Percent Word Problems Flashcards
what does “percent” mean?
divide by 100 (ex. 500% means 500/100 or 5)
how do you express a decimal as a percent?
multiply by 100 and attach % sign
how do you express a fraction as a percent?
multiply by 100 and attach % sign
how do you go from percent to decimal?
drop % sign and divide by 100
what are the two methods that can be used to find the percent of an unknown amount?
1) represent the unknown amount by x
2) assume the unknown amount is 100 items
what does “percent of” mean?
it indicates you will be multiplying a given percent by a given number (ex: 40 percent of 100 is (40/100)*100 = 40
various “percent of” translations:
1/10 percent of x -> (1/10)/100 = 1/1000 ->x/1000
700 percent of x -> 700/100 -> 7x
what are examples of “what percent” problems
1: 100 is what percent of 50
how do you attack a “what percent” problem?
let “what percent” be represented by x/100
how would you set up the equation to solve “105 is what percent of 15?”
105 = (x/100)*15
what is the formula for “percent less than” problems?
final value = (initial value)*(1 - (“percent less than”/100)), where “percent less than” is the percentage amount that it is reduced - so if we are told the value is reduced 20% the last part would be 1 - 20/100
“percent less than” to “percent of” translations
what is the formula for “percent greater than” problems?
final value = (initial value)*(1 -+(“percent greater than”/100)), where “percent greater than” is the percentage amount that it is increased
in percent greater than problems, x% greater than y is equivelant to?
(100+x)%*y
“percent greater than” to “percent of” translations
if we increase something by 100% what does that do to the size of it?
doubles it, increases by 2 times - > 100 % greater than z = (1+100/100)z = (200/100)z - >translates to 200% of z
“percent greater than” or markups, and “percent less than” mark down with variables are the same, you just use a variable instead of the actual % - true or false?
true
how do you handle successive percent changes?
multiply the successive changes
ex: in attached photo
what does “percent change” of a value indicate
the size of the increase or decrease of a value after a change in that value has occurred
percent increase is simply a…
percent change of a value that has gone up
percent decrease is a
percent change in a value in that has gone down
what is the formula for percent change?
% change = ((final value - initial value)/initial value) * 100
what other formulas can you use to calculate % change?
the percent greater than and percent less than formulas
if you discount a $100 dress by 20%, it then costs $80. Will marking up the discounted dress by 20% get you back to the original price of $100?
no, since 20% of the smaller number 80 is not 20, its 16, so increasing the cost of the dress by 20% yields a price of $96
what is percent profit?
when we express profit as a percentage of cost. So % profit = (profit/cost)*100
can percent profit be negative?
yes, if costs exceed revenue your % profit will be negative since it will be % profit = (-profit/cost)*100
how do you find the fractional change of something?
use the percent change formula without the multiplication by 100 at the end. ex: what is the fractional change in the price of a house that went from 250k to 450k dollars? -> (450-250)/250=150/250=3/5
n is what percent of x (in addition to being formulated as n=(p/100)*x) could be expressed as?
n/x, since if n=2, and x=3 it would read, 2 is what percent of 3, and that is .66 from which you can get 66%
