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# TIPS & TRICKS ON DECIMAL - PowerPoint PPT Presentation

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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Longer means harder??

Find the for us !

125 x 32

125 x 8 x 4

VS

Easier path

3+2 or not?

=

2+3

(1+2)+4 or not?

1+(2+4)

=

LAWS OF ARITHMETICS or not?

• 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 )

3 x 2 or not?

= 2 x 3

LAWS OF ARITHMETICS or not?

• 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 )

= or not?

(3x2)+(3x5)

3x(2+5)

LAWS OF ARITHMETICS or not?

• 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 or not?

• 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 = ½ 0.25 = ¼

• 0.125 = 1/8 0.2 = 1/5

• 0.04 = 1/25 0.008 = 1/125

1) 5 x 64 x 25 x 125 x 68 or not?

= 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 or not?

2667 x 999

= 2667 x ( 1000 – 1 )

= 2667 x 1000 – 2667

= 2 667 000 – 2667

= 2 664 333

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 or not? 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 or not? 11

12 x 111.1

= 1333.2

12 x 11.11

= 133.32

12 x 1.111

= 13.332

1 2 or not?

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

1 2 1 2 or not?

+ 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 or not?

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 or not? +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 or not?

3.94 – 0.75 – 1.25

= 3.94 - 2

= 1.94

0.75+1.25=

7) or not?325 000 ÷ 125

325 000 ÷ 125

= 325 000 ÷

= 325 000 x

= 325 x 8

= 2600

Change to 1000

8) (9999+9997+…… +9003+9001 ) or not? – (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 or not? 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

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