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TIPS & TRICKS ON DECIMAL

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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  1. TIPS & TRICKS ON DECIMAL

  2. 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. 3+2 = 2+3

  4. (1+2)+4 1+(2+4) =

  5. 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 )

  6. 3 x 2 = 2 x 3

  7. 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 )

  8. = (3x2)+(3x5) 3x(2+5)

  9. 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 (+) = (-)

  10. 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 = ½ 0.25 = ¼ • 0.125 = 1/8 0.2 = 1/5 • 0.04 = 1/25 0.008 = 1/125

  11. 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

  12. 2) 2667 x 999 2667 x 999 = 2667 x ( 1000 – 1 ) = 2667 x 1000 – 2667 = 2 667 000 – 2667 = 2 664 333

  13. 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

  14. 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

  15. Multiplication of 11 12 x 111.1 = 1333.2 12 x 11.11 = 133.32 12 x 1.111 = 13.332

  16. 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

  17. 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

  18. 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

  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

  20. 6) 3.94 – 0.75 – 1.25 3.94 – 0.75 – 1.25 = 3.94 - 2 = 1.94 0.75+1.25=

  21. 7) 325 000 ÷ 125 325 000 ÷ 125 = 325 000 ÷ = 325 000 x = 325 x 8 = 2600 Change to 1000

  22. 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

  23. 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

  24. 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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