Monday, 1 October 2018

P1 Percentage

PERCENT
"Percent % " means
"per 100"   or  'out of 100'  or  ‘per 100 of the total value’.
         -> the first quantity usually represents a part of, or a change in, the second quantity.

Defining Percent
Percent means “per 100” =>
            60% = 60 / 100
            25% = 25 / 100

Example:
What is 1 per 100 as a percent?
    1 per 100 means ‘1 out of 100’  -> 1 is 1% out of a total value of 100 -> 1%  

Relating to Fractions:
  => Part/Whole x 100 = % 

Diagram illustration:

Examples
 (a) What is the 25 per 100 in percent?

       25 per 100 -> 25%
       Diagram illustration:
             
 (b)  What is the percent of 100 out of 100?
       100 per 100 -> 100%
               

Why do we use percentage?
We can use percentage to help us:

(1) Compare 1 quantity with another.
            
     Duracell battery last 35% longer as compared to the next competing batteries
  (2) Express how large or small one quantity to the total quantity

               25% out of the full battery (out of 100%) is left

(3) Express change(increase or decrease) of quantity in relative to its original quantity.


Calculating Percentage
Common sentence construct in Percent:
            P as a percentage of Q -> OF VALUE.

   The OF ‘VALUE’ is the Total Value -> it has a percent of 100% (or as stated)
     
Formula
                        Percent = (Required) Value   x 100%
                                             Total Value

Example: 
     Express 20 cm as a percentage of 250cm.

Formula Method
Step1: Circle/Underline Keyword [20cm, as a percentage, 250]
Step2: Write Formula. Which value is required [percent]? and ‘fill in’ given values
            Percent = Given Value x 100
                              Total Value
         --> answer required is 20 as a percent of 250 --> percent of given value
                        250 is the total value, and 20 is the given value  
                   
Step3: Solve             
                        Percent of 20cm = 20
                                    100             250
                        Percent of 20cm = 20 x 100
                                                        250
                                                   = 8%

Example:
40% of a number is 76. What is 100% of this number?
Step1: Circle/Underline Keyword [40% of number, 76, 100%]
Step2: Draw/Write Formula. Which value is required [percent]? ‘Fill in’ given values
            Percent = Given Value x100
                            Total Value

         --> answer required is value of 100% of number
                                               
                         40 = 76
                        100  Total value
Step3: Solve
                         40 = 76
                        100   Total value
              Total value = 76 x 100
                                            40
                                = 190
Example
40% of a number is 76. What is 150% of this number?
Method
Step1: Underline Keyword [40% of number, 76, 150%]
Step2: Write Formula. Which value is required [percent]? and ‘fill in’ given values
            Percent of a given value = Given Value
                         100                         Total Value
         --> answer required is value of 150% of number,   40% is 76   
                   
       
       Formula 150% required is
            Percent = Given Value x 150
                              Total Value                       
40 = 76  x 150
     Total value
Step3: Solve
              Total value = 76 x 150
                                             40 

                                 = 285
One-percent Method
This method is to compute the value of 1%, and then multiply it with the required value. It is similar to the cross-multiply method. It provides a more detailed breakdown for easy understanding.

Example:
Express 50 cm as a percentage of 250cm
Step 1: Circle/Underline keywords. Determine value for 100% -> 250cm
Step 2: Find value of 1%
             100 % - > 250
                  1% - > 250 / 100
                   1% -> 2.5cm
Step3: Solve
50cm -> 50 / 2.5 (per 2.5 -> divide)
         = 20%

VIDEOS
Solving Percentage Question : using the 1% method
https://www.youtube.com/watch?v=jvT41F4Aje8&feature=youtu.be

Solving Percentage Question : Using Model
https://www.youtube.com/watch?v=1q-dvhX3lEs&feature=youtu.be

 Converting Percent to Fractions
Percent can be expressed as #/100
            29% is 29/100 (29/100 is a fraction)
Example
Convert 15% to fraction.
Method
Step1: Express percent as  #/100
15% = 15/100
Step2: Simplify fraction to lowest term
        = 15 3 /100 20
               = 3 / 20
Example:
 (1) 0% = 0/100
             = 0
(2) 100% = 100/100
                = 1
(3) 120% = 100/100 + 20 1 /100 5
            = 1 + 1/5
            = 1 1/5

Converting Fractions to Percent
Example:
Express 1/2 as percentage

Step 1: Multiply by 100
            ½ x 100 = 50
Step 2: Express the fraction as percent
             1/2 as percent is  50%

Example:
Express 3/4 as a percentage
Step 1: Multiply by 100
            ¾ x 100 = 75
Step 2: Express the fraction as percent

            ¾ as percent is 75%

Converting Percent to Decimal
Example
Express 26% as a decimal.
Method:
Step1: Change % to    #/100
            26% - > 26/100
Step2: Change    2/100 to 0.#
            26/100 = 0.26
Example
  Express 37% as a decimal.
Method:
Step1: Insert decimal point (if required)
            37% = 37.0%
Step2: Shift decimal 2 places to the left
            37.0% = 0.37

Converting Decimals to Percent
Example
 Convert 0.345 to percent
Method
Step: Move Decimal point 2 places to the right
            0.345 = 0.0345 x 100% = 34.5%

SUMMARY
Expressing Percentages as Fractions and Decimals
Percentage
÷ 100
Fractions
Decimals
8%
8 ÷100 = 8 / 100
 2/25
0.08
25%
25 ÷ 100 = 25 / 100
 1/4
0.25
30%
30 ÷ 100 = 30 / 100
 3/10
0.3
50%
50÷ 100 = 30 / 100
 1/2
0.5
62.5%
62.5 ÷ 100 = 625 / 1000
 5/8
0.625
75%
75 ÷100 = 75 / 100
 3/4
0.75
80%
80 ÷ 100 = 80 / 100
 4/5
0.8
97.5%
97.5 ÷ 100 = 975 / 1000
 39/40
0.975
                      ~~~~ END ~~~~ :)
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