How can i use the percent .what number is 40% of can u solve this one, too.: 45 is 25% of what you

I've been waiting for someone to ask this question.  It's one of my favorite questions to answer.

percent means out of 100 so 1% = 1/100 and 40%=40/100 or 1/25
so for percent of a number, 'of' means multiply so 40% of 500= 40/100 times 500 or 20000/100 or 200

if you multiply a fraction by its recipricol (the number fliped upside down) the you will get 1 so if you multiply 1/2 by 2/1 then you will get 1

thus
percent is out of 100 so 1%=1/100  25%=25/100
if you represent 45 out of something as 45/x then you multiply it by the reciprocal of the fraction that is supposed to be equal (1/2 =2/4) then you will get 1
so 45/x times reciprocal of 100/25 then you will get 1/1 or 4500/25x
so you divide to find x and get 180
so 45 is 25% of 180

The following is extra
   as stated above 'of' can be taken as multiply so
   45 is 25% of 180 can be rewriten as
   45=25/100 times 180
   but we don't know that 180 is the answer so we replace it with x then            solve for x

200 is 40% of 500. 
45 is 25% of 180.

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