搜狗做题网简便运算,这里还有几道,不好意思,麻烦了
来源：学生作业帮 编辑：搜狗做题网作业帮 分类：数学作业 时间：2024/05/13 20:18:47
简便运算,这里还有几道,不好意思,麻烦了
①2009×2010-1/2009+2008×2010
②1/3+3/4+2/5+5/7+7/8+9/20+10/21+11/24+19/35
③5/9×79又6/17+50×1/9+11/9×5/17
④1×2×3+2×4×6+...+100×200×300/2×3×4+4×6×8+...+200×300×400
①2009×2010-1/2009+2008×2010
②1/3+3/4+2/5+5/7+7/8+9/20+10/21+11/24+19/35
③5/9×79又6/17+50×1/9+11/9×5/17
④1×2×3+2×4×6+...+100×200×300/2×3×4+4×6×8+...+200×300×400
①2009×2010-1/2009+2008×2010
=(2009×2010-1)/(2009+(2009-1)(2009+1))
=(2009×(2009+1)-1)/(2009+2009²-1)
=(2009²+2009-1)/(2009²+2009-1)
=1;
②1/3+3/4+2/5+5/7+7/8+9/20+10/21+11/24+19/35
=1/3+3/4+2/5+5/7+7/8+（4+5)/20+(3+7)/21+(3+8)/24+(14+5)/35
=1/3+3/4+2/5+5/7+7/8+1/5+1/4+1/7+1/3+1/8+1/3+2/5+1/7
=(1/3+1/3+1/3)+(3/4+1/4)+(2/5+1/5+2/5)+(5/7+1/7+1/7)+(7/8+1/8)
=1+1+1+1+1
=5;
③5/9×79又6/11+50×1/9+11/9×5/17
=(5/9)×(79+6/11+50+5/11)
=(5/9)×130
=650/9;
④1×2×3+2×4×6+...+100×200×300/2×3×4+4×6×8+...+200×300×400
=(1×2×3+2×4×6+...+100×200×300)/4×(1×2×3+2×4×6+...+100×200×300)
=1/4;
很高兴为您解答,skyhunter002为您答疑解惑
如果本题有什么不明白可以追问,
再问： 第三道应该是50吧
再答： 5/9×79又6/11+50×1/9+11/9×5/17 =(5/9)×(79+6/11+10+5/11) =(5/9)×90 =50; 嗯啊，忘了
=(2009×2010-1)/(2009+(2009-1)(2009+1))
=(2009×(2009+1)-1)/(2009+2009²-1)
=(2009²+2009-1)/(2009²+2009-1)
=1;
②1/3+3/4+2/5+5/7+7/8+9/20+10/21+11/24+19/35
=1/3+3/4+2/5+5/7+7/8+（4+5)/20+(3+7)/21+(3+8)/24+(14+5)/35
=1/3+3/4+2/5+5/7+7/8+1/5+1/4+1/7+1/3+1/8+1/3+2/5+1/7
=(1/3+1/3+1/3)+(3/4+1/4)+(2/5+1/5+2/5)+(5/7+1/7+1/7)+(7/8+1/8)
=1+1+1+1+1
=5;
③5/9×79又6/11+50×1/9+11/9×5/17
=(5/9)×(79+6/11+50+5/11)
=(5/9)×130
=650/9;
④1×2×3+2×4×6+...+100×200×300/2×3×4+4×6×8+...+200×300×400
=(1×2×3+2×4×6+...+100×200×300)/4×(1×2×3+2×4×6+...+100×200×300)
=1/4;
很高兴为您解答,skyhunter002为您答疑解惑
如果本题有什么不明白可以追问,
再问： 第三道应该是50吧
再答： 5/9×79又6/11+50×1/9+11/9×5/17 =(5/9)×(79+6/11+10+5/11) =(5/9)×90 =50; 嗯啊，忘了