几道简便运算:(求思路和过程)(1)777×6+111×58(2)20092009×2008-20082008×2009(3)a=1+3+5+.+99+101 b=2+4+6+.+98+100 则a、b两数大数比小数多多少?(4)(7.88+6.77+5.66)×(9.31+10.98+10)-(7.88
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![几道简便运算:(求思路和过程)(1)777×6+111×58(2)20092009×2008-20082008×2009(3)a=1+3+5+.+99+101 b=2+4+6+.+98+100 则a、b两数大数比小数多多少?(4)(7.88+6.77+5.66)×(9.31+10.98+10)-(7.88](/uploads/image/z/1987488-0-8.jpg?t=%E5%87%A0%E9%81%93%E7%AE%80%E4%BE%BF%E8%BF%90%E7%AE%97%EF%BC%9A%EF%BC%88%E6%B1%82%E6%80%9D%E8%B7%AF%E5%92%8C%E8%BF%87%E7%A8%8B%EF%BC%89%EF%BC%881%EF%BC%89777%C3%976%EF%BC%8B111%C3%9758%EF%BC%882%EF%BC%8920092009%C3%972008%EF%BC%8D20082008%C3%972009%EF%BC%883%EF%BC%89a%3D1%2B3%2B5%2B.%2B99%2B101+b%3D2%2B4%2B6%2B.%2B98%2B100+%E5%88%99a%E3%80%81b%E4%B8%A4%E6%95%B0%E5%A4%A7%E6%95%B0%E6%AF%94%E5%B0%8F%E6%95%B0%E5%A4%9A%E5%A4%9A%E5%B0%91%3F%EF%BC%884%EF%BC%89%287.88%EF%BC%8B6.77%EF%BC%8B5.66%EF%BC%89%C3%97%EF%BC%889.31%EF%BC%8B10.98%EF%BC%8B10%EF%BC%89%EF%BC%8D%EF%BC%887.88)
几道简便运算:(求思路和过程)(1)777×6+111×58(2)20092009×2008-20082008×2009(3)a=1+3+5+.+99+101 b=2+4+6+.+98+100 则a、b两数大数比小数多多少?(4)(7.88+6.77+5.66)×(9.31+10.98+10)-(7.88
几道简便运算:(求思路和过程)
(1)777×6+111×58(2)20092009×2008-20082008×2009(3)a=1+3+5+.+99+101 b=2+4+6+.+98+100 则a、b两数大数比小数多多少?(4)(7.88+6.77+5.66)×(9.31+10.98+10)-(7.88+6.77+5.66+10)×9.31+10.98)
几道简便运算:(求思路和过程)(1)777×6+111×58(2)20092009×2008-20082008×2009(3)a=1+3+5+.+99+101 b=2+4+6+.+98+100 则a、b两数大数比小数多多少?(4)(7.88+6.77+5.66)×(9.31+10.98+10)-(7.88
(1)777×6+111×58
=111×(7×6)+11×58 仔细观察题目中的数字777 与111正好是 777是111的倍数这样我
=111*42+111*58 们可以造出公因式,来用乘法分配律计算
=111(42+58)
=11100
(2)20092009×2008-20082008×2009 ∵本题的解答技巧类似,不过本题稍微复杂些
=2009×10001-2008×10001 20092009与20082008有公因数10001
=2009*2008(10001-10001)
=0
(3)讲:a=1+3+5+.+99+101 b=2+4+6+.+98+100 ∴a-b=(1+3+5+7…101)-(2+4+6+.+98+100 )=1+3+5+.+99+101 -2-4-6-8-…-100=101-100+99-98+.+3-2+1=50+1=51
(4)(7.88+6.77+5.66)×(9.31+10.98+10)-()+(7.88+6.77+5.66)×1010.98)
∵
(7.88+6.77+5.66)×(9.31+10.98+10)=(7.88+6.77)×(9.31+0.98)+(7.88+6.77+5.66)×10 ∵(7.88+6.77+5.66+10)×9.31+10.98)=7.88+6.77+5.66)×(9.31+10.98)+10×(9.31+10.98) ∴(7.88+6.77+5.66)×(9.31+10.98+10)-(7.88+6.77+5.66)×1010.98)=(7.88+6.77+5.66)×(9.31+10.98)+(7.88+6.77+5.66)×10-[(7.88+6.77+5.66)×(9.31+10.98)+10×(9.31+10.98)]=(7.88+6.77+5.66)×(9.31+10.98)+(7.88+6.77+5.66)×10-(7.88+6.77+5.66)×(9.31+10.98)-10×(9.31+10.98) 为了方便就记 a=7.88+6.77+5.66 b=9.31+10.98 ∴(7.88+6.77+5.66)×(9.31+10.98)+(7.88+6.77+5.66)×10-(7.88+6.77+5.66)×(9.31+10.98)-10×(9.31+10.98) =ab+10a-ab-10b=10a-10b=10(a-b) ∴(7.88+6.77+5.66)×(9.31+10.98+10)-(7.88+6.77+5.66+10)×(9.31+10.98)=10(7.88+6.77+5.66-9.31-10.98)=10×0.02=0.2
(1)777×6+111×58
=111*42+111*58
=111(42+58)
=11100
(2)20092009×2008-20082008×2009
=2009*2008(10001-10001)
=0
(3)a=1+3+5+......+99+101 b=2+4+6+......+98+100 则a、b两数大数比...
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(1)777×6+111×58
=111*42+111*58
=111(42+58)
=11100
(2)20092009×2008-20082008×2009
=2009*2008(10001-10001)
=0
(3)a=1+3+5+......+99+101 b=2+4+6+......+98+100 则a、b两数大数比小数多多少?
a-b=101-100+99-98+......+3-2+1=50+1=51
(4)(7.88+6.77+5.66)×(9.31+10.98+10)-(7.88+6.77+5.66+10)×(9.31+10.98)
=(7.88+6.77+5.66)×(9.31+10.98)+(7.88+6.77+5.66)×10-(7.88+6.77+5.66)×(9.31+10.98)-10×(9.31+10.98)
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