how to draw a regular polygon quadrilateral using 360 degrees protractor

Materials: piece of coupon, ruler, eraser, 360 degrees protractor, crayons, pencil
1. Position the 360 degrees protractor 0 degree parallel to x- axis.

2. Mark the following degree measures 45degrees, 135 degrees, 225 degrees, and
   315 degrees. see the figure below:

3. Remove the protractor and connect the points. Color the polygon and the background.
     Now it's a quadrilateral





 
 



how to draw a regular polygon triangle using 360 degrees protractor

Materials:   paper, ruler, pencil, 360 degrees protractor, eraser and crayons.

1. place the 360 degrees protractor on the paper. the 0 degrees above the y- axis.

2. Mark the following degree measure 0 degree, 120 degrees and 240 degrees
    as shown in the figure below.

 

3. Remove the protractor and connect the points and color  . Now,  it's a triangle

 

how to divide fractions

Observe the fractions from division mathematical operation and changed to multiplication process.

 

 

 

 

 It can also be factored as seen in the second column then easily eliminating common factors from numerator and denominator.  

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how to find the common ratio of geometric sequence

A sequence is geometric sequence if the sequence reveals a common ratio.  To get the common ratio divide the 2nd term with the first term or  the 3rd term with the 2nd term,  ....:
Examples of sequences
1. 1, 5, 25, 125....
    5  =   5            the common the ratio is 5    indicated as     r= 5    the ratios were all checked
    1                     ( don't  jump to conclusion if  only one ratio is tested..)    

     25 = 5 
      5

      125 =5
       25

  2. 100, 50, 25, 5......
        50  =   1                r= 1
       100      2                     2

        25   =   1
        50        2

        5      =   1
       25          2  

  

In # 3 the common ratio of the geometric sequence  , r= 1/2
        
Practice Test
Find the common ratio of the following geometric sequences
1.   1, 4, 16, 64 ...
2.   1/2, 1, 2, 4,....
3.   500, 250, 125, ....
4    1/9, 1, 9, 81,...
5.  -5, 25, - 125,....
6.   1/3, 1/9, 1/27, . . .

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how to multiply fraction and fraction, improper fraction, whole number, mixed numbers etc.

To multiply fraction and fraction


To multiply fraction and fraction

To multiply fraction and whole number

To multiply fraction and improper fraction

To multiply fraction and mixed number

To multiply 2 mixed numbers

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how to add fraction and whole number, improper fraction, mixed numbers

Addition of fraction and whole numbers
Examples:
1. 1/3 + 5 = 5 1/3
2. 4/6 + 12 = 12 4/6   or 12 2/3

Addition of fraction and improper fraction
Pre requisite : how to add fractions with different denominators
Examples:
1. 2/5 + 9/4 =

    2(4)  + 9 (5)   =
    5(4)      4(5)

      8   + 45       = 
      20    20     

        53    or 2 13/20
        20

2.    5/7 + 6/5 =

       5(5) + 6(7)  =
       7(5)    5(7)

         25   +  42    =
         35       35 

         67     or  1 32/35
         35



Addition of fraction and mixed numbers
Examples:
1. 4/9 + 3 1/4 =

     4/9 +  13/4                      3  1/4 = (4)(3)+1 =13/4   changed to improper fraction

      4(4)  + 13 (9) =
     9(4)        4(9)

      16     +   117  =
      36           36

      133    or  3 25/36
       36
Addition of mixed numbers and mixed numbers

2.  2 2/3  + 4 1/5  =       both mixed numbers

     8/3   +  21/5   =           changed to improper fractions

     8(5)   + 21(3)  =
     3(5)       5(3)

      40    +   63  =
      15         15

      103  or   6  13/15
       15  

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how to divide integers

To divide integers with like signs, divide the integers and quotient is always positive.

Examples:
1. (-20)/(-5) = 4      positive quotient
2. (100)/(10) = 10   positive quotient

To divide integers with unlike signs, the quotient is always negative

Examples:
1. (-36)/ (6) = -6   negative quotient
2. (81)/ (-9) = -9  negative quotient

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