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
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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