Again.
This time we're going to talk about operations on fractions. Let's start easy: multiplication. Multiplying fractions is the easiest, god damn. You multiply straight across, numerator to numerator and denominator to denominator.
THIS IS THE SIMPLEST THING YOU WILL EVER DO WITH FRACTIONS.
It's all downhill from there.
Sigh.
Look guys I don't want to keep talking about fractions. Lowest common denominators are such a pain in the ass, do you even know? Here is how we do it in calculus: "Oh, you have to add
But for some reason, people in lower division math expect you to add them by doing more work by finding a lowest common denominator when that is really completely unnecessary.
You can tell your math teachers I said that. It means something because I am a math major on the internet.
So according to wikipedia (I stole their definition because I hate LCDs that much), "the lowest common denominator or least common denominator (abbreviated LCD) is the least common multiple of the denominators of a set of vulgar fractions. It is the smallest positive integer that is a multiple of the denominators." Vulgar fractions??? WIKI STOP CONFUSING ME. Also integers are whole numbers - hey that definition was simple!
What the fuck does that actually MEAN though? It means that if your denominators are 4 and 6 as in the above example, you should be finding the lowest number that fits in both 4 and 6's multiplication tables. 4×2 is 8, you can't get that out of 6, 4×3 is 12, and - hey! 6×2 is also 12! Suddenly you have a lowest common denominator: 12. So you multiply
This is really important and I cannot stress this enough: YOU NEED TO MULTIPLY THE NUMERATOR TOO. This ONLY works because any number over itself is equal to 1, and multiplying anything by 1 does not change your answer. If you forget and instead of multiplying
Are we clear? We're never going to change denominators without remembering the numerators too? Okay. Good.
Unlike multiplication, which goes straight across top to top and bottom to bottom, addition is different. You don't add denominators. That's why they need to be the same number in the first place. If you add
You need to convert those fractions to the same denominator, which in this case is easy because 2×2 = 4.
I'm going to cover one more thing here and that is inverses, which I mentioned briefly in the post about subtraction and division being LIES. Every integer (whole number, remember?) can be written in the form of a fraction, as I also mentioned there. 3 can also be written as
An inverse is something that multiplies with its original to equal one. For example:
Thus you see that
Remember how I said that division was really multiplying by the inverse? Guess how you divide fractions!
WHOA HOLD UP, you mean you have to DIVIDE by FRACTIONS sometimes? Yes, dear blog-reader, you do. It happens with alarming frequency in the middle of integrals, as a matter of fact! So how do you do it? You multiply by the inverse you ignorant oaf! God, have you even been paying attention?!
And now it's a normal multiplication which, as stated in the beginning of this post, is the simplest thing you will ever do with fractions.
NEXT TIME: THE NUMBER LINE. It is way more interesting than fractions, you guys.
* Do I even really need to say this anymore? codecogs.com. In fact I'm just going to put this in the blog info and stop amending it to posts.
** If this post was insufficient (which, let's be honest, it probably was), please direct yourself here, where you will find a far more comprehensive explanation of how to find LCDs and shit.
*** Inverses are also called reciprocals when applied to fractions but I forgot to mention it because I hate fractions too much to remember that shit.
Hey I just did the fractions part 1 and 2 quizzes yesterday lmao
ReplyDeleteI got 20/20 and 19/20 because I brain-flubbed on one that was multiplication of two negatives and forgot that two wrongs make a right. And yeah, the book goes on and on about the LCD and also makes you CANCEL when doing multiplication of fractions.