Answer + solution:
1. 7/10 + 2/10 = 9/10 self-explanatory
2. 4 + 7/15 = 60/15 + 7/15 = 67/15 convert to common denominator
3. 8 2/3 + 7 1/4 = 26/3 + 29/4 = (26 × 4 + 29 × 3)/12 = 191/12 convert to improper fraction and use the butterfly method
4. 6 7/5 + 9 3/5 = (6+9) + 10/5 = 15 + 2 = 17 solve the numbers and fractions separately since the denominators are the same.
5. 5/9 - 3/9 = 2/9 self-explanatory
6. 6 - 4 2/3 = 2 - 2/3 = 6/3 - 2/3 = 4/3 simplify and then solve
7. 9 2/3 - 4 1/5 = 5 + 2/3 - 1/5 = 5 + (2×5 - 3×1)/15 = 5+7/15 = 82/15 simplify and solve, again
8. 14 3/7 - 9 5/6 = 5 + 3/7 - 5/6 = 5 + (3(6)-7(5))/42 = (210-17)/42= 193/42 same method.
9. 2/3 x 9/12 = 2/3 × 3/4 = 2/4 = 1/2 simplify and then multiply
10. 4 x 2/8 x 16/20 = 4 × 1/4 × 4/5 = 4/5 simplify and then cancel terms
11. 5 2/4 x 6 3/4 = 22/4 × 27/4 = (11×17)/8 = 297/8 expand then slowly multiply
12. 10 ÷ 3/15 = 10 × 15/3 = 10 × 5 = 50 note that with division with fractions, we can simply multiply with their reciprocals instead.
13. 25/10 ÷ 5 5/3 ÷ 5/15 = 5/2 ÷ 20/3 ÷ 1/3 = 5/2 × 3/20 × 3 = 5/2 × 9/20 = 45/40 = 9/8 simplify and then multiply one by one. any order.