This Say Yes Pt. 2 is like 3,000 times better than the track the lyrics were originally from…if you ever release Greatest Story Never Told, use Say Yes Pt. 2 instead of the original song!!!
Image from
So it can be difficult for people to do long multiplication in their heads. Luckily, the distributive property of multiplication and division can make it easier. Distributive property: a(b + c)=ab + ac. This can help, because basically, if you have two numbers multiplied by each other, you can split one or both of the numbers into smaller, more manageable digits–and you multiply the groups together. This can be easier than trying to carry digits in your head like you carry digits when doing long division on paper.
So say you have 17*15. You can split that into (10 + 7)(10 + 5). That equals, somewhat in the order you would do it doing long multiplication on paper (you can do it in any order you want)–(5 * 7) + (5 * 10) + (10 * 7) + (10 * 10). That’s 35 + 50 + 70 + 100, which is pretty easy to remember when you’re doing it in your head, as opposed to trying to carry digits etc like you do when figuring out long multiplication on paper. (I didn’t do it in the “FOIL (first-outer-inner-last)” order, I wanted to keep the order more like when you do long multiplication on paper.)
Just read about this JUMP system which is supposed to make math easier for kids (and adults) to learn–I’m going to look into, that’s what I want to do too, make a system like that!
Other very important algebra for breaking down math problems:
(a + b)/c = a/c + b/c. This is really because of the distributive property: dividing by c is the same as multiplying by 1/c. So (a + b)/c is the same as (1/c)(a+b)=(1/c)a + (1/c)b=a/c + b/c.
So you may be in algebra or algebra II, and be introduced to negative exponents. Here’s a good way of understanding how they work. When you have an exponent, like b^x, where b is the base, you can split b into b*1, since all numbers are itself times one, this may make it easier to understand. Then b^x means you have 1 times a series of multiplications of b’s x long. So that’s why b^x, where x is zero, is 1: you have a 1with no b’s being multiplied; if x is 1 you have 1 times one b, which equals b; b^2=1*b*b, and so on. Now, if x is negative, that means you have 1 being divided by a series of a multiplication of b’s x long. So b^-1 equals 1/b, b^-2 equals 1/(b^2), and so on.
The movie the Matrix has many homages in it to the movie Commando.
Check out this scene at 2:55 in this video of the mall fight in Commando where all the cops pile on Arnold and he throws them off–exactly like when all of those Agents pile on Neo and he throws them off. Here’s the Matrix Reloaded fight, the part is at 4:50-5:03.
Then there’s the scene where Arnold goes “shopping” for weapons…
at 1:32 in this video he discovers the secret room in the store filled with racks of like unlimited machine guns and other weapons…it’s EXACTLY like in the Matrix where the good guys go in that virtual room with like racks of like unlimited machine guns and other weapons
Here’s the Matrix homage to the Commando “shopping” scene:
Then of course, Arnold’s name is Colonel Matrix in the movie…yay!
I looked up this album after hip hop producer Just Blaze used the image of the cover as his Twitter icon. What…is…going…on…in…this…video??? Some sort of weird alien multi-gendered Grand Theft Auto hip hop animation…with bear roars…???
I once bought a Frank Zappa CD, it was all barber shop music. It took me a long time to discover his really awesome prog rock/jazz fusion/jazz rock/psychadelic rock like on Hot Rats and Chunga’s Revenge, where his guitar is comparable to that of guitarists like John McLaughlin in the Mahavishnu Orchestra.
Okay…here’s a type of algebra transformation that can be counterintuitive if you get stuck at a certain point but is very important!
Say you have odds=p/(1-p), where p=probability. How do you solve for probability in terms of odds? You might start with multiplying both sides by (1-p) which leaves you with odds(1-p)=p. You might think, rats, that’s still too many p’s everywhere! If you multiply that out, you get odds-odds(p)=p. Rats, still too many p’s! But you can get rid of some of the p’s by dividing both sides by p–you’re trying to get rid of as many p’s as possible. So dividing both sides by p, you get (odds/p)-odds=1. Yay! Don’t worry that you got rid of the p on the right side, you still have one on the left side. Now you only have one p: (odds/p)=1+odds.
Then flip that over, p/odds=1/(1+odds). Then p=odds/(1+odds).
Then you can simplify that even more, if you want! You can divide both the top and bottom of the right side by odds (the same as multiplying both the top and bottom by odds^-1). The top, odds/odds=1. The bottom, (1+odds)/odds=(odds^-1 +1). So that’s p=1/(odds^-1 +1).
Wow, great new hip hop from Just Blaze. This plus him producing for the next Eminem album (even though I’ve never liked Eminem, the production will make up for it!) totally makes up for there being no Just Blaze beats on the Blueprint 3.
