This part is interesting. In the last section we saw that we could \textbf{not} further simplify terms that were different such as \(2x + 4y\). But now with multiplication and division we can! \(2x \times 4y = 8xy\) and \(2x \div 4y = \frac{\cancel{2}x}{\cancel{4}y} = \frac{x}{2y}\). Isn't that cool?

Okay, now you guys try:
 \begin{examplebox}                                                                                             
     \subsection{Examples}                                                                                      
     \begin{questions}                                                                                          
         \Question[6] Multiplications                                                                           
             \begin{multicols}{3}                                                                               
             \begin{parts}                                                                                      
                 \part \(4 \times 3a = \)                                                                    
                 \begin{solutionordottedlines}[1cm]                                                             
                 12a                                                                                            
                 \end{solutionordottedlines}                                                                    
                 \part \(2d \times 5e = \)                                                                  
                 \begin{solutionordottedlines}[1cm]                                                             
                 10de                                                                                           
                 \end{solutionordottedlines}                                                                    
                 \part \(4m \times 5m = \)                                                                 
                 \begin{solutionordottedlines}[1cm]                                                             
                 $20m^2$                                                                                          
                 \end{solutionordottedlines}                                                                    
                 \part \(3p \times 2pq = \)                                                                
                 \begin{solutionordottedlines}[1cm]                                                             
                 $6p^2q$
                 \end{solutionordottedlines}                                                                    
                 \part \(3x \times (-6) = \)                                                                
                 \begin{solutionordottedlines}[1cm]                                                             
                 $-18x$                                                                                           
                 \end{solutionordottedlines}                                                                    
                 \part \(-5ab \times -3bc = 15abc^2\)                                                           
                 \begin{solutionordottedlines}[1cm]                                                             
                 $15abc^2$                                                                                        
                 \end{solutionordottedlines}                                                                    
             \end{parts}                                                                                        
             \end{multicols}                                                                                    
         \Question[6] Divisions                                                                                 
             \begin{multicols}{3}                                                                               
             \begin{parts}                                                                                      
                 \part \(24x \div 6 = \)                                                                      
                 \begin{solutionordottedlines}[1cm]                                                             
                 4x                                                                                             
                 \end{solutionordottedlines}                                                                    
                 \part \(36a\div 4 = \)                                                                       
                 \begin{solutionordottedlines}[1cm]                                                             
                 9a                                                                                             
                 \end{solutionordottedlines}                                                                    
                 \part \(-18x^2 \div (-3) = \)                                                              
                 \begin{solutionordottedlines}[1cm]                                                             
                 $6x^2$                                                                                           
                 \end{solutionordottedlines}                                                                    
                 \part \(\frac{15a}{3} = 5a\)                                                                   
                 \begin{solutionordottedlines}[1cm]                                                             
                 $5a$                                                                                             
                 \end{solutionordottedlines}                                                                    
                 \part \(\frac{12x}{21} = \frac{4x}{7}\)                                                        
                 \begin{solutionordottedlines}[1cm]                                                             
                 $\frac{4x}{7}$                                                                                   
                 \end{solutionordottedlines}                                                                    
                 \part \(\frac{-24xy}{6y} = \)                                                               
                 \begin{solutionordottedlines}[1cm]                                                             
                 $-4x$                                                                                            
                 \end{solutionordottedlines}                                                                    
             \end{parts}                                                                                        
             \end{multicols}                                                                                    
     \end{questions}                                                                                            
 \end{examplebox}                                                                                               


 \begin{exercisebox}                                                                                            
     \subsection{Exercises}                                                                                     
     \begin{questions}                                                                                          
         \Question[6] Rewrite as a single fraction:                                                             
             \begin{multicols}{3}                                                                               
             \begin{doublespace}                                                                                
             \begin{parts}                                                                                      
                 \part \(\frac{2a}{5} \times \frac{a}{4}=\frac{2a^2}{20}=\frac{a^2}{10}\)                       
