Question

小学5年级数学题（分数的简便运算）：

1： 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 2： 1/5×7 + 1/7×9 + 1/9×11 + 1/ 11×13 + 1/ 13×15 3： 6/1×7 － 6/7×13 － 6/13×19－ ．．．－6/97×103

Answer 1

1. 5/2 -（ 3/2 + 4/5 ） 

2. 7/8 + （ 1/8 + 1/9 ） 
3. 5/6 + （ 1/2 + 2/3 ） 
4. 9/7 - （ 2/7 - 10/21 ） 
5. 3/7 + 49/9 + 4/7 
6. 8/9 + 15/36 + 3/27 
7. 5/2 - （ 3/2 + 4/5 ） 
8. 7/8 + （ 1/8 + 1/9 ） 
9. 9/7 - （ 2/7 - 10/21 ）
10. 1/5 + （ 3/7 + 8/10 ）
1. 1/3 + 3/4 + 1/5
2. 3/8 + 8/3 - 1/2
3. 5/6 + 1/12 + 3/4
4. 30/46 - 1/2 + 7/23
5. 8/11 + 2/6 + 7/33
6. 19/8 - 1/2 - 3/4
7. 7/25 + 3/10 - 2/5
8. 18/121 - 1/2 + 9/11
9. 6/17 - 1/51 - 1/34 
10.8/15 + 7/3 - 8/5
1. 3/7 × 49/9 - 4/3 
2. 8/9 × 15/36 + 1/27 
3. 12× 5/6 – 2/9 ×3 
4. 8× 5/4 + 1/4 
5. 6÷ 3/8 – 3/8 ÷6 
6. 4/7 × 5/9 + 3/7 × 5/9 
7. 5/2 -（ 3/2 + 4/5 ） 
8. 7/8 + （ 1/8 + 1/9 ） 
9. 9 × 5/6 + 5/6 
10. 3/4 × 8/9 - 1/3 
11. 7 × 5/49 + 3/14 
12. 6 ×（ 1/2 + 2/3 ） 
13. 8 × 4/5 + 8 × 11/5 
14. 31 × 5/6 – 5/6 
15. 9/7 - （ 2/7 – 10/21 ） 
16. 5/9 × 18 – 14 × 2/7 
17. 4/5 × 25/16 + 2/3 × 3/4 
18. 14 × 8/7 – 5/6 × 12/15 
19. 17/32 – 3/4 × 9/24 
20. 3 × 2/9 + 1/3 
21. 5/7 × 3/25 + 3/7 
22. 3/14 ×× 2/3 + 1/6 
23. 1/5 × 2/3 + 5/6 
24. 9/22 + 1/11 ÷ 1/2 
25. 5/3 × 11/5 + 4/3 
26. 45 × 2/3 + 1/3 × 15 
27. 7/19 + 12/19 × 5/6 
28. 1/4 + 3/4 ÷ 2/3 
29. 8/7 × 21/16 + 1/2 
30. 101 × 1/5 – 1/5 × 21 
1. 3/7 × 49/9 - 4/3 
2. 8/9 × 15/36 + 1/27 
3. 12× 5/6 – 2/9 ×3 
4. 8× 5/4 + 1/4 
5. 6÷ 3/8 – 3/8 ÷6 
6. 4/7 × 5/9 + 3/7 × 5/9 
7. 5/2 -（ 3/2 + 4/5 ） 
8. 7/8 + （ 1/8 + 1/9 ） 
9. 9 × 5/6 + 5/6 
10. 3/4 × 8/9 - 1/3 
11. 7 × 5/49 + 3/14 
12. 6 ×（ 1/2 + 2/3 ） 
13. 8 × 4/5 + 8 × 11/5 
14. 31 × 5/6 – 5/6 
15. 9/7 - （ 2/7 – 10/21 ） 
16. 5/9 × 18 – 14 × 2/7 
17. 4/5 × 25/16 + 2/3 × 3/4 
18. 14 × 8/7 – 5/6 × 12/15 
19. 17/32 – 3/4 × 9/24 
20. 3 × 2/9 + 1/3 
21. 5/7 × 3/25 + 3/7 
22. 3/14 ×× 2/3 + 1/6 
23. 1/5 × 2/3 + 5/6 
24. 9/22 + 1/11 ÷ 1/2 
25. 5/3 × 11/5 + 4/3 
26. 45 × 2/3 + 1/3 × 15 
27. 7/19 + 12/19 × 5/6 
28. 1/4 + 3/4 ÷ 2/3 
29. 8/7 × 21/16 + 1/2 
30. 101 × 1/5 – 1/5 × 21 

Answer 2

1： 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90
=(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)+(1/9-1/10)
=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1/3-1/10
=7/30

2： 1/5×7 + 1/7×9 + 1/9×11 + 1/ 11×13 + 1/ 13×15
=1/2×(1/5-1/7)+1/2×(1/7-1/9)+1/2×(1/9-1/11)+1/2×(1/11-1/13)+1/2×(1/13-1/15)
=1/2×(1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15)
=1/2×(1/5-1/15)
=1/2×2/15
=1/15

3：　6/1×7　－　6/7×13　－　6/13×19－　．．．－6/97×103
=(1-1/7)-(1/7-1/13)-(1/13-1/19)-......-(1/97-1/103)
=1-1/7-1/7-1/13+1/13-1/19-......-1/97+1/103
=1-1/7-1/7+1/103
=5/7+1/103
=522/721

Answer 3

1： 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 =(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)+(1/9-1/10) =1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10 =1/3-1/10 =7/30 2： 1/5×7 + 1/7×9 + 1/9×11 + 1/ 11×13 + 1/ 13×15 =1/2×(1/5-1/7)+1/2×(1/7-1/9)+1/2×(1/9-1/11)+1/2×(1/11-1/13)+1/2×(1/13-1/15) =1/2×(1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15) =1/2×(1/5-1/15) =1/2×2/15 =1/15 3： 6/1×7 － 6/7×13 － 6/13×19－ ．．．－6/97×103 =(1-1/7)-(1/7-1/13)-(1/13-1/19)-......-(1/97-1/103) =1-1/7-1/7-1/13+1/13-1/19-......-1/97+1/103 =1-1/7-1/7+1/103 =5/7+1/103 =522/721