# ZeroSum Ruler (home)

## Blogging on math education and other related things

### Wanna be a Math Hero? Answer these questions!September 17, 2012

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These Math students need YOUR help.

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If you’ve checked all recent posts on Facebook, refreshed your Twitter page until it can be refreshed no more, all of your Pinterest friends seem to be on vacation and your email is all read, why not answer some Math questions?

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I’ve been addicted to this site since last night, which in 2012 terms is an eternity.  All I can imagine are kids all over the US toiling away at their Math homework, one hand on head, one wrapped around a pencil, foregoing food, sleep, showering, just to get tomorrow’s math work complete in time for their teachers to put a small check in the corner.   Hey, maybe a few teachers are stickerers, I don’t know.  Personally, I’m a grape-flavored stamper.  So here I come to the rescue!  The THANK YOU! emails are cool to get; I do feel a bit like a hero today.

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Questions range from “Plz help me graph y = 45x + 40” to “What is the square root of 1 – i?  So try it out!  It’s a great way to put that advanced degree to good use!

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### I can read your mind! (well, Algebra can :)January 9, 2011

If you have a good handle on your Algebra, you can read anyone’s mind!  This video (click the red triangle to go to the YouTube video) is just one case where I can read your mind straight through the computer! It’s true!   Can you develop an algebra trick that reads your friend’s mind? I bet you can!

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### All too common math mistakes!June 16, 2010

One of my grad school professors called the mistake (a+b)^2 = a^2 + b^2 the “freshman dream”.  I guess he meant freshmen in college, but freshmen in high school make the same mistake.  Come to think of it, a lot of people make the same mistake.  What other mistakes are common in Algebra?

Here are just a few I can think of:

x = 1.     NO.  Well, sometimes, but definitely not always.

-7 + 5 = -12.  NO.  This one’s a never and the reason I developed the ZeroSum ruler.

(a+b)^2 = a^2 + b^2.  NOPE.  There’s a middle term in there.  Write it out.  Don’t be lazy.  Find it.

1/2 = 2.  NO.  “1 out of 2″ is not 2.

(x + 2) + (x - 5) = x^2 – 3x - 10.  NO.  This is an addition problem, not a multiplication problem.

(x+2) – (x - 5) = -3.  NOPE again.  That little – sign is a -1 in disguise and needs to be distributed.

(2/5)(7/3) = ….<blank>….  NO.  Multiply the numerators together and the denominators together to get 14/15.  Easy!

“Thirty percent of 140 = 140/.3″.  NO.  You’re going to get a huge number.  “OF” means to multiply, not divide.

|-5| = 5, so |5| = -5.  NO.  Absolute value is always a positive number.  It represents a distance.  Even if you walk backwards, you’re still moving some distance.

“find x^2 if x = -5″.  Answer: -25.  NO.  Jut because the TI-83 says -25 doesn’t mean it’s right.  Calculators use PEMDAS, which states multiplication comes after exponents.  Remember a few mistakes back that the little – sign is a -1 in disguise.  It’s the same here.  If you put “-5^2″ into the calculator, the calculator will square 5 and then multiply by -1.  To square the entire -5, use ( ).  Or just remember that a negative number raised to any even power will always be positive.

(x^4)(x^5) = x^20.  NO!  This is a common mistake kids make.  But if they start by thinking about what “x^4″and “x^5″ mean, it’s easy to see that (x^4)(x^5) expands to (xxxx)(xxxxx).  Parenthesis right next to each other tell us to multiply, so you end up with (xxxxxxxxx) or x^9 or x^(4+5).

(x^4)^5 = x^9.  No, too.  x^4 = (xxxx) and the “^5″ means you have 5 (xxxx)’s.  So (x^4)^5 expands to (xxxx)(xxxx)(xxxx)(xxxx)(xxxx).  Parenthesis right next to each other still say “multiply” so we have 20 x’s in a row, or x^20.

I know there are more.  What did I miss?