Before we begin, let's review the pieces of a division problem:

\(\displaystyle {\begin{array}[b]{r} \ \textup{ quotient}\\ \textup{ divisor}{\overline{\smash{)}\ \textup{dividend}}}\\\end{array}}{ \ \ \ \space}\)

The quotient is the answer to the division problem. The dividend is the number that gets divided by the divisor. 

One way to solve a division problem is to create an area model. The divisor equals the number of squares that make up the base of the area model. The dividend equals the number of total squares used. Fill the squares up from the base until you've used the correct number of squares. The height of the area model will be the quotient: 

\(\displaystyle 30\times\) __________ \(\displaystyle =600\)

Another way to solve a division problem is to think of it as a multiplication problem. What number times the divisor equals the dividend? 

\(\displaystyle \frac{\begin{array}[b]{r}30\\ \times \ \ \ 20\end{array}}{\frac{\begin{array}[b]{r}{\color{Red} 00}\\ \ +\ {\color{Red} 600} \end{array}}{\ }} \\ {\ \ \ \ \ \ \ \ \ \ \ 600}\)

This means that \(\displaystyle 13\times {\color{Red} 20}=600\); thus, \(\displaystyle {\begin{array}[b]{r} \ \textup{ {\color{Red} 20}}\\ \textup{ 30}{\overline{\smash{)}\ \textup{600}}}\\\end{array}}{ \ \ \ \space}\)

\(\displaystyle \frac{3}{10}+\frac{1}{2}\)

In order to solve this problem, we first need to make common denominators. 

\(\displaystyle \frac{1}{2}\times\frac{5}{5}=\frac{5}{10}\)

Now that we have common denominators, we can add the fractions. Remember, when we add fractions, the denominator stays the same, we only add the numerator. 

 \(\displaystyle \frac{3}{10 }+\frac{5}{10}=\frac{8}{10}\)

\(\displaystyle \frac{8}{10}\) can be reduced be dividing both sides by \(\displaystyle 2\).

\(\displaystyle \frac{8}{10} \div\frac{2}{2}=\frac{4}{5}\)

\(\displaystyle \frac{1}{8}+\frac{1}{3}\)

In order to solve this problem, we first need to make common denominators. 

\(\displaystyle \frac{1}{8}\times\frac{3}{3}=\frac{3}{24}\)

\(\displaystyle \frac{1}{3}\times\frac{8}{8}=\frac{8}{24}\)

Now that we have common denominators, we can add the fractions. Remember, when we add fractions, the denominator stays the same, we only add the numerator. 

\(\displaystyle \frac{3}{24}+\frac{8}{24}=\frac{11}{24}\)

\(\displaystyle \frac{3}{8}+\frac{1}{4}\)

In order to solve this problem, we first need to make 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 fractions, the denominator stays the same, we only add the numerator. 

\(\displaystyle \frac{3}{8}+\frac{2}8{=\frac{5}{8}}\)

\(\displaystyle \small \frac{1}{7}+\frac{4}{14}\)

In order to solve this problem, we first need to make common denominators. 

\(\displaystyle \frac{1}{7}\times\frac{2}{2}=\frac{2}{14}\)

Now that we have common denominators, we can add the fractions. Remember, when we add fractions, the denominator stays the same, we only add the numerator. 

\(\displaystyle \small \frac{2}{14}+\frac{4}{14}=\frac{6}{14}\)

\(\displaystyle \small \frac{6}{14}\) can be reduced by dividing \(\displaystyle \small 2\) by both sides. 

\(\displaystyle \small \frac{6}{14}\div\frac{2}{2}=\frac{3}{7}\)

\(\displaystyle \frac{1}{3}+\frac{1}2{}\)

In order to solve this problem, we first need to make common denominators. 

\(\displaystyle \frac{1}3{\times\frac{2}{2}=\frac{2}{6}}\)

\(\displaystyle \frac{1}{2}\times\frac{3}{3}=\frac{3}{6}\)

Now that we have common denominators, we can add the fractions. Remember, when we add fractions, the denominator stays the same, we only add the numerator. 

\(\displaystyle \frac{2}{6}+\frac{3}{6}=\frac{5}{6}\)

\(\displaystyle \frac{1}{7}+\frac{1}{3}\)

In order to solve this problem, we first need to make common denominators. 

\(\displaystyle \frac{1}{7}\times\frac{3}{3}=\frac{3}{21}\)

\(\displaystyle \frac{1}{3}\times \frac{7}{7}=\frac{7}{21}\)

Now that we have common denominators, we can add the fractions. Remember, when we add fractions, the denominator stays the same, we only add the numerator. 

\(\displaystyle \frac{3}{21}+\frac{7}{21}=\frac{10}{21}\)