Linux the Penguin Teaches You: Fractions
Once again, I am Professor Linux, and this is 'GRE Math for the CellaPhobic'.
If you are looking for 'Architecture 101', you're in the wrong building.
Today we will be talking about fractions.
But not the delicious type of pie.
You didn't honestly think that this post would include apple pies, or pumpkin pie, or something like that did you?
I mean... can you imagine me cooking a fucking pie?
I can't roll out dough, or mix things, I have flippers.
So there will be no pie in this lecture.
But there will be plenty of fractions.
(and close ups of my face)
Enough of these silly close ups!
Let's get to work on fractions.
Adding and subtracting fractions
In order to add or subtract a fraction, the two fractions must share a common denominator.
Because we both know you're an idiot
...I'm sure you need reminding about what is the numerator and what is the denominator.
Now that you've had that little refresher course, let's get back to it.
Once again you can only add fractions that have a common denominator.
This is because the denominator will not change during the equation. The only numbers we will actually be adding are the numerators.
For those of you who love formulas, here's the formula for adding and subtracting fractions.
BUT we CANNOT add 3/5 + 2/10
...at least, not without changing the fractions so they share a common denominator.
Thankfully 3/5 and 2/10 have a very easy common multiple of 10. So, we change 3/5 to 6/10 (remember - whenever you change the denominator, you have to change the numerator by the same amount).
At this point you should ALWAYS check the answers given on the GRE. Sometimes the answer is simplified, sometimes it is not. Why do extra work if you don't have to?
If you do not see 8/10, simplify that shit.
Subtracting fractions follows the same rules: as long as there is a common denominator, go for it.
If there isn't a common denominator, make one.
(with paper and scissors, you can make anything)
Multiplying and dividing fractions
Unlike addition and subtraction, when you multiply or divide a fraction you do change the denominator.
Which means a common denominator is not necessary
Again for you formula junkies, here's the formula for multiplying fractions:
Now, dividing fractions is just as simple as multiplying them...
...Because its the exact same as multiplying them.
You see, when you're given a problem like:
3/7 ÷ 4/10, all you need to do is invert the second fraction and multiply instead. So:
3/7 ÷ 4/10 becomes 3/7 x 10/4
Though the GRE is unlikely to ask you a question as simple as 1/4 + 3/8, the Quantitative Comparision section commonly asks you to compare two fractions.
Comparing two fractions is easy... if they have the same denominator.
We can easily look at 3/8 and say it's smaller than 5/8.
Lets bring out our pies again.
It's pretty easy to tell which is bigger.
Comparing two fractions is ALSO easy if they have the same numerator.
If the numerators are the same, the frraction with the smaller denomiator will always be larger.
For fractions without common denominators, you have several options.
This is a terrible option during a test.
You can just start drawing pies willy nilly while you're being timed.
2. Change the denominator
This can be a great solution if there is an easy-to-find common denominator.
Consider the following problem:
250 can easily be converted to 1000 by multiplying the entire equation by four.
So 120/250 becomes 480/1000
Obviously 763 is larger than 480, so column B is larger than column A.
THIS is the trick to use on the GRE
You see in any fraction, if the numerator of the first fraction times the denominator of the second fraction is greater than the denominator of the first fraction times the numerator of the second fration, than the first fraction is larger than the second.
Wait... you need that said in a less confusing way?
Say we have a fraction a/b and we want to know if it is larger than fraction c/d.
Well, all we need to do is mutiply a and d, and compare that to b times c.
if ad > than bc, then the fraction a/b is greater than the fraction c/d
Ergo, if ad < bc, then the fraction c/d is greater than the fraction a/b
Lets use real numbers as an example, shall we?
Using the formual (ad and bc) we get 5(11) and 7(9)
B ecause the GRE never wants to make anything easy for you, they might give you a fraction within a fraction.
There are two ways to handle this sort of problem:
1. Find the least common multiple of all the denominators in the problem
Lets take (7/9 - 1/6) ÷ (1/3 + 1/2)
With a little math (ok... a lot of math) we can work out that the least common multiple for 9, 6, 3, 2 is 18.
So, we multiply the entire equation by 18.
That gives us [(18/1 x 7/9) - (18/1 x 1/6)] ÷ [(18/1 x 1/3) + (18/1 x 1/2)]
Which we can simplify to [(2/1 x 7/1) - (3/1 x 1/1)] ÷ [(6/1 x 1/1) + (9/1 x 1/1)]
Which we can THEN simplify to 2(7) - 3(1) ÷ 6(1) + 9(1)
2. Treat each fraction as it's own problem, and solve them separately:
Lets use an example, shall we?
(7/9 - 1/6) / (1/3 + 1/2)
If we seperate this into two different equations we get 7/9 - 1/6 and 1/3 + 1/2
7/9 - 1/6 becomes 14/18 - 3/18 = 11/18
1/3 + 1/2 becomes 2/6 + 3/6 = 5/6
(11/18) ÷ (5/6) = 11/18 x 6/5
gracieabrams
tangentwithtanner
discoholicmusic
areudirty
turnnoffyourmind
jimmyeatworldofficial
romaincrisis