MATH STUDY SKILLS Presented by Janice Levasseur

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MATH STUDY SKILLS Presented by Janice Levasseur Powered By Docstoc
					     % and the
 BASIC PERCENT
   EQUATION

MSJC ~ Menifee Valley Campus
Math Center Workshop Series
                   Janice Levasseur
            % Percents %
• Percent means “parts of 100” or “per 100”
• A percent can be written using a percent
  sign (%), as a fraction, or as a decimal
  Converting a % to a Fraction
• To convert a percent to a fraction,
  translate the % symbol:
• Remove the % sign and divide by 100
  (“per 100”)
Ex: Convert 27% to a fraction
           27      Simplify ? No . . .
  27%                         done
          100
Ex: Convert 25% to a fraction
       25      
25%               Simplify?     YES!
      100
       1    Simplify? No . . .
     
       4              done
Ex: Convert 130% to a fraction
       130
130%         Simplify?    Yes!
       100                 Improper
                           Fraction
         30
    1
        100   Simplify?    Yes!

         3
    1        Simplify? No . . .
        10              done
             1
Ex: Convert 3 % to a fraction
 1      1              1
             Divide
   % 3                 100
 3     100   fractions 3

      1 100 1 1
            
      3 1       3 100
        1
          Simplify? No . . .
      300
                   done
Ex: Convert 0.5% to a fraction
0.5% 
       0.5    Divide decimals?
       100    Decimal  Fraction
       1
       100
       2
      1 100 1 1            1
                    
      2 1      2 100      200
             Simplify?   No . . .
                         done
Your Turn to Try a Few
   Converting a % to a Decimal
• To convert a percent to a decimal,
   translate the % symbol:
• Remove the % sign and divide by 100
  (“per 100”) or
• Move the decimal point two places to the left
Ex: Convert 27% to a decimal
27% = 27    100    27.0 =
                          0.27

Ex: Convert 25% to a decimal
25% = 25    100    25.0 =
                          0.25
Ex: Convert 130% to a decimal
 130% = 130  100  130.0=
                         1.30

Ex: Convert 0.5% to a decimal
 0.5% = 0.5  100  0.5 = 0.005
            1
 Ex: Convert % to a decimal
            3
• We are starting with a percent written as a
fractional percent
• First convert the fractional percent to a
fraction (drop the % sign and divide by 100)

1        1 1    1                 Fraction
   100                        form of
3        3 100 300                the
                                  answer
Ex: cont.   • Recall: To convert a fraction to
            a decimal number, divide the
            numerator by the denominator

  1              .0033
                                0.003
 300        300 1.0000
                  900
                  1000
                   900
                   100
Your Turn to Try a Few
  Converting a Fraction to a %
• To convert a fraction to a percent,
  reverse the procedure for converting a
  percent to a fraction:
• Multiply by 100 and add the % sign
Ex: Convert ¼ to a percent
1          1 100
   100%       %
4          4 1
           100
              %     Simplify? Yes!
            4
       = 25%
Ex: Convert 1 ½ to a percent
 1         3 100
1  100%       %
 2         2 1
           300
              %     Simplify? Yes!
            2
        = 150%
Ex: Convert 5/8 to a percent
5                        Simplify?
           5 100
   100%          500
                 %     % Yes!
8          8 1       8
            4
         62 % Simplify? Yes!
            8
            1
         62 % Simplify? No . . .
            2            done
Ex: Convert 5/6 to a percent
5                        Simplify?
           5 100
   100%          500
                 %     % Yes!
6          6 1       6
            2
         83 % Simplify? Yes!
            6
            1
         83 % Simplify? No . . .
            3            done
Your Turn to Try a Few
  Converting a Decimal to a %
• To convert a decimal to a percent,
  reverse the procedure for converting a
  percent to a decimal:
• Multiply by 100 and add the % sign 
• Move the decimal point two places to the
  right
 Ex: Convert 0.36 to a %
0.36 100%  0.36 = 36%



 Ex: Convert 0.01 to a %
0.01 100%  0.01 = 1%
  Ex: Convert 3.19 to a %
 3.19 100%  3.19 = 319%


  Ex: Convert 0.005 to a %
0.005    100%    0.005 = 0.5%
Your Turn to Try a Few
        The BASIC PERCENT
             EQUATION
 • The Basic Percent Equation is given by
   Percent x Base = Amount
• The Percent has the percent sign %
• The Base always follows the word “of”
• The other number is the Amount
      Ex: 5% of 120 is what?
• Identify the three components (remember,
the base always follows “of”, the
multiplication, and the equals.
                Percent = 5%
                Base = 120 (follows “of”)
                Amount = Unknown “what”  a
  • Translate the English statement to the Basic
  Percent Equation:
                      5% x 120 = a
Ex: Cont.         5% of 120 is what?
 • Now solve the mathematical equation:
 5% x 120 = a       Rewrite the % in working form

