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TIPS & TRICKS ON DECIMAL. How do you judge if a mathematical expression is difficult or not?. Longer means harder??. Find the for us !. 125 x 32. 125 x 8 x 4. VS. Easier path. 3+2. =. 2+3. (1+2)+4. 1+(2+4). =. LAWS OF ARITHMETICS.

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TIPS & TRICKS ON DECIMAL

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Tips tricks on decimal

TIPS & TRICKS ON DECIMAL


How do you judge if a mathematical expression is difficult or not

How do you judge if a mathematical expression is difficult or not?

Longer means harder??

Find the for us !

125 x 32

125 x 8 x 4

VS

Easier path


Tips tricks on decimal

3+2

=

2+3


Tips tricks on decimal

(1+2)+4

1+(2+4)

=


Laws of arithmetics

LAWS OF ARITHMETICS

  • Commutative Law for Addition:

    • a + b = b + a

    • 3 + 2 = 2 + 3

  • Associative Law for Addition :

    • ( a + b ) + c = a + ( b + c )

    • ( 327 + 125 ) + 875 = 327 + ( 125 +875 )


Tips tricks on decimal

3 x 2

= 2 x 3


Laws of arithmetics1

LAWS OF ARITHMETICS

  • Commutative Law for Multiplication:

    • a x b = b x a

    • 3 ( 2 )= 2 ( 3 )

  • Associative Law for Multiplication :

    • ( a x b ) x c = a x ( b x c )

    • ( 3 x 2 ) 5 = 3 ( 2 x 5 )


3x 2 5

=

(3x2)+(3x5)

3x(2+5)


Laws of arithmetics2

LAWS OF ARITHMETICS

  • Distributive Law :

    • a ( b + c ) = a(b) + a(c)

    • 3 ( 2 + 5 )= 3 ( 2 ) + 3 ( 5 )

    • a ( b - c ) = ab - a(c)

    • 3 ( 5 - 2 )= 3 ( 5 ) - 3 ( 2 )

    • (+) x (+) = (+)

    • (+) x (-) = (-)

    • (-) x (+) = (-)


Tricks

TRICKS

  • try to change the number to sub multiple of ten ( hundred, thousand ……..)

    • 999 = 1000 – 1

    • 5 x 200 = 1000

    • 4 x 250 = 1000

    • 8 x 125 = 1000

    • Change a decimal to fraction

    • 0.5 = ½0.25 = ¼

    • 0.125 = 1/80.2 = 1/5

    • 0.04 = 1/250.008 = 1/125


1 5 x 64 x 25 x 125 x 68

1) 5 x 64 x 25 x 125 x 68

= 5 x ( 2 x 4 x 8 ) x 25 x 125 x 68

= (5 x 2) x (4 x 25) x (8 x 125) x 68

= 10 x 100 x 1000 x 68

= 68 000 000

Commutative law

Associative law


2 2667 x 999

2) 2667 x 999

2667 x 999

= 2667 x ( 1000 – 1 )

= 2667 x 1000 – 2667

= 2 667 000 – 2667

= 2 664 333


3 65 7x1 64 65 7x0 36 65 7

3)65.7x1.64 + 65.7x0.36 - 65.7

65.7 x 1.64 + 65.7 x 0.36 - 65.7

= 65.7 x 1.64 + 65.7 x 0.36 - 65.7 x 1

= 65.7 ( 1.64 + 0.36 – 1 )

= 65.7 ( 1 )

= 65.7

Distributive

law


Multiplication of 11

Multiplication of 11

  • 12 x 11 = 132

  • 12 x 111 = 1332

  • 12 x 1111 = 13332

  • 19 x 11 = 209

  • 19 x 111 = 2109

  • 19 x 1111 = 21109

  • 19 x 11111 = 211109

1 9

1 9

+ 1 9 0

2 1 0 9

1 9

1 9

1 9

+ 1 9 0

2 1 1 0 9


Multiplication of 111

Multiplication of 11

12 x 111.1

= 1333.2

12 x 11.11

= 133.32

12 x 1.111

= 13.332


Tips tricks on decimal

1 2

0

+ 1 2 1

1 2 1 2

12 x 101

= 1212

12 x 1010

= 12120

12 x 1001

= 12012

1.2 x 100.1 = 120.12

0

1 2

0

+ 1 2 1

1 2 1 2 0

1 2

0

0

+ 1 2 1

1 2 0 1 2


Tips tricks on decimal

1 2 1 2

+ 1 2 1 2 1

1 3 3 3 2

1212 x 11

= 13332

1212 x 1010

= 1224120

1212 x 1001

= 1213212

121.2 x 100.1 = 12132.12

0

1 2 1 2

0

+ 1 2 1 2 1

1 2 2 4 1 2 0

1 2 1 2

0

0

+ 1 2 1 2 1

1 2 1 3 2 1 2


4 2013 201 3 20 13 2 013

4) 2013+201.3+20.13+2.013

2013 + 201.3 + 20.13 + 2.013

= 2013 ( 1 + 0.1 + 0.01 +0.001 )

= 2013 ( 1.111 )

= (2000 + 13) ( 1.111)

= 2222 + 14.443

= 2236.443

Distributive

law


5 1 1 3 3 5 5 7 7 9 9 11 11 13 13 15 15 17 17 19 19

5) 1.1 + 3.3 + 5.5 + 7.7 + 9.9 + 11.11 +13.13 +15.15 +17.17+ 19.19

1.1 + 3.3 + 5.5 + 7.7 + 9.9 + 11.11 +13.13 +15.15 +17.17+ 19.19

= 1.1 (1 + 3 + 5 + 7 + 9) +1.01 (11 +13 +15 +17+ 19)

= 1.1 (25) + 1.01 (75)

= 27.5 + 75.75

= 103.25

Distributive Law


6 3 94 0 75 1 25

6) 3.94 – 0.75 – 1.25

3.94 – 0.75 – 1.25

= 3.94 - 2

= 1.94

0.75+1.25=


7 325 000 125

7) 325 000 ÷ 125

325 000 ÷ 125

= 325 000 ÷

= 325 000 x

= 325 x 8

= 2600

Change to 1000


8 9999 9997 9003 9001 1 3 997 999

8) (9999+9997+…… +9003+9001 ) – (1+3+ ……+997 +999)

(9999+9997+…… +9003+9001 ) – (1+3+ ……+997+999)

= 9 000 x 500

= 4 500 000

1 10 : 5 odd numbers

1 1 000 : 500 odd numbers


9 2000 x 1999 1999 x 1998 1998 x 1997 1997 x 1996 4 x 3 3 x 2 2x1

9) 2000 x 1999 – 1999 x 1998 + 1998 x 1997 – 1997 x 1996 + …… + 4 x 3 – 3 x 2 + 2x1

2000 x 1999 - 1999 x 1998 + 1998 x 1997 - 1997 x 1996+……+ 4x3 - 3x2 +2x1

= 1999 (2000 – 1998) + 1997 (1998 – 1996) + …… + 3(4 – 2) + 1x2

= 1999 (2) + 1997 (2) + …… + 3(2) + 1(2)

= 2 (1999+ 1997 + …… + 3 +1)

= 2 ( 2000 ) ( 1000/2)

= 2 000 000

Distributive Law


10 1998 x 19991999 1999 x 19981998

10) 1998 x 19991999 – 1999 x 19981998

1998 x (1999 x 10000 +1999) – 1999 x (1998 x 10000+1998)

= 1998 x [1999 x (10000 + 1) ] – 1999 x [1998 x (10000+1)]

= 1998 x 1999 x 10001 – 1999 x 1998 x 10001

= 0


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