$\displaystyle \frac{1}{4}+\frac{1}{2}$

In order to solve this problem, we first have to find common denominators. 

$\displaystyle \frac{1}{2}\times\frac{2}{2}=\frac{2}{4}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator. 

$\displaystyle \frac{1}{4}+\frac{2}{4}=\frac{3}{4}$

$\displaystyle \frac{1}{5}+\frac{1}{2}$

In order to solve this problem, we first have to find common denominators. 

$\displaystyle \frac{1}{5}\times\frac{2}{2}=\frac{2}{10}$

$\displaystyle \frac{1}{2}\times \frac{5}{5}=\frac{5}{10}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator. 

$\displaystyle \frac{2}{10}+\frac{5}{10}=\frac{7}{10}$

$\displaystyle \frac{1}{3}+\frac{2}{5}$

In order to solve this problem, we first have to find common denominators. 

$\displaystyle \frac{1}{3}\times\frac{5}5{}=\frac{5}{15}$

$\displaystyle \frac{2}{5}\times\frac{3}{3}=\frac{6}{15}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator. 

$\displaystyle \frac{5}{15}+\frac{6}{15}=\frac{11}{15}$

$\displaystyle \frac{1}{2}+\frac{2}{7}$

In order to solve this problem, we first have to find common denominators. 

$\displaystyle \frac{1}{2}\times\frac{7}{7}=\frac{7}{14}$

$\displaystyle \frac{2}{7}\times\frac{2}{2}=\frac{4}{14}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator. 

$\displaystyle \frac{7}{14}+\frac{4}{14}=\frac{11}{14}$

$\displaystyle \frac{3}{4}+\frac{1}{3}$

In order to solve this problem, we first have to find common denominators. 

$\displaystyle \frac{3}{4}\times\frac{3}{3}=\frac{9}{12}$

$\displaystyle \frac{1}{3}\times\frac{4}{4}=\frac{4}{12}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator. 

$\displaystyle \frac{9}{12}+\frac{4}{12}=\frac{13}{12}$

$\displaystyle \frac{13}{12}=1\frac{1}{12}$ because $\displaystyle 12$ can go into $\displaystyle 13$ one time, with one left over. 

$\displaystyle \frac{5}{6}+\frac{2}{4}$

In order to solve this problem, we first have to find common denominators. 

$\displaystyle \frac{5}{6}\times\frac{2}{2}=\frac{10}{12}$

$\displaystyle \frac{2}{4}\times\frac{3}{3}=\frac{6}{12}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator. 

$\displaystyle \frac{10}{12}+\frac{6}{12}=\frac{16}{12}$

$\displaystyle \frac{16}{12}=1\frac{4}{12}=1\frac{1}{3}$ because $\displaystyle 12$ and go into $\displaystyle 16$ one time with four left over. $\displaystyle \frac{4}{12}$ can be reduced to $\displaystyle \frac{1}{3}$ by dividing the numerator and the denominator by $\displaystyle 4$

$\displaystyle \frac{2}{3}+\frac{1}{7}$

In order to solve this problem, we first have to find common denominators. 

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

$\displaystyle \frac{1}{7}\times\frac{3}{3}=\frac{3}{21}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator. 

$\displaystyle \frac{14}{21}+\frac{3}{21}=\frac{17}{21}$

$\displaystyle \frac{2}{3}+\frac{1}2{}$

In order to solve this problem, we first have to find common denominators. 

$\displaystyle \frac{2}{3}\times\frac{2}{2}=\frac{4}{6}$

$\displaystyle \frac{1}{2}\times\frac{}3{3}=\frac{3}{6}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator. 

$\displaystyle \frac{4}{6}+\frac{3}{6}=\frac{7}{6}$

$\displaystyle \frac{7}{6}=1\frac{1}{6}$ because $\displaystyle 6$ can go into $\displaystyle 7$ one time with $\displaystyle \frac{1}{6}$ left over. 

$\displaystyle \frac{1}{4}+\frac{4}{8}$

In order to solve this problem, we first have to find common denominators. 

$\displaystyle \frac{1}{4}\times\frac{2}{2}=\frac{2}{8}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator. 

$\displaystyle \frac{2}{8}+\frac{4}{8}=\frac{6}{8}$

$\displaystyle \frac{6}{8}\div\frac{2}{2}=\frac{3}{4}$

$\displaystyle \frac{4}6{+\frac{3}{8}}$

In order to solve this problem, we first have to find common denominators. 

$\displaystyle \frac{4}{6}\times\frac{4}{4}=\frac{16}{24}$

$\displaystyle \frac{3}{8}\times\frac{3}{3}=\frac{9}{24}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator. 

$\displaystyle \frac{16}{24}+\frac{9}{24}=\frac{25}{24}$

$\displaystyle \frac{25}{24}=1\frac{1}{24}$ because $\displaystyle 24$ can go into $\displaystyle 25$ one time with $\displaystyle 1$ left over.