If I had a penny for every time I saw this mathematical mistake I'd be a BILLIONAIRE!

[srmichael]

So seeing a classic mathematical mistake in a recent thread prompted me to list out 5 of the most common mistakes I see kids make. Feel free to add to my list as I know there are many more out there. I figure this thread can also do a lot of good by consolidating many of the mistakes that we see posters on this forum do and thus, hopefully, not continue to do.

1) INCORRECT: Improper expansion of a binomial:$\displaystyle (x\pm 3)^2 = x^2+9$
CORRECT: $\displaystyle (x\pm 3)^2 = x^2\pm 6x+9$

2) INCORRECT: Taking the square root of each individual term:$\displaystyle \sqrt{x^2+9} = x+3$
CORRECT: $\displaystyle \sqrt{x^2+9}=\ literally \ \sqrt{x^2+9}$ Obviously, if $\displaystyle x^2$ was an actual number than just add it to 9 and take the square root of the resulting number.

3) INCORRECT: Cancelling a term when it is being added or subtracted with another term:$\displaystyle \frac{x+5}{x}=\frac{\otimes+5}{\otimes}=5$ (The $\displaystyle \otimes$ means the "x" is being cancelled. Couldn't figure out how to do a strikethrough on it )
CORRECT: $\displaystyle \frac{x+5}{x}=\frac{x}{x}+\frac{5}{x}=1+\frac{5}{x}$ (for this specific example)

4) INCORRECT: Failing to apply the exponent to a number when simplifying a rational expression:$\displaystyle (\frac{4x^4y^2}{z^3})^3 = \frac{4x^{12}y^6}{z^9}$
CORRECT: $\displaystyle (\frac{4x^4y^2}{z^3})^3 = \frac{4^3x^{12}y^6}{z^9}=\frac{64x^{12}y^6}{z^9}$

5) INCORRECT: Thinking a number raised to a -1 makes the value negative:$\displaystyle 5^{-2} = -25$
CORRECT: $\displaystyle 5^{-2} = \frac{1}{5^2}=\frac{1}{25}$

 

[JeffM]

I promise not to do it again (unless denis distracts me).

 

[daon2]

I attached some of these to my recent syllabus for a calculus course. I quickly learned that no one pays attention to a syllabus, let alone anything attached to it.

 

[Nehushtan]

Couldn't figure out how to do a strikethrough on it

$\displaystyle \dfrac{\not x + 5}{\not x}$

 

[srmichael]

$\displaystyle \dfrac{\not x + 5}{\not x}$

Not quite. But good try.

 

[lookagain]

So seeing a classic mathematical mistake in a recent thread prompted me to list out 5 of the
most common mistakes I see > > > kids < < < make.

I would choose the word "inexperienced." There are middle-aged and senior-aged students who make them, too.


- - - - - - - - - - - - - - - - - - -


Here is another one that some people with doctorates in mathematics (that I have personally come to know) don't know:


Incorrect:


$\displaystyle Example:$


$\displaystyle -5x < 30$


$\displaystyle \dfrac{-5x}{-5} < \dfrac{30}{-5}$


$\displaystyle x > -6$


- - - - - - - - - - - - - - - - - - - -


Correct:


$\displaystyle -5x < 30$


$\displaystyle \dfrac{-5x}{-5} > \dfrac{30}{-5}$


$\displaystyle x > -6$

 

[soroban]

Hello, Nehushtan!

A few at a higher level . . .


INCORRECT: .$\displaystyle \log(A + B) \:=\:\log A + \log B$

CORRECT: .No simplification is possible.


INCORRECT: .$\displaystyle \sin(A+B) \:=\:\sin A + \sin B$

CORRECT: .$\displaystyle \sin(A+B) \:=\:\sin A\cos B + \cos A\sin B$


Recently I saw this in a post:

. . $\displaystyle \sin 3x + \cos 3x \:=\:3(\sin x + \cos x)$


~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


I see that \cancel does not work here.

I am forced to use \rlap.

\rlap{///}abc writes the "///" on top of the "abc": .$\displaystyle \rlap{///}abc$


\dfrac{x^2 + \rlap{/}x + 6}{\rlap{/}x} \;=\; x^2 + 6

. . produces: .$\displaystyle \dfrac{x^2 + \rlap{/}x + 6}{\rlap{/}x} \;=\;x^2+6$


$\displaystyle - - - - - - - - - - - - - - - - - - - - - - - - - - -$


Some mathematical jokes . . .

. . $\displaystyle \displaystyle \frac{1\rlap{/}6}{\rlap{/}64} \:=\: \frac{1}{4} \qquad\quad \frac{1\rlap{/}9}{\rlap{/}95} \:=\:\frac{1}{5} \qquad\quad \frac{2\rlap{/}6}{\rlap{/}65} \:=\:\frac{2}{5}$

 

[Deleted member 4993]

[h=2]If I had a penny for every time I saw this mathematical mistake I'd be a BILLIONAIRE![/h]So seeing a classic mathematical mistake in a recent thread ...

Sir Michael do not exaggerate!!

Billionaires will have at least 10¹¹ pennies.

If you saw one mistake/sec - that would take at least 3168 years!!!

You may be old - old like an English knight - but surely you jest!!!!