Step-by-step explanation:

1. 5/9 + 2/6

= (5 × 6)/(9 × 6) + (2 × 9)/(6 × 9)

= 30/54 + 18/54

= 48/54

= (48 ÷ 6)/(54 ÷ 6)

= 8/9 ✓

2. 15/16 - 6/8

= (15 × 8)/(16 × 8) - (6 × 16)/(8 × 16)

= 120/128 - 96/128

= 24/128

= (24 ÷ 8)/(128 ÷ 8)

= 3/16 ✓

3. 6 1/3 - 4 3/12

= 19/3 - 51/12

= (19 × 12)/(3 × 12) - (51 × 3)/(12 × 3)

= 228/36 - 153/36

= 75/36

= (75 ÷ 3)/(36 ÷ 3)

= 25/12

= 2 1/12 ✓

4. 1 7/10 - 3/7

= 17/10 - 3/7

= (17 × 7)/(10 × 7) - (3 × 10)/(7 × 10)

= 119/70 - 30/70

= 89/70

= 1 19/70 ✓

5. (4 3/4 - 2 1/8) + 1 2/10

= (19/4 - 17/8) + 12/10

= (152/32 - 68/32) + 12/10

= 84/32 + 12/10

= (84 ÷ 4)/(32 ÷ 4) + 12/10

= 21/8 + 12/10

= (21 × 10)/(8 × 10) + (12 × 8)/(10 × 8)

= 210/80 + 96/80

= 306/80

= (306 ÷ 2)/(80 ÷ 2)

= 153/40

= 3 33/40 ✓