%\addcontentsline{toc}{section}{Activity 1.12}
\section*{Activity 1.12}

In this activity, we want to explore what happens to the product when we multiply two numbers and then increase the first number by 1 and decrease the second number by 1.

\begin{enumerate} \item \textbf{{\large When we multiply a number by itself!}}\\ \begin{tabular}{|c|c|} \hline A & B\\ \hline $7\times 7 = 49$ & $8\times 6 = 48$\\ \hline $8\times 8 = 64$ & $9\times 7 = 63$\\ \hline \end{tabular} The general equation for this problem can be written as follows!\\ If $x^2 = k$, then $(x+1)(x-1) = k-1$\\ General statement!\\ If we multiply a number by itself and the product is equal to $k$, and then we increase the first number by 1 and decrease …show more content…
\item \textbf{When the first number is smaller than the second number.}\\ \begin{tabular}{|c|c|} \hline A & B\\ \hline $3\times 6 = 18$ & $4\times 5 = 20$\\ \hline $6\times 9 = 54$ & $7\times 8 = 56$\\ \hline \end{tabular} The general equation for this problem can be written as follows!\\ If $x\times y = k$; where $y = x+3$, then $(x+1)(y-1) = k+2$\\ General statement!\\ If the product of two numbers is equal to $k$; whereby the first number is equal to the second number minus three, and then we increase the first number by 1 and decrease the second number by 1, the product will be $k+2$. \end{enumerate} \item \textbf{{\large When two factors are 4 apart!}} \begin{enumerate} \item \textbf{When the first number is bigger than the second number.}\\ \begin{tabular}{|c|c|} \hline A & B\\ \hline $7\times 3 = 21$ & $8\times 2 = 16$\\ \hline $9\times 5 = 45$ & $10\times 4 = 40$\\ \hline \end{tabular} The general equation for this problem can be written as