We can compute $21\times 17$ by filling in the missing numbers and adding the results. So, let's find the missing values:

\begin{align*} {\color{blue}{20}}\times {\color{red}{10}} &= \fbox{$\,200\,$}\\[5pt] {\color{blue}{20}}\times {\color{red}{7}} &= \fbox{$\,140\,$}\\[5pt] {\color{blue}{1}}\times {\color{red}{10}} &= \fbox{$\,10\,$}\\[5pt] {\color{blue}{1}}\times {\color{red}{7}} &= \fbox{$\,7\,$}\\[5pt] \end{align*}

Let's now add these results:

\[ \begin{array}{cccccccc} %& \!\!\!\! {\small\color{blue}1} \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \\ & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 4 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\ \hline & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 5 \!\!\!\! & \!\!\!\! 7 \!\!\!\! \end{array} \]

Therefore,

\[ 21\times 17 = 357. \]

We can compute $39\times 18$ by filling in the missing numbers and adding the results. So, let's find the missing values:

\begin{align*} {\color{blue}{30}}\times {\color{red}{10}} &= \fbox{$\,300\,$}\\[5pt] {\color{blue}{30}}\times {\color{red}{8}} &= \fbox{$\,240\,$}\\[5pt] {\color{blue}{9}}\times {\color{red}{10}} &= \fbox{$\,90\,$}\\[5pt] {\color{blue}{9}}\times {\color{red}{8}} &= \fbox{$\,72\,$}\\[5pt] \end{align*}

Let's now add these results:

\[ \begin{array}{cccccccc} & \!\!\!\! {\small\color{blue}2} \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \\ & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 4 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! 9 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! 7 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\ \hline & \!\!\!\! 7 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 2 \!\!\!\! \end{array} \]

Therefore,

\[ 39\times 18 = 702. \]

First, let's write our factors in expanded form:

\begin{align} 54 &= {\color{blue}{50}} + {\color{blue}{4}}, \qquad 37 = {\color{red}{30}} + {\color{red}{7}} \end{align}

Next, we multiply both numbers in the first factor's expanded form by both numbers in the second factor's expanded form:

• First, we multiply ${\color{blue}{50}}$ by ${\color{red}{30}}$ and ${\color{red}{7}} \mathbin{:}$ \begin{align} {\color{blue}{50}} \times {\color{red}{30}} &= 1,500 \\[5pt] {\color{blue}{50}} \times {\color{red}{7}} &= 350 \end{align}

• Then, we multiply ${\color{blue}{4}}$ by ${\color{red}{30}}$ and ${\color{red}{7}} \mathbin{:}$ \begin{align} {\color{blue}{4}} \times {\color{red}{30}} &= 120 \\[5pt] {\color{blue}{4}} \times {\color{red}{7}} &= 28 \end{align}

Let's now add all our results:

\[ \begin{array}{cccccccc} %& \!\!\!\! \!\!\!\! & \!\!\!\! {\small\color{blue}1} \!\!\!\! & \!\!\!\! \!\!\!\! & \\ & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 5 \!\!\!\! & \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 5 \!\!\!\! & \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 8 \!\!\!\! \\ \hline & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 9 \!\!\!\! & \!\!\!\! 9 \!\!\!\! & \!\!\!\! 8 \!\!\!\! \end{array} \]

Therefore,

\[ 54 \times 37 = 1,998. \]

First, let's write our factors in expanded form:

\begin{align} 14 &= {\color{blue}{10}} + {\color{blue}{4}}, \qquad 19 = {\color{red}{10}} + {\color{red}{9}} \end{align}

Next, we multiply both numbers in the first factor's expanded form by both numbers in the second factor's expanded form:

• First, we multiply ${\color{blue}{10}}$ by ${\color{red}{10}}$ and ${\color{red}{9}} \mathbin{:}$ \begin{align} {\color{blue}{10}} \times {\color{red}{10}} &= 100 \\[5pt] {\color{blue}{10}} \times {\color{red}{9}} &= 90 \end{align}

• Then, we multiply ${\color{blue}{4}}$ by ${\color{red}{10}}$ and ${\color{red}{9}} \mathbin{:}$ \begin{align} {\color{blue}{4}} \times {\color{red}{10}} &= 40 \\[5pt] {\color{blue}{4}} \times {\color{red}{9}} &= 36 \end{align}

Let's now add all our results:

\[ \begin{array}{cccccccc} & \!\!\!\! {\small\color{blue}1} \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \\ & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! 9 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! 4 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\ \hline & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 6 \!\!\!\! & \!\!\!\! 6 \!\!\!\! \end{array} \]

Therefore,

\[ 14 \times 19 = 266. \]

To figure out the total number of hours Sarah will spend at school in $25$ weeks, we need to compute the value of

\[ 32 \times 25. \]

First, let's write our factors in expanded form:

\begin{align} 32 &= {\color{blue}{30}} + {\color{blue}{2}}, \qquad 25 = {\color{red}{20}} + {\color{red}{5}} \end{align}

Next, we multiply both numbers in the first factor's expanded form by both numbers in the second factor's expanded form:

• First, we multiply ${\color{blue}{30}}$ by ${\color{red}{20}}$ and ${\color{red}{5}} \mathbin{:}$ \begin{align} {\color{blue}{30}} \times {\color{red}{20}} &= 600 \\[5pt] {\color{blue}{30}} \times {\color{red}{5}} &= 150 \end{align}

• Then, we multiply ${\color{blue}{2}}$ by ${\color{red}{20}}$ and ${\color{red}{5}} \mathbin{:}$ \begin{align} {\color{blue}{2}} \times {\color{red}{20}} &= 40 \\[5pt] {\color{blue}{2}} \times {\color{red}{5}} &= 10 \end{align}

Let's now add all our results:

\[ \begin{array}{cccccccc} & \!\!\!\! {\small\color{blue}1} \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \\ & \!\!\!\! 6 \!\!\!\! & \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! 4 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \hline & \!\!\!\!8 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 0 \!\!\!\! \end{array} \]

Therefore, Sarah will spend $800$ hours at school.

To figure out the total number of sold tickets, we need to compute the value of

\[ 85 \times 16. \]

First, let's write our factors in expanded form:

\begin{align} 85 &= {\color{blue}{80}} + {\color{blue}{5}}, \qquad 16 = {\color{red}{10}} + {\color{red}{6}} \end{align}

Next, we multiply both numbers in the first factor's expanded form by both numbers in the second factor's expanded form:

• First, we multiply ${\color{blue}{80}}$ by ${\color{red}{10}}$ and ${\color{red}{6}} \mathbin{:}$ \begin{align} {\color{blue}{80}} \times {\color{red}{10}} &= 800 \\[5pt] {\color{blue}{80}} \times {\color{red}{6}} &= 480 \end{align}

• Then, we multiply ${\color{blue}{5}}$ by ${\color{red}{10}}$ and ${\color{red}{6}} \mathbin{:}$ \begin{align} {\color{blue}{5}} \times {\color{red}{10}} &= 50 \\[5pt] {\color{blue}{5}} \times {\color{red}{6}} &= 30 \end{align}

Let's now add all our results:

\[ \begin{array}{cccccccc} & \!\!\!\! {\small\color{blue}1} \!\!\!\! & \!\!\!\! {\small\color{blue}1} \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \\ & \!\!\!\! \!\!\!\! & \!\!\!\! 8 \!\!\!\! & \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! 4 \!\!\!\! & \!\!\!\! 8 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \hline & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 6 \!\!\!\! & \!\!\!\! 0 \!\!\!\! \end{array} \]

Therefore, the theater sold $1,360$ tickets.