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 \begin{enumerate}
 \item Fill in the missing digits. Prove that the solutions are unique. Assume the divisions have no remainders. \\
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\item \textbf{Royal Forks and Knives Problem}. The Queen's pantry has one drawer that contains forks and knives. The Royal servants take some of them out to set the table for a Royal dinner. Every individual table setting has exactly one fork and one knife. The servants use 2/3 of the forks and 3/5 of the knives in the drawer.
 \begin{enumerate}

\item Consider the fraction of the total number of knives and forks that are being used for the Royal dinner. How many different fractions are possible?


\item Find a formula that tells you the fraction in use if you know the fraction of forks in use and fraction of knives in use?

\end{enumerate}
 \item Constructively prove that between any two distinct fractions there is another fraction. That is, I want a formula for such a fraction given the surrounding fractions.

\item \begin{enumerate}
 \item \label{samedenominator} Write a formula for subtracting fractions of the same denominator and justify it using our part-whole definition of fraction.
 \item Derive a general formula for subtraction of fractions using our golden rule of equivalence and (\ref{samedenominator}).
 \end{enumerate}
 \end{enumerate}


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