states this: Only 3 of the same Roman Numeral may be used in a row. That means that “IIII” would be an incorrect representation of the value 4 because it has 4 of the same numeral (I) in a row, a direct violation of Rule 3. So does this mean that there is no proper way to represent the value 4?

Don’t Worry… There is still a way to represent the value 4. And it is by using “letter subtraction.”

“Letter Subtraction?” Letter subtraction occurs when the Roman Numeral for a certain value isn’t in correct least-to-greatest order.

Demonstration As we did before, identify a value on the chart below that is greater than 1 but less than 5? (Our value is 4.) I=1 V=5 X=10 L=50 C=100 D=500 M=1000 As indicated before, we can see that there are no values that are above 1 but less than 5. And so we conclude that the representation for the value 4 is IIII. But, we cannot use more than 3 of the same numeral in a row, so we have to go with Plan B.

“Plan B: Letter Subtraction” Since we couldn’t find any value on the chart between 1 and 5, and 1 doesn’t work, we must use the closest value on the chart besides I. I=1 V=5 X=10 L=50 C=100 D=500 M=1000 We can see that the closest value to 4 is 5, represented by V. But our value isn’t 5!!!!!

“Plan B: Letter Subtraction” So, we must subtract 1 from 5 to get 4. Which of the numerals on the chart equals 1? I=1 V=5 X=10 L=50 C=100 D=500 M=1000 We can see that the numeral I represents 1. So how do we arrange them?

“Plan B: Letter Subtraction” We cannot arrange them as VI; that would equal the value 6. Instead, we must arrange them the opposite way: IV. Recall that letter subtraction occurs when the numerals aren’t arranged in the order of “greatest-to-least.” This fits the description perfectly!

“B” Careful The value 49 can’t be represented as IL. Instead, you take L (50) and subtract 10 (X) and then add on the 9 (IX.) So, the value to represent 49 is XLIX Confusing, but it’s true.

PRACTICE

Practice: Represent these values as Roman Numerals. VALUENUMERAL CHART I=1 V=5 X=10 L=50 C=100 D=500 M=1000

Practice: Represent these values as Roman Numerals. VALUEANSWERS X 2. XXXV 3. LXIV 4. LXXII 5. DC 6. DLXVII 7. CM 8. MII

Practice: Try it again without the chart! VALUEANSWERS XXIII 2. IV 3. CII 4. XXXVII 5. MMXV 6. CMXXXII 7. CXXIII 8. C

Practice: “Translate” these Roman Numerals into numbers. ROMAN NUMERALNUMERAL CHART 1. CV 2. DCIII 3. IV 4. LXV 5. XLV 6. CCCXXXIII 7. MMMXVI 8. LIII I=1 V=5 X=10 L=50 C=100 D=500 M=1000

Practice: “Translate” these Roman Numerals into numbers. ROMAN NUMERALANSWERS 1. CV 2. DCIII 3. IV 4. LXV 5. XLV 6. CCCXXXIII 7. MMMXVI 8. LIII

Practice: “Translate” these Roman Numerals into numbers WITHOUT THE CHART! ROMAN NUMERALANSWERS 1. VIII 2. DCLXVI 3. CCC 4. D 5. DXXIV 6. CD 7. MIV 8. CLX

Congratulations! You are now Roman Numeral experts! (Teachers, if you want a printable list with Roman Numeral values, go to