Sunday, January 3, 2010

FORM 2 and FORM 3/ Topic 1 - DIRECTED NUMBERS.

In this topic, the BoDMAS theory plays an important part:
B = Bracket (Kurungan)
o = of 
D = Division (Bahagi)
M = Multiplication (Darab)
A = Addition (Tambah)
S = Subtraction (Tolak)
This means that when you do operations on numbers, please follow the BoDMAS law.

Examples:
(a)   3 + 2 x 5 = 30 (Wrong)  ........  3 + 2 x 5 = 13 (Correct)
(b)   5 - 2 x 4 =  12 (Wrong) ........  5 - 2 x 4  = - 3 (Correct)

Students must also know how to Add/Subtract/Multiply/Divide all the categories of numbers
Numbers are categorised as: Whole Numbers (Nombor Bulat)
                                            Fractions (Pecahan)
                                            Decimals (Perpuluhan)
                                            Negative Numbers (Nombor Negatif)

1.1  Operations on Whole Numbers:
(a).  3 + 5 x 4 - 2  =  3 + 20 -2
                            = 23 - 2
                            = 21

(b).  36 - 21÷ 7 + 4 x 5 =  36 - 3 + 20
                                    =  33 + 20  (we can subtract first, it is allowed)
                                    = 53
        Note:
        36 - 3 + 20 = 36 + 20 - 3
                          = 53
        36 - 23 = 13 (Wrong !!)   

1.2  Operations on Fractions:
(a)   Addition and Subtraction uses the same law, i.e. the denominator MUST be the same.
        e.g.
               + 2  =  5  + 6
                 3        5         15
                                  =   11
                                       15

(b)   Multiplication uses the law of cancellation (nominator versus denominator)
e.g.
3   x  2  =
4       9

31   x  21  =    1       
42       93        6

(c)   Division uses the law where the "second" term is made to inverse , and the " ÷ " sign is changed  to   " x "  e.g.


1  ÷ 3    =    1  x 4
2     4           2     3
              =   2
                   3

1.3  Operations on Decimals:
(a)   Addition/Subtraction uses the same technique:  Place the decimal point on the same line.
e.g.             234.76 + 45.02  =   234.76
                                                 45.02  +
                                               ---------
                                               279.78
                                              ----------
(b)  Multiplication:  Just multiply like whole numbers and then count the decimal places.
e.g.           12.54 x 0.004 = 5016   (multiplying  1254 x 4)

                                                 = 0.05016  (5 decimal places: two from 12.54 and 3 from 0.004)

(c)  Division is rather unique:  The denominator Must be changed to a whole number before dividing, thus in the proses changes the decimal point of the numerator as well....
 e.g.            

16.44 ÷ 0.02 =

16.44 
  0.02

1644
   2
=  822


1.4   Operations on Negative Numbers:
(a)  When adding/subtracting Negative Numbers, always follow the "Credit and Debit" Law (Hukum Dapat dan Hutang)  e.g.
  1.    3 + 5 = 8       (dapat 3, dapat 5 = dapat 8)
  2.    -3 +5 = 2       (hutang 3, dapat 5 = ada 2)
  3.    3 - 5  = -2      (dapat 3, hutang 5 = hutang 2)
  4.   -3 - 5 = -8       (hutang 3, hutang 5 = hutang 8
(b)  When Multiplying/Dividing, use the law of symbols:
       i.e.    + + = +     -  -  = +         +  -  =  -        -  + = - 
               GG = G     BB =G          BG = B         GB = B
e.g.
  1.   3 x (-5) =  -15
  2.  -3 x 5    =  -15
  3.  -3 x (-5) =  15  
  4.   4 ÷  -4  =  -16
  5.   -4 ÷ -4  =  16 
Now you can try as many exercises as you can following the knowledge you've gained from all the articles above...
Have a nice day !!

2 comments:

Anonymous said...

Macam mana kita nak terang pada student kalau soalannya mcm ni:

1. -3+(-5)= (kalau saya, saya cakap hutang 3 dan hutang lg 5)
2. -3-(-5)= (kalau yg ini sy x th nak terang mcm mana)
3. 3-(-5)=

DESS said...

1. -3 + (-5) = hutang 3 tambah hutang 5 = hutang 8
Betul macam anda kata.
2. -3 - (-5) = (hutang 3) tolak (hutang 5)
Hutang anda RM3 shj tetapi ada org tolong bayar utk RM5. Jadi anda ada lebih RM2 lah....
Disini, anda boleh mula terangkan konsep (-)(-)=+,
(+)(-)= -, (-)(+)= - dan (+)(+) = +.
Good Luck.., Have a nice day...