 0.05 x 120 = a     Perform the math operation

 6.00 = a

  Therefore, 5% of 120 is 6.
      Ex: What is 6.3% of 150?
Identify the three components (remember, the base
always follows “of”, the multiplication, and the equals.
      Percent = 6.3%
      Base = 150 (follows “of”)
      Amount = Unknown “what”  a
 • Translate the English statement to the
 Basic Percent Equation:     a = 6.3% x 150
Ex: Cont. What is 6.3% of 150?
 • Now solve the mathematical equation:
 a = 6.3% x 150     Rewrite the % in working form

 a = .063 x 150     Perform the math operation

 a = 9.45

  Therefore, 9.45 is 6.3% of 150.
     Ex: 5% of what is 28?
• Identify the three components (remember,
the base always follows “of”, the
multiplication, and the equals.
Percent = 5%
Base = Unknown “what”  b (follows “of”)
Amount = 28
• Translate the English statement to the Basic
Percent Equation:   5% x b = 28
Ex: Cont. 5% of what is 28?
 • Now solve the mathematical equation:
 5% x b = 28        Rewrite the % in working form
                    Solve the equation by
 0.05 x b = 28      dividing both sides by 0.05
                    or multiply by 100/5
 100/5 x 0.05 x b = 100/5 x 28
 20 x 0.05 x b = 20 x 28
 b = 560
  Therefore, 5% of 560 is 28.
   Ex: What % of 32 is 20?
• Identify the three components (remember,
the base always follows “of”, the
multiplication, and the equals.
Percent = Unknown “what”  p
Base = 32 (follows “of”)
Amount = 20
• Translate the English statement to the Basic
Percent Equation: p x 32 = 20
Ex: Cont. What % of 32 is 20?
 • Now solve the mathematical equation:
 p x 32 = 20        Solve the equation by
                    dividing both sides by 32

 p = 0.625     This is the decimal form of the
               percent. Rewrite using the % sign
  p = 0.625 = 62.5%

  Therefore, 62.5% of 32 is 20.
Your Turn to Try a Few
Ex: The human body contains
206 bones. The fingers and the
toes contain a total of 56 small
  bones, or phalanges. What
  percent of the bones of the
     body are phalanges?
      Find the sentence that will be your
      equation (percent, base, amount, of, “is”)
  • Identify the three components (remember,
  the base always follows “of”, the
  multiplication, and the equals: What percent
  of the bones of the body are phalanges?
   Percent = Unknown “what”  p
   Base = Bones of the body (follows “of”)
   Amount = phalanges
   Multiplication “of” Equals “is”
• Write a hybrid sentence – half in math, half in
English: p x bones of the body = phalanges
Translate the hybrid sentence into the Basic Percent Equation
The human body contains 206 bones. The fingers and the toes contain a total of 56
small bones, or phalanges. p x bones of the body = phalanges

                                    p x 206 = 56
  • Now solve the mathematical equation:
     p x 206 = 56            Solve the equation by
                             dividing both sides by 206
      p = 0.2718 . . . This is the decimal form of the
                       percent. Rewrite using the % sign
      p = 0.2718 . . . = 27.2%
       Therefore, about 27.2% of bones are phalanges.
Ex: The new 8-mile nature trail
 is 125% of the length of the
        original trail.
How long was the original trail?
      Find the sentence that will be your
      equation (percent, base, amount, of, “is”)
 • Identify the three components (remember, the
 base always follows “of”, the multiplication, and the
 equals: The new 8-mile nature trail is 125% of the
 length of the original trail.

     Percent = 125%
     Base = Original trail length = b (follows “of”)
     Amount = New 8-mile trail
     Multiplication “of”    Equals “is”
• Write a hybrid sentence – half in math, half in English:
           125% x original trail = new trail
• Translate the hybrid sentence into the Basic
Percent Equation 125% x original trail = new trail
                      125% x b = 8
• Now solve the mathematical equation:
1.25 x b = 8   Solve the equation by dividing both
               sides by 1.25 or multiply by 100/125
100/125 x 1.25 x b = 100/125 x 8
4/5 x 1.25 x b = 4/5 x 8                 32/5 = 6.4
b = 6.4        Therefore, the original trail was 6.4 miles.
Ex: A medical supply company
charges 5% of the order total as
a shipping and handling charge.
  If the shipping and handling
charge is $38.75, what was the
        cost of the order?
       Find the sentence that will be your
       equation (percent, base, amount, of, “is”)
  • Identify the three components (remember,
  the base always follows “of”, the
  multiplication, and the equals: 5% of the order
  total as a shipping and handling charge.
   Percent = 5%
   Base = Order total = b (follows “of”)
   Amount = S&H charge
   Multiplication “of”  Equals “is”
• Write a hybrid sentence – half in math, half in
English: 5% x order total = S & H
 • Translate the hybrid sentence into the Basic
 Percent Equation
                    5% x order total = S & H
                        5% x b = 38.75
• Now solve the mathematical equation:
0.05 x b = 38.75 Solve the equation by dividing both
                  sides by 0.05 or multiply by 100/5
100/5 x 0.05 x b = 100/5 x 38.75
20 x 0.05 x b = 20 x 38.75
b = 775
Therefore, the cost of the order was $775.00.
             More Practice:
Ex: 26.1% of the 364 patients admitted
 in an emergency room are admitted
    due to an auto accident injury.
   How many patients are admitted
    due to an auto accident injury?
      Find the sentence that will be your equation
      (percent, base, amount, of, “is”)
• Identify the three components (remember, the base
always follows “of”, the multiplication, and the equals:
26.1% of the 364 patients admitted in an emergency room are admitted due
to an auto accident injury.


     Percent = 26.1%
      Base = Admitted patients (follows “of”)
     Amount = Admitted due to auto accident = a
     Multiplication “of” Equals “is”
• Write a hybrid sentence – half in math, half in
English: 26.1% x admitted patients = admitted due
               to auto accident
• Translate the hybrid sentence into the Basic Percent Equation
   26.1% of the 364 patients admitted in an emergency room are admitted due to
   an auto accident injury.


  26.1% x admitted patients = admitted due to auto accident

     26.1% x 364 = a
   • Now solve the mathematical equation:
     .261 x 364 = a            Solve the equation by
                               multiplying
      95.004 = a
                           Therefore, 95 patients were admitted
                           due to an auto accident injury.

				
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