Solve the equations:

1. $\frac{2}{7} + \frac{3}{5} = \frac{35}{35}$
2. $\frac{3}{4} + \frac{1}{12} = \frac{46}{46}$
3. $\frac{2}{7} + \frac{1}{5} = \frac{17}{35}$
4. $\frac{2}{5} + \frac{4}{9} = \frac{38}{45}$
5. $\frac{1}{2} + \frac{3}{14} = \frac{5}{7}$
6. $\frac{5}{8} + \frac{3}{10} = \frac{37}{40}$
7. $\frac{5}{10} + \frac{3}{20} = \frac{13}{20}$
8. $\frac{4}{5} + \frac{1}{25} = \frac{21}{25}$
9. $\frac{3}{7} + \frac{2}{8} = \frac{19}{28}$
10. $\frac{6}{11} + \frac{7}{33} = \frac{25}{33}$

[tex]\frac{2}{7} + \frac{3}{5}[/tex]
To add these fractions, find a common denominator. The least common denominator (LCD) of 7 and 5 is 35.
Convert each fraction:
[tex]\frac{2}{7} = \frac{2 \times 5}{7 \times 5} = \frac{10}{35}[/tex]
[tex]\frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35}[/tex]
Add the fractions:
[tex]\frac{10}{35} + \frac{21}{35} = \frac{31}{35}[/tex]
The right side is [tex]\frac{35}{35}[/tex]. Since [tex]\frac{31}{35} \neq \frac{35}{35}[/tex], this equation is incorrect.
[tex]\frac{3}{4} + \frac{1}{12}[/tex]
The LCD of 4 and 12 is 12.
Convert each fraction:
[tex]\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}[/tex]
[tex]\frac{1}{12} = \frac{1}{12}[/tex]
Add them:
[tex]\frac{9}{12} + \frac{1}{12} = \frac{10}{12} = \frac{5}{6}[/tex]
The right side is [tex]\frac{46}{46} = 1[/tex]. Since [tex]\frac{5}{6} \neq 1[/tex], this equation is incorrect.
[tex]\frac{2}{7} + \frac{1}{5}[/tex]
LCD of 7 and 5 is 35.
Convert:
[tex]\frac{2}{7} = \frac{10}{35}[/tex] and [tex]\frac{1}{5} = \frac{7}{35}[/tex]
Add:
[tex]\frac{10}{35} + \frac{7}{35} = \frac{17}{35}[/tex]
The right side is [tex]\frac{17}{35}[/tex]. Correct!
[tex]\frac{2}{5} + \frac{4}{9}[/tex]
LCD of 5 and 9 is 45.
Convert:
[tex]\frac{2}{5} = \frac{18}{45}[/tex] and [tex]\frac{4}{9} = \frac{20}{45}[/tex]
Add:
[tex]\frac{18}{45} + \frac{20}{45} = \frac{38}{45}[/tex]
The right side is [tex]\frac{38}{45}[/tex]. Correct!
[tex]\frac{1}{2} + \frac{3}{14}[/tex]
LCD of 2 and 14 is 14.
Convert:
[tex]\frac{1}{2} = \frac{7}{14}[/tex] and [tex]\frac{3}{14} = \frac{3}{14}[/tex]
Add:
[tex]\frac{7}{14} + \frac{3}{14} = \frac{10}{14} = \frac{5}{7}[/tex]
The right side is [tex]\frac{5}{7}[/tex]. Correct!
[tex]\frac{5}{8} + \frac{3}{10}[/tex]
LCD of 8 and 10 is 40.
Convert:
[tex]\frac{5}{8} = \frac{25}{40}[/tex] and [tex]\frac{3}{10} = \frac{12}{40}[/tex]
Add:
[tex]\frac{25}{40} + \frac{12}{40} = \frac{37}{40}[/tex]
The right side is [tex]\frac{37}{40}[/tex]. Correct!
[tex]\frac{5}{10} + \frac{3}{20}[/tex]
LCD of 10 and 20 is 20.
Convert:
[tex]\frac{5}{10} = \frac{10}{20}[/tex] and [tex]\frac{3}{20} = \frac{3}{20}[/tex]
Add:
[tex]\frac{10}{20} + \frac{3}{20} = \frac{13}{20}[/tex]
The right side is [tex]\frac{13}{20}[/tex]. Correct!
[tex]\frac{4}{5} + \frac{1}{25}[/tex]
LCD of 5 and 25 is 25.
Convert:
[tex]\frac{4}{5} = \frac{20}{25}[/tex] and [tex]\frac{1}{25} = \frac{1}{25}[/tex]
Add:
[tex]\frac{20}{25} + \frac{1}{25} = \frac{21}{25}[/tex]
The right side is [tex]\frac{21}{25}[/tex]. Correct!
[tex]\frac{3}{7} + \frac{2}{8}[/tex]
LCD of 7 and 8 is 56.
Convert:
[tex]\frac{3}{7} = \frac{24}{56}[/tex] and [tex]\frac{2}{8} = \frac{14}{56}[/tex]
Add:
[tex]\frac{24}{56} + \frac{14}{56} = \frac{38}{56} \neq \frac{19}{28}[/tex]
The right side is [tex]\frac{19}{28}[/tex]. Incorrect.
[tex]\frac{6}{11} + \frac{7}{33}[/tex]
LCD of 11 and 33 is 33.
Convert:
[tex]\frac{6}{11} = \frac{18}{33}[/tex] and [tex]\frac{7}{33} = \frac{7}{33}[/tex]
Add:
[tex]\frac{18}{33} + \frac{7}{33} = \frac{25}{33}[/tex]
The right side is [tex]\frac{25}{33}[/tex]. Correct!

In summary, the correct equations based on the calculations are 3, 4, 5, 6, 7, 8, and 10.