Roman Numerals Explained With Many Examples

in this video we're going to talk about roman numerals so the first thing you need to know is the letters and the numbers that relate to them is equivalent to one corresponds to is equal to 10 and represents 50 is 100 think of century which is 100 years equals 500 and finally is one thousand millennium represents one thousand years now let's work on some practice problems so let's say if gave you this number what number does that correspond to if you have three i's it's basically add in one three times so this corresponds to three now what about what is that equal to so corresponds to five and is one so this is five plus one plus one so this is equal to seven so based on those two examples try these two convert these roman numerals into numbers and feel free to pause the video is equal to ten is five and is one so we have ten plus five plus one plus one ten plus five is 15 1 plus 1 is 2 so this adds up to 17 so is equivalent to 17. now for the next example we know it's is 10 is five so fifty plus ten is sixty sixty plus five is sixty-five so that's it for those two examples now let's try two more but let's use large numbers so let's say we have and also so go ahead and convert those two roman numerals into numbers so is hundred represents 50 is five and is one so we have hundred plus fifty that's one fifty and then five plus one plus one is seven so this turns out to be one fifty seven now what about the second example go ahead and try that one so we have which is 100 plus another and then plus which is 50 plus 2x so and is 10 and 10 is five and then is one so one hundred plus hundred is two hundred and then fifty plus ten plus ten that's seventy five plus one is six so this adds up to 276. now what is the difference between the values of these two roman numerals so what do you think they equal are they the same they both contain and an so we know stands for five stands for one the only difference is the order in which the letters are written so does the order matter let's find out vi stands for six plus or five plus one is equal to six now what you need to know is that when you're arranging roman numerals if you're going from big number to small number what you need to do is you need to add now if you're going from small number to big number then you need to subtract ran out of space there now you don't want to say one minus 5 because that's going to give you negative number so you don't want to subtract it that way you want to subtract the big number by the small number so it's going to be 5 minus 1 which is 4. so you need to know that iv is equal to 4 whereas the vi is equal to 6. now go ahead and try these two examples and ix so is 10 is 1. are we adding or are we subtracting well we're going from big number to small number so therefore we need to add so this is going to be 10 plus 1 which is 11. now is 1 is 10 so this time we're going from small number to big number so we need to subtract but we're going to subtract it this way 10 minus 1 is 9. so is 9 is 11. so go ahead and try these two xc and cx feel free to pause the video so is 10 is 100 so we're going from small number to large number therefore we need to subtract so this is going to be hundred minus 10 which is 90. now for the other one it's hundred and then ten so we're going from big to small number therefore we need to add so this is going to be hundred and ten so hopefully this gave you good idea of when you need to add compared to when you need to subtract so let's try some harder examples go ahead and convert the following roman numeral into number so we have an which is ten represents hundred represents five represents one so notice that here the numbers are increasing and then here it's decreasing so here it's not in descendant order which means we need to subtract those numbers so let's focus on xc xc represents 100 minus 10 which is 90. so this whole thing is 90. so we have 90 and then plus 5 plus 1. so these numbers are in descendant order which means we need to add them so this is equal to 96 now let's go ahead and try these two examples dc ix and also cd iv so feel free to pause the video and try those two problems so we know that represents 500 is 100 is one is ten so going from five hundred to one hundred to one it's in descending order which is what it should be so we need to add five hundred plus one hundred is six hundred now looking at the last two notice that it's in ascendant order it's going up it's going from small number to big number so therefore we need to subtract so 10 minus 1 is 9. so this is going to be 600 plus 9 which is so dci represents that number now let's try this example is 100 is 500 is 10 is 50. is 1 and is 5. looking at the first two numbers notice that we're going from small number to big number so therefore subtraction is what we got to use so this is going to be 500 minus 100 and that's 400 now the situation is the same for the next two we're going from small number to big number and so we got to subtract 50 by 10 which is 40. and for the last two we could see the same situation so it's going to be 5 minus 1 which is four four hundred plus forty plus four is equal to four hundred and forty four and so that is the value of now let's work backwards let's convert number into roman numeral so how can we convert 18 into roman numeral feel free to try that problem so 18 is basically 10 plus 5 plus three and three is basically one plus one plus one and so what you wanna do is when you have number break it down into numbers that contain let's say ten fifty hundred five hundred thousand five or one you want to break it down into numbers of the roman numerals so we know that 10 is 5 is and 1 is and we have three of them so 18 is basically let's try another example 34. go ahead and convert that into roman numeral so 30 is 10 plus 10 plus 10 so that's 30. now four we don't want to say that's one plus one plus one plus one rather it's easier to say four is five minus one so since we have subtraction we need to write the letters in reverse order so 10 is so we have three letters and this is going to be and that's but instead of writing which is six we need to write iv which is 4. so don't forget to reverse it when dealing with subtraction so 34 is going to represent iv try two more examples and 176 go ahead and work on those so 97 is 90 plus 5 plus 1. plus another one now ninety we don't wanna represent that as fifty plus ten plus ten plus ten plus ten it's easier to say that it's hundred minus ten and so since we have subtraction situation we need to reverse the letters so we know 100 is century that's is 10 so we're not going to write but rather xc to represent 90. and then 5 is is 1. so this is going to be so that's 97 now what about 176 so we could say this is hundred plus fifty plus 10 plus 10 plus 5 plus 1. so we have no numbers in ascendant order so we can just write it like this 100 is 50 is is 10 and there's another 10 and then so 176 is simply let's try one more problem let's convert the year 1846 into roman numerals go ahead and try it so let's break it down into small numbers so we have thousand and then 800 which we can write it as 500 plus 100 plus 100 plus 100 and then 46 we can write that as 40 plus six and six is going to be five plus one so that's one thousand eight hundred and forty six so four thousand we can just write and for five hundred we could say that that's and then we have three 100s so that's going to be and so far the numbers are in descendant order we're going from big numbers to small numbers now 40 40 is really 50 minus 10. so we need to write two numbers in reverse 50 is 10 is so 40 is going to be not lx because that's 60 but rather xl in reverse order and then 5 plus 1 that's just going to be vi so our answer is what we see right here so the year 1846 can be written as md cccc xlvi and that's it you