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Answer:
5. 13 ÷ 13/25
13 × 25/13
13÷13 × 25/13÷13
1 × 25/1
1 × 25
= 25
6. 27/31 ÷ 18
27/31 × 1/18
27/558 ÷ 9/9
= 3/62
7. 1 1/4 ÷ 5/15
1×4+1/4 ÷ 5/15
5/4 × 15/5
5÷5/4 × 15/5÷5
1/4 × 15/1
= 15/4
8. 4 3/8 ÷ 2 1/3
4×8+3/8 ÷ 2×3+1/3
35/8 ÷ 7/3
35/8 × 3/7
35÷7/8 × 3/7÷7
5/8 × 3/1
5/8 × 3
= 15/8
9. 3 3/4 ÷ 1 1/4
3×4+3/4 ÷ 1×4+1/4
15/4 ÷ 5/4
15/4 × 4/5
15÷5/4÷4 × 4÷4/5÷5
3/1 × 1/1
3 × 1
= 3
10. 2 6/13 ÷ 1 9/39
2×13+6/13 ÷ 1×39+9/39
32/14 ÷ 48/39
32/14 × 39/48
32÷8/14 × 39/48÷8
4/14 × 39/6
4÷2/14 × 39/6÷2
2/14 × 39/3
78/42 ÷ 6/6
= 13/7 or 1 6/7
11. (4/9 × 3) ÷ (3/5 - 1/3)
(12/9) ÷ (3×3/5×3 - 1×5/3×5)
(12/9 ÷ 3/3) ÷ (9/15 - 5/15)
4/3 ÷ 4/15
4/3 × 15/4
4÷4/3÷3 × 15÷3/4÷4
1/1 × 5/1
1 × 5
= 5
12. (2 4/9 × 6/11) ÷ (5 3/4 - 1/3)
(2×9+4/9 × 6/11) ÷ (5×4+3/4 - 1/3)
(22/9 × 6/11) ÷ (23/4 - 1/3)
(22÷11/9÷3 × 6÷3/11÷11) ÷ (23×3/4×3 - 1×4/3×4)
(2/3 × 2/1) ÷ (69/12 - 4/12)
(2/3 × 2) ÷ 65/12
4/3 ÷ 65/12
4/3 × 12/65
4/3÷3 × 12÷3/65
4/1 × 4/65
4 × 4/65
= 16/65