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Wednesday, December 18, 2013

Pam's Percent Post

Notes:
  • Percent means/is an equivalent fraction that is out of 100.

ex. 9/10 x 10/10 = 90/100 or 90%.

  • Percent is out of 100 because "It's just right" and it's "easily seen", and it could also be a friendly number.
  • The percent symbol (%) includes two zeros and the division sign. The division sign is the 1__ and the two zeros are _00 making it 100.
  • In French, the word percent is split into two parts, "per" being "out of" and "cent" being "100".
  • You may be asked, is 205% still a percent? even though it's past 100? It still can be. It's 205/100.
  • Percent can be an "improper fraction" meaning that the numerator is greater than the denominator in a fraction. Another word for this could be "Top Heavy". ex. 5/4
100%- means all, whole, everything.

50% - means half, part/whole, 20/40 or 50/100

   %    |  apples
  100  |   40
    50  |   20
*We divided both sides by 2.

10% - is 10/100

   %    |  apples
  100  |   40
   10   |    4

25% means 25/100 or 1/4
 
   %    | apples   
 100   |    40
   25   |    10
*We divided both sides by 4.

1% - means 1 out of 100 or 1/100
*To find 1% of something, divide the number by 100.

   %    | apples
   100 | 40
     1   | 0.4
*We divided by 100 on both sides (what you do to one side, to do to the other).

Representing Percent



180 %







____________________________________________________________________________








0.6%

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    12 3/8 %
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FRACTION - DECIMAL - PERCENT

3/40   Numerator ÷ Denominator = Decimal
                           ÷ 40 = 0.0.75  x 100   =   7.5  or 7.5%
                                            1     x 100        100
_____________________________________________________________________________________               

DECIMAL - PERCENT - FRACTION

0.0064    0.0064  x 100      0.64  or 0.64%        0.0064
                   1       x  100     100                             10000

_________________________________________________________________________

PERCENT - DECIMAL - FRACTION

0.3% ÷ 100  =  0.003    3     
                                         1000

_________________________________________________________________________

                                                PERCENT OF A NUMBER

MENTAL MATH                                                                     CALCULATOR

20% of 60 -             %  |  #                                                    20   20 ÷ 100 = 0.2
                             100  | 60                                                  100
                (÷ 5)       20  | 12                                                
                                                                                             0.2 x 60 = 12

* 0.2 is 20% and you must find the decimal of 
the percent by dividing the percent by 100.
                                                                                                                                                        

0.1% of 40  -          %   |  #                                                  0.1     0.1 ÷ 100 = 0.001
                              100 | 40                                                100
              (÷ 1000)   0.1 | 0.04
                                                                                            0.001 x 40 = 0.04
* when dividing 10, 100, 1000, etc, you
move the decimal place by how much zeros
there are in the number you are dividing by.
When there is no decimal, the decimal is always
on the right side of the ones place value.
     
                                                                                                                                                        
250% of 400 -        %  |  #                                                  250           250 ÷ 100 = 2.5
                             100 | 400                                               100
                     (x2)  200 | 800
       (÷ 2 from 100)    50 |  200                                              2.5 x 400 = 1000


800 + 200 = 1000

                           
___________________________________________________________________________

5.                                                 COMBINING PERCENT                                                     

Question 7 -page 149                                                            
                                                                                             
A herd of 100 caribou was moved to a new 
location. The population increased by 10%
the first year and then increased by 20% the
second year.
a) Find the population after the second 
year.

b) Explain why there was not a 30% increase
in population over the two years.
__________________________________________________________________________

WORK :




first year

                  - The caribou population (the whole or 100%) was increased by 10%, meaning that 10% was added to the whole, so you could just find 110%.
   
            100%         - caribou
            + 10%        -increase in population
            110%

             110            110 ÷ 100 = 1.10
             100                                            1.10 x 100 = 110



    second year


- This is now the new percent since you are trying to find
a percent of a percent. You try to find 20% of 110 caribou
instead of the original 100 caribou. The 20% must be added into
the 100% (110 caribou)
or only use one step:

             100%             120 ÷ 100 = 1.20    1.20 x 110 = 132
            + 20%                                    1
             120%               On the second year, there were 132 caribou.



explanation

There was not a 30% increase over the years because if it was
30% increase, it would of been 130 caribou. This was not the same
and we did not get the same answer as a 30% increase because in the process
of finding 20% of 110 caribou and adding the 20%, we also had a new 100% or
a new all. This is finding a percent of a percent.

__________________________________________________________________________

Show You Know pg. 148

What is the final sale price at each store? Which is a better buy?
Explain your thinking.
Store A : 50% one day only
Store B : 25% off one day followed
by 25% off the reduced price the
second day

example price for both BAGS : $50

Store A
for one day:
50% off (discount ) of $50.
Since this is the discount, the discount is what you save, while the sale price is what
you pay. You could just find the sale price but since this is 50%,
you could just half the number at this point.

50÷2 = 25

$25 is the reduced price, or the amount you are now paying (not including taxes).


Store B

first day:
25% off of $50

 25       25 ÷ 100 = 0.25
100

0.25 x 50 = $12.50

Since this price is the discount, we try to find the sale price. The
sale price is 75% (subtracting 25 off of 100).
Then we subtract $12.50 from $50 = $37.50
You pay $37.50.

* You could have just found 75% of $50 rather than finding 25%
then subtracting that number from the regular price.

second day:
25% off of $37.50 (new 100%)

 25      25 ÷ 100 = 0.25
100

0.25 x 37.50 = $9.38

$37.50 - $9.38 = $28.12
conclusion

In conclusion to this math problem, store a would have been the better buy.
Store A is offering $25 for a bag while Store B is offering $28.12 on the second day.
If you choose Store A over Store B, you'll save $3.12 compared to Store B's price.
Again, for Store B, it's different from Store A because Store B includes you to find
a percent of a percent meaning there will be a new 100%.

 Overall, Store A has a better buy.

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