Percent Equations

Key Questions

  • Answer:

    See example

    Explanation:

    Using an example:

    Suppose we had a big animal sanctuary for cats and dogs.

    We had say 30 cats and 50 dogs

    So by proportion we have:

    #color(blue)("Using format type 1")#

    #"cats : dogs " ->30:50->3:5# as ratio (proportions)

    But for #3:5# we have 3 parts in combination with 5 parts giving a proportion total of #3+5=8#

    Converting this to fractions and hence percentage

    Cats
    #=3/(3+5)=3/8 -> 3/8xx100% =color(white)("ddd") 37.5%" of the whole"#
    Dogs
    #=5/(3+5)=5/8->5/8xx100% = color(white)("ddd")ul(62.5%" of the whole" #
    #color(white)("ddddddddddddddddd")"Added up "->100.0%" all of the whole"#

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

    #color(blue)("Using format type 2 - Fraction format") #

    #("cats")/("dogs") ->30/50 ->3/5 larr" This is NOT a fraction of the whole"#

    Again we have

    #("cats")/("cats + dogs")->3/(3+5)xx100% = 37.5%" of the whole"#

    #("dogs")/("cats + dogs")->5/(3+5)xx100% =ul( 62.5%" of the whole")#
    #color(white)("ddddddddddddddddddddddddddd")100.0%#

  • Rememdber that "per" means "divided by", and "cent" means 100, so "percent" means "divided by 100" or "out of 100."

    If a question says "A is a 29% of B," then you can write

    #A=29/100 B#.


    I hope that this was helpful.

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