Adding and Subtracting Fractions… the crisscross method! June 6, 2011

Afterwards, you will invariably need to reduce your fraction.  To do this quickly, and without thinking, bust out your TI-83 graphing calculator and press:

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MATH > 1:Frac > ENTER > ENTER

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Not knowing how to add and subtraction fractions with just a pencil and piece of paper is not good, but if you’re in a pinch and have a history term paper due, go for it.  The above TI-83 button commands also work to convert rational decimals back into their fractions.

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Disclaimer: In no way will this method help do anything except get through your current homework assignment on adding and subtracting fractions.  I know you don’t believe me because my 12-year old self wouldn’t believe me, but solving fraction problems without a calculator is an important piece of higher math.

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calculators KILL negatives! (uh, raised to even exponents, that is:) May 17, 2010

 

What’s negative 2 to the fourth power?  16?  -16?  If you put “-2^4″ into the TI-83, you get -16.  But we know that (-2)(-2) = 4 and (-2)(-2) = 4, and (4)(4) = 16.  So why does the calculator give us -16?

 

This post is no doubt for the high schooler and not for someone addicted to the )( buttons on the calculator like I am.  I parenthesize.  It comes from a fear that something will go negative that should be positive.  I have reminded my students more times than I can count to parenthesize, so many times, in fact, that I am more than sure that most tune me out as soon as they hear the first syllable.  But still the negative raised to an even number sneaks past the best of ‘em.

 

The evil negative base reared its ugly head again today when I graded papers on the geometric sequence an = a1 • r^(n-1) where:

an = the value of the nth term

a1 = first term’s value

r = ratio of change (ie “doubling” would be 2)

n = the terms placement (ie: 5th term would be n = 5)

 

“Find a7 if a1 = 5 and r = -2.”  The answer I or course got more than the correct answer was ” -320″.  What should the answer be?  “320″.  The problem should be written out first as: 5(-2)^(7-1) to make the process clear.

 

At least no one gave -1,000,000 as an answer.  There’s still hope!