Complete the following problems on equivalent fractions and adding fractions:

To find equivalent fractions, multiply both the numerator and the denominator by the same non-zero number.

*a) For $\frac{1}{3}$:

$$\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \boxed{\frac{2}{6}}$$ $$\frac{1}{3} = \frac{1 \times 3}{3 \times 3} = \boxed{\frac{3}{9}}$$

*b) For $\frac{1}{4}$:

$$\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \boxed{\frac{2}{8}}$$ $$\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \boxed{\frac{3}{12}}$$

*c) For $\frac{1}{5}$:

$$\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \boxed{\frac{2}{10}}$$ $$\frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \boxed{\frac{3}{15}}$$

*d) For $\frac{1}{6}$:

$$\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \boxed{\frac{2}{12}}$$ $$\frac{1}{6} = \frac{1 \times 3}{6 \times 3} = \boxed{\frac{3}{18}}$$

*e) For $\frac{1}{7}$:

$$\frac{1}{7} = \frac{1 \times 2}{7 \times 2} = \boxed{\frac{2}{14}}$$ $$\frac{1}{7} = \frac{1 \times 3}{7 \times 3} = \boxed{\frac{3}{21}}$$

*f) For $\frac{1}{8}$:

$$\frac{1}{8} = \frac{1 \times 2}{8 \times 2} = \boxed{\frac{2}{16}}$$ $$\frac{1}{8} = \frac{1 \times 3}{8 \times 3} = \boxed{\frac{3}{24}}$$

To add fractions with the same denominator, add the numerators and keep the denominator the same. Simplify the result if possible.

*a) $\frac{1}{2} + \frac{1}{2} = \frac{1+1}{2} = \frac{2}{2} = \boxed{1}$

*b) $\frac{1}{3} + \frac{1}{3} = \frac{1+1}{3} = \boxed{\frac{2}{3}}$

*c) $\frac{1}{4} + \frac{1}{4} = \frac{1+1}{4} = \frac{2}{4} = \boxed{\frac{1}{2}}$

*d) $\frac{1}{5} + \frac{1}{5} = \frac{1+1}{5} = \boxed{\frac{2}{5}}$

*e) $\frac{1}{6} + \frac{1}{6} = \frac{1+1}{6} = \frac{2}{6} = \boxed{\frac{1}{3}}$

*f) $\frac{1}{7} + \frac{1}{7} = \frac{1+1}{7} = \boxed{\frac{2}{7}}$

*g) $\frac{1}{8} + \frac{1}{8} = \frac{1+1}{8} = \frac{2}{8} = \boxed{\frac{1}{4}}$

*h) $\frac{1}{9} + \frac{1}{9} = \frac{1+1}{9} = \boxed{\frac{2}{9}}$

*i) $\frac{1}{10} + \frac{1}{10} = \frac{1+1}{10} = \frac{2}{10} = \boxed{\frac{1}{5}}$

*j) $\frac{2}{5} + \frac{1}{5} = \frac{2+1}{5} = \boxed{\frac{3}{5}}$

*k) $\frac{3}{6} + \frac{1}{6} = \frac{3+1}{6} = \frac{4}{6} = \boxed{\frac{2}{3}}$

*l) $\frac{4}{7} + \frac{2}{7} = \frac{4+2}{7} = \boxed{\frac{6}{7}}$

*m) $\frac{5}{8} + \frac{1}{8} = \frac{5+1}{8} = \frac{6}{8} = \boxed{\frac{3}{4}}$

*n) $\frac{6}{9} + \frac{2}{9} = \frac{6+2}{9} = \boxed{\frac{8}{9}}$

*o) $\frac{7}{10} + \frac{1}{10} = \frac{7+1}{10} = \frac{8}{10} = \boxed{\frac{4}{5}}$

*p) $\frac{8}{11} + \frac{2}{11} = \frac{8+2}{11} = \boxed{\frac{10}{11}}$

*q) $\frac{9}{12} + \frac{1}{12} = \frac{9+1}{12} = \frac{10}{12} = \boxed{\frac{5}{6}}$

*r) $\frac{10}{13} + \frac{2}{13} = \frac{10+2}{13} = \boxed{\frac{12}{1