Math Section Tips Post

Fractions and Percentages

For those of you who have problems with fractions and percentages on the SAT, GRE, or GMAT, or those who encounter them daily at work (especially those of you whose jobs help change the world for the better!), I present you with some tips:

MEMORIZE THE FOLLOWING COMMONLY USED FRACTIONS (AND THEIR CORRESPONDING DECIMALS FOR CALCULATOR USERS):


1/3 = 33%    **   .333 = 1/3

2/3 = 66% ** .667 = 2/3

1/4 = 25%    **  .25  = 1/4

3/4 = 75% ** .75 = 3/4

1/5 = 20%    **   .2   = 1/5

2/5 = 40% ** .4 = 2/5

1/10 = 10%   **   .1    = 1/10

1/2 = 50% (I know, duh, but it never hurts..)

CONVERTING FROM PERCENT TO FRACTION


    


50 “per cent” means 50 for every 100, or 50/100.  Reduce to 1/2.  20 “per cent” means 20 for every 100, reduce to 1/5.


    


CONVERTING FROM FRACTION TO PERCENT


    


1/3 = x/100 then CROSS MULTIPLY TO SOLVE   or (even easier) DIVIDE 1 by 3 (remember for certain tests such as the SAT calculators are legal) THEN ADD TWO ZEROES (1/3 × 100 = .33 × 100 = 33 percent). 


    


(side note: be careful to use correct terminology when speaking about fractions.   For example,  “one third” means “1 divided by 3” in your calculator (1/3) or “3 (L-shaped divisor sign) 1.00” when doing long division.  Be careful: Don't say “one into 3” or “3 divided by one” because these expressions are incorrect.   Students who like do use long division commonly mistake the two terms, because 1 (long division sign) 3 is actually “3 divided by 1,” not “1 divided by 3.”)


    


THE WORD “OF”


    


This is perhaps the most important idea when it comes to dealing with multiple fractions at once.  The word “OF” ALWAYS MEANS MULTIPLY.  “One third of one fifth” means multiply the fractions.  “75 percent of 80 percent” means multiply the percentages.  Get a calculator and try it. 


    


More examples of this:


    


FRACTIONS OF FRACTIONS


    


Simply write both fractions and multiply.  top by top, bottom by bottom.  ex.  1/2 of 1/2 = 1/4, 1/3 of 1/3=1/9. 


    


FRACTIONS OF PERCENTAGES  (EX. 1/8 OF 60%)


    


Divide 1 by 8, multiply result by .60


    


PERCENTAGES OF PERCENTAGES


    


Move decimal of both figures to the left 2 places, multiply (ex. 50% of 50% = .5 x .5 = .25), then add the zeroes back.


    


PERCENT CHANGE


    


difference/original x 100


    


For example, what is the percent change from 50 inches to 80 inches?


    


(80-50)/50 = (30/50) x 100 = 60 percent. 


    


Please note that the “original” signifies the first term or term that denotes the starting point.  And that 60 percent MORE than 50 is 80, but that 60 percent LESS than 80 is not 50. 


    


This is because the “original” in the first equation is 50, but in the second situation the original is 80.  PERCENT CHANGE DEPENDS ON WHERE YOU START AS MUCH AS YOU MUCH YOU CHANGE.   


    


Ok, that's all for today.  I am 100% tired! 

 

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