Each dime is worth \(\displaystyle 10\cent\) and each nickel is worth \(\displaystyle 5\cent\).

We have two dimes and one nickel. 

\(\displaystyle \frac{\begin{array}[b]{r}10\cent\\ +\ 10\cent\end{array}}{ \ \ \ \space 20\cent}\) \(\displaystyle 5\cent\)

\(\displaystyle \frac{\begin{array}[b]{r}20\cent\\ +\ 5\cent\end{array}}{ \ \ \ \space 25\cent}\)

Each penny is worth \(\displaystyle 1\cent\) and each nickel is worth \(\displaystyle 5\cent.\)

We have six pennies and three nickels. 

\(\displaystyle \frac{\begin{array}[b]{r}1\cent\\ \ 1\cent\\ 1\cent\\ \ 1\cent\\ 1\cent\\ +\ 1\cent\end{array}}{ \ \ \ \space 6\cent}\) \(\displaystyle \frac{\begin{array}[b]{r}5\cent\\ 5\cent\\ +\ 5\cent\end{array}}{ \ \ \space 15\cent}\)

\(\displaystyle \frac{\begin{array}[b]{r}6\cent\\ +\ 15\cent\end{array}}{ \ \ \ \space 21\cent}\)

Each nickel is worth \(\displaystyle 5\cent\) and each dime is worth \(\displaystyle 10\cent\).

We have three nickels and three dimes.

 \(\displaystyle \frac{\begin{array}[b]{r}5\cent\\ \ 5\cent\\ +\ 5\cent\end{array}}{ \ \ \space 15\cent}\) \(\displaystyle \frac{\begin{array}[b]{r}10\cent\\ 10\cent\\ \ +\ 10\cent\end{array}}{ \ \ \ \space 30\cent}\)

\(\displaystyle \frac{\begin{array}[b]{r}15\cent\\ +\ 30\cent\end{array}}{ \ \ \ \space 45\cent}\)

Each quarter is worth \(\displaystyle 25\cent\) and each nickel is worth \(\displaystyle 5\cent\).

We have one quarter and two nickels.

 \(\displaystyle 25\cent\) \(\displaystyle \frac{\begin{array}[b]{r}5\cent\\ +\ 5\cent\end{array}}{ \ \ \space 10\cent}\)

\(\displaystyle \frac{\begin{array}[b]{r}25\cent\\ +\ 10\cent\end{array}}{ \ \ \ \space 35\cent}\)

Each dime is worth \(\displaystyle 10\cent\) and each penny is worth \(\displaystyle 1\cent\).

We have five dimes and five pennies. 

\(\displaystyle \frac{\begin{array}[b]{r}10\cent\\ \ 10\cent\\ 10\cent\\ \ 10\cent\\+\ 10\cent\end{array}}{ \ \ \ \space 50\cent}\) \(\displaystyle \frac{\begin{array}[b]{r}1\cent\\ \ 1\cent\\ 1\cent\\ \ 1\cent\\+\ 1\cent\end{array}}{ \ \ \ \space 5\cent}\)

\(\displaystyle \frac{\begin{array}[b]{r}50\cent\\ +\ 5\cent\end{array}}{ \ \ \space 55\cent}\)

Each dime is worth \(\displaystyle 10\cent\) and each penny is worth \(\displaystyle 1\cent\). 

We have three dimes and eight pennies. 

 \(\displaystyle \frac{\begin{array}[b]{r}10\cent\\ \ 10\cent\\ +\ 10\cent\end{array}}{ \ \ \ \space 30\cent}\)  \(\displaystyle \frac{\begin{array}[b]{r}1\cent\\1\cent\\1\cent\\1\cent\\1\cent\\1\cent\\1\cent\\ +\ 1\cent\end{array}}{ \ \ \ \space 8\cent}\)

\(\displaystyle \frac{\begin{array}[b]{r}30\cent\\ +\ 8\cent\end{array}}{ \ \ \space 38\cent}\)

The number \(\displaystyle 1\) as a word is one. 

In this series we are counting by \(\displaystyle 10\). When counting by \(\displaystyle 10\), \(\displaystyle 30\) is between \(\displaystyle 20\) and \(\displaystyle 40.\)

The only sequence from above that adds \(\displaystyle 4\) each time is \(\displaystyle 8,12,16\)

\(\displaystyle 8+4=12\)

\(\displaystyle 12+4=16\)

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

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.