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Basic Percent Problem

  1. Jun 17, 2015 #1
    If I am looking for 88% 50, I can put the percent sign on the other number and flip the order of the numbers:

    88% of 50 = 50% of 88 = 44.

    I can solve this numerically but I don't understand conceptually why this works. Why does this work?
     
  2. jcsd
  3. Jun 17, 2015 #2
    Conceptually it's the same thing as (2 x 3) = (3 x 2)
    Percentages are ratios, but are equivalent to a real number and can be treated in exactly the same way.
     
    Last edited: Jun 17, 2015
  4. Jun 17, 2015 #3

    billy_joule

    User Avatar
    Science Advisor

    This may help:

    0.88*50 = (10/10) * 0.88*50 = (10*0.88) * (50/10) = 88 * 0.50
     
  5. Jun 17, 2015 #4

    Mark44

    Staff: Mentor

    Let me fix that for you ...
    0.88*50 = (100/100) * 0.88*50 = (100*0.88) * (50/100) = 88 * 0.50
     
  6. Jun 17, 2015 #5
    Thank you everyone. Mark44, thanks for clearing that up! This does make sense. It's basically the Commutative Property of Multiplication.
     
  7. Jun 17, 2015 #6

    Mark44

    Staff: Mentor

    It's a bit more than that. Your question was why 88% of 50 is the same as 50% of 88. Writing the percent figures as decimal fractions, we have
    ##.88 * 50 = \frac{88}{100} \cdot 50 = 88 \cdot \frac{50}{100} = \frac{50}{100} \cdot 88##
    The latter expression is the same as 50% of 88.

    In the two middle expressions in my equation, I am using the idea that ##\frac a b \cdot c## is equal to ##a \cdot \frac c b##. IOW, it doesn't matter which fraction has the denominator. ##\frac a b \cdot c = a \cdot \frac 1 b \cdot c## and I can group the 1/b factor with either the first number or the last.
     
  8. Jun 17, 2015 #7

    billy_joule

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    Science Advisor

    Oops, thanks!
     
  9. Jun 17, 2015 #8
    So, they are equivalent expressions like was mentioned before. The form a/b * c = a * c/b clears it up. Thank you again.
     
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