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Wednesday, December 18, 2013

Andrei's Percent

Percent is another way of writing a ratio when the second term of the ratio is 100.  Percent comes from the Latin words pars per centum meaning parts per hundred. We use % to express percent.

Example:
18/100 = 18%

25/100 = 25%

 If the denominator is not 100,  multiply the numerator and the denominator with the same number which will make the denominator equal to 100.

Example:

4/5 =4/5 x 20/20 = 80/100  or 80%

1/2 = 1/2 x 50/50 = 50/100 or 50%   means half of whole

1/10 = 1/10 x 10/10 = 10/100 or 10%  means 1 part of a whole

1/4 = 1/4 x 25/25 = 25/ 100 or 25%  means quarter of a whole
















































































































































































































   













3. Converting Percent to Decimal to Fraction

Fraction to  Decimal  to  Percent

3/40         =     0.075   =    7.5%

to decimal
divide 3/40 = .075
to percent
move the decimal point 2 places to the right and add the percent % sign
    0.075 = 7.5%



Decimal  to Percent to  Fraction

0.0064     =   0.64%      =  0.0064/10000  or       4/625
                                                             



to percent
move the decimal point two places to the right and add the percent sign %
    0.0064 = 0.64%
to fraction
multiply both the top and bottom by 10 for every number after the decimal point
0.0064/1  x 10 000 /10 000 =  64/ 10 000  or 4/625




Percent to Decimal  to  Fraction

75%   =       0.75        =     75/100 or 3/4

to decimal
move the decimal point 2 places to the left and remove the % sign
75% = 0.75
to fraction
75/100 = 3/4

4. Finding Percent of  a number
 
  solve:
                                                                
  a. 20% of 60
      Mental Math                                                                   Calculator

      100% of 60 is 60                                                          convert 20% to decimal
      10% of 60 is 6                                                               20%  is 0.20
       20% is 10% + 10%                                                      multiply 0.20 by 60
       10% + 10% = 6 + 6                                                      0.20 x 60 = 12
        20% = 12

   b0.1% 
        Mental Math                                                                Calculator

       100% of 40 is  40                                                        convert 0.1% to decimal
       10% of 40 is  4                                                             0.1% is .001
       1% of 40 is  0.4                                                            multiply .001 by 40
        0.1% of 40 is  0 .04                                                     0.001 x 40 = 0.04
        0.1 % of 40  = 0 .04




   c.  250% of 400
       Mental Math                                                                 Calculator

       100% of 400  is 400                                                    convert 250% to decimal
       50% of 400 is 200 ( 400/2)                                         250%  is 2.50
       250% is 100% + 100% + 50%                                   multiply 2.50 by 400
       100% + 100% + 50% =  400 + 400 + 200                2.50 x 400 = 1000
       250% of 400  = 1000

5. Combining Percents

   * Discount is  a deduction from the usual cost of something.
   * Sale Price is the price of a good service that is being offered at a discount.
   * Total price with taxes is the total amount and tax charges for all items being purchased.

Example:
    * A herd of 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 30% increase in population over  two years.
  
 Solution:
  
      a.  Population of caribou is 100
           increase in first year    is  10%
                 10%  of 100   or  0.10  x 100 = 10
           population of caribou after one year is 100 + 10 = 110

          New population of caribou ( after one year)  is 110
           increase  in second year is  20%  
                 20% of 110 or  0.20  x  110 = 22
           population of caribou after second year is 110 + 22 = 132
                    
       b.  There was not a 30% increase in population over two years because after a year, the
             population increased by 10% , it became 110 and this new population was increased 
             by 20% which gave a total population of 132 caribou after the second year.
             If population was increased by 30% over two years,  the original population 100 will be 
             increased by 30%  which will result to 130 population.


*Show you know*
     What is the final price at each store.  Which is the 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:
     Store A :  50% of $200 (one day only)
                      0.50 x 200 = 100
    Find the discount price:
                      200 - 100 = 100
    The discount price is $100.

    Store B:  25% discount of $200 on the first day
                    0.25 x 200 = 50
     Find the discount price
                     $200 - 50 = 150
     The discount price after the first day is $150.
     
     The discount  on the sale price the second day is  25% of $150.
                   0.25 x 150 = 37.5
      Find the discount price:
                   $150 - 37.5 = $112.50
       The final discount price after the second day is $ 112.50.


     *** Store A gives the better buy than store B.  The 25% discount followed by another 25%
           is not the same as 50% discount from the original price because the discount on the 
           second day is only 25% of  $150 and not 25% of $200.


      The original price is $200.  The selling price after two 25% discount is $112.50
                   $200 - $112.50 = $87.50
                   $87.50 ÷ 200 = 0.4375  or  0.44  which is 44%
  
     ***  The total discount offered by store B is 44% which is less than 50% discount offered
            by Store A, therefore Store A gives the better buy.
         



 Video that will help us understand how to find a percent of a number.


 


      





























































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































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