Question

急！我的数学底子不好!所以肯请各位老师帮我解答一下以下数学题！最好要有详细的解题过程！谢谢!

（用简便方法计算怎么算啊？）
1.5/6+11/12+19/20+29/30+41/42+55/56
2.99-97+95-93+91-89+...+7-5+3-1
3.(784*322-213)/(321*784+571)
4.（2890+5/6+7/8+7/10）/(5/6+7/8+7/10)
5.511*373737/737373

Answer 1

1.原式=1*6-1/6-1/12-1/20-1/30-1/42-1/56
裂项后=6-1/(2*3)-1/(3*4)-1/(4*5)-1/(5*6)-1/(6*7)-1/(7*8)
=6-(1/2-1/3)-(1/3-1/4)-(1/4-1/5)-(1/5-1/6)-(1/6-1/7)-(1/7-1/8)
=6-1/2+1/3-1/3+1/4-1/4+1/5-1/5+1/6-1/6+1/7-1/7+1/8
=6-1/2+1/8
=11/2+1/8
=45/8

2.原式=99+95+91+...+7+3-97-93-89-...-5-1
观察后发现每次加减都等于2
即=2*[（99-3）/4+1]
=2*25
=50

3.原式=（784×321+784-213）/(784*321+571)
=（784×321+571）/(784*321+571)
=1

4.想不出来

5.原式=511*[(37*10101)/(73*10101)]
=511*37/73
=7*37
=259

Answer 2

1.5/6+11/12+19/20+29/30+41/42+55/56
=5*(1/2-1/3)+11*(1/3-1/4)+19*(1/4-1/5)+29*(1/5-1/6)+41*(1/6-1/7)+55*(1/7-1/8)
=5/2+(6/3+8/4+10/5+12/6+14/7)-55/8
=5/2+(2*5)-55/8
=(20+80-55)/8
=45/8
=5.625

2.99-97+95-93+91-89+...+7-5+3-1
此单数个数共有50个,二项合并的话,就还有25个.
(99-97)+(95-93)+(91-89)+....+(7-5)+(3-1)
=2+2+2+....+2+2 (共有25个2)
=2*25
=50.

Answer 3

(1)原式=1-1/6+1-1/12+1-1/20+1-1/30+1-1/42+1-1/56
=6-1/2*3-1/3*4-1/4*5-1/5*6-1/6*7-1/7*8
=6-1/2+1/3-1/3+1/4-1/4+1/5-1/5+1/6-1/6+1/7-1/7+1/8
=6-1/2+1/8
=45/8

Answer 4

4. 5/6+7/8+7/10＝289/120 原式＝（2890＋289/120）*120/289＝1200＋1＝1201 明白