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Ex: Determine Percent of Change - Increase and Decrease - YouTube
Channel: Mathispower4u
[0]
we want to determine the percent of
[1]
change based upon each description
[4]
the percent of change formula is given
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here below
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where the percent of change is equal to
[8]
the new amount
[10]
minus the original amount this gives us
[12]
the amount of change and then we divide
[15]
by the original amount
[16]
this quotient gives us the percent of
[18]
change as a decimal so to convert to a
[20]
percentage
[21]
we multiply by 100 not a percent sign or
[24]
we can just think of multiplying by 100
[26]
percent
[27]
looking at all of our descriptions above
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the amounts change from the first amount
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to the second amount so the new amount
[33]
is always going to be the second amount
[35]
or second value
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and the original amount is always going
[40]
to be the first amount or the first
[42]
value
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in each case it's changing from the
[49]
first amount to the second amount
[52]
so for our first description the
[53]
quantity decreases from 20 to 15
[57]
so the percent of change
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is going to be equal to 15 minus 20
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divided by 20.
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again we have the new amount minus the
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original amount divided by the original
[71]
amount
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and then times one hundred percent
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notice here we'd have fifteen minus
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twenty that's going to be negative five
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so we have negative five
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divided by twenty times one hundred
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percent
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this does simplify to negative 1 4 let's
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just go to the calculator
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when we find this product though we
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won't enter the percent sign in the
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calculator
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so we have negative 5 20
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or negative 5 divided by 20
[99]
times 100
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which is equal to negative 25
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so the percent of change is negative 25
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percent notice how it's negative this
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indicates we have a decrease but because
[111]
the decrease is mentioned in the
[112]
description we don't include the
[114]
negative
[116]
this is a 25 percent decrease
[118]
if the question was give the percent of
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change we would say negative 25 percent
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but because of the description including
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decrease we don't include the negative
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next we have a quantity that increases
[128]
from 15 to 20.
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so again now 20 is a new amount so our
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numerator is going to be 20
[135]
minus 15
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divided by the original amount of 15
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times 100 percent
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well twenty minus fifteen is equal to
[145]
five so now we have five fifteenths or
[148]
one third i'll leave it as five
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fifteenths
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times one hundred percent
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and now we'll go back to the calculator
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so now we have in parentheses five
[158]
divided by 15
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closed parenthesis times 100
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so now the percent of change is
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approximately 33.3 percent
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notice how this time it's positive
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which indicates we have an increase
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which we do know though because it does
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tell us that
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so if something changes from 15 to 20
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that would be a 33.3 percent increase or
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approximately
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next we have the price of a latte drops
[188]
from three dollars 12 cents to
[190]
2.83 cents
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so again the lower price here is the new
[194]
amount
[195]
so we'd have
[196]
2.83
[198]
minus 3.12
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divided by the original amount of three
[203]
dollars and 12 cents or just 3.12
[207]
times 100
[209]
which is going to be equal to well this
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difference here is now negative
[212]
which we do know because
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we do have a decrease or a drop in price
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so we have negative 0.29
[220]
divided by 3.12
[222]
times 100
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back to the calculator
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in parenthesis we have negative 0.29
[233]
divided by 3.12
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close parenthesis times 100.
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so we have approximately negative 9.3
[243]
percent
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which means we have a 9.3 percent
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decrease
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and for our last question the cost of
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gasoline rose from two dollars
[256]
eighty-three cents to three dollars 12
[258]
cents now the new price is the higher
[260]
price
[261]
so we have 3.12 minus 2.83
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divided by the original of 2.83
[270]
times 100
[273]
now this difference is going to be
[274]
positive
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0.29 or positive 0.29
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and of course the denominator is
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different from the last time
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so now we'll go back to the calculator
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open parenthesis 0.29
[292]
divided by 2.83
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close parenthesis times 100 to convert
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to a percentage
[300]
so we have approximately 10.2 percent
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again notice how it's positive
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indicating we have an increase which is
[307]
correct we have approximately 10.2
[309]
percent increase
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okay i hope you found this helpful
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