                 \begin{solutionordottedlines}[1cm]                                                             
                 $\frac{a^2}{10}$                                                                                 
                 \end{solutionordottedlines}                                                                    
                 \part \(\frac{3x}{7} \times \frac{5y}{12}=\frac{15xy}{84}=\frac{5xy}{28}\)                     
                 \begin{solutionordottedlines}[1cm]                                                             
                 $\frac{5xy}{28}$                                                                                 
                 \end{solutionordottedlines}                                                                    
                 \part \(\frac{4p}{q} \times \frac{3}{2p}=\frac{12p}{2pq}=\frac{6}{q}\)                         
                 \begin{solutionordottedlines}[1cm]                                                             
                 $\frac{6}{q}$                                                                                    
                 \end{solutionordottedlines}                                                                    
                 \part \(\frac{15}{x} \times \frac{2}{3x}=\frac{30}{3x^2}=\frac{10}{x^2}\)                      
                 \begin{solutionordottedlines}[1cm]                                                             
                 $\frac{10}{x^2}$                                                                                 
                 \end{solutionordottedlines}                                                                    
                 \part \(\frac{2x}{3} \div \frac{3x}{5}=\frac{2x}{3} \times \frac{5}{3x}=\frac{10}{9}\)         
                 \begin{solutionordottedlines}[1cm]                                                             
                 $\frac{10}{9}$                                                                                   
                 \end{solutionordottedlines}                                                                    
                 \part \(\frac{6a}{7b} \div \frac{2ab}{3}=\frac{6a}{7b} \times                                  
 \frac{3}{2ab}=\frac{18}{14b^2}=\frac{9}{7b^2}\)                                                                
                 \begin{solutionordottedlines}[1cm]                                                             
                 $\frac{9}{7b^2}$                                                                                 
                 \end{solutionordottedlines}                                                                    
             \end{parts}                                                                                        
             \end{doublespace}                                                                                  
             \end{multicols}                                                                                    
         \Question[6] Simplify                                                                                  
             \begin{multicols}{3}                                                                               
             \begin{parts}                                                                                      
                 \part \(5c \times 2d = 10cd\)                                                                  
                 \begin{solutionordottedlines}[1cm]                                                             
                 10cd                                                                                           
                 \end{solutionordottedlines}                                                                    
                 \part \(-6l \times (-5m)= 30lm\)                                                               
                 \begin{solutionordottedlines}[1cm]                                                             
                 30lm                                                                                           
                 \end{solutionordottedlines}                                                                    
                 \part \(-2m \times (-4m)= 8m^2\)                                                               
                 \begin{solutionordottedlines}[1cm]                                                             
                 $8m^2$                                                                                           
                 \end{solutionordottedlines}                                                                    
                 \part \(24a^2 \div 8 = 3a^2\)                                                                  
                 \begin{solutionordottedlines}[1cm]                                                             
                 $3a^2$                                                                                           
                 \end{solutionordottedlines}                                                                    
                 \part \(7 \times 15p \div 21 = 5p\)                                                            
                 \begin{solutionordottedlines}[1cm]                                                             
                 $5p$                                                                                             
                 \end{solutionordottedlines}                                                                    
                 \part \(18y \div 6 \times 2= 6y\)                                                              
                 \begin{solutionordottedlines}[1cm]                                                             
                 $6y$                                                                                             
                 \end{solutionordottedlines}                                                                    
             \end{parts}                                                                                        
             \end{multicols}                                                                                    
         \Question[8] Simplify by first cancelling out common factors:                                          
             \begin{multicols}{4}                                                                               
             \begin{doublespace}                                                                                
             \begin{parts}                                                                                      
                 \part \(\frac{14p}{21} =\frac{2p}{3}\)                                                         
                 \begin{solutionordottedlines}[1cm]                                                             
                 $\frac{2p}{3}$                                                                                   
                 \end{solutionordottedlines}                                                                    
                 \part \(\frac{22x^2}{33} =\frac{2x^2}{3}\)                                                     
                 \begin{solutionordottedlines}[1cm]                                                             
                 $\frac{2x^2}{3}$                                                                                 
                 \end{solutionordottedlines}                                                                    
                 \part \(\frac{2xy}{6xy}=\frac{1}{3}\)                                                          
                 \begin{solutionordottedlines}[1cm]                                                             
                 $\frac{1}{3}$                                                                                    
                 \end{solutionordottedlines}                                                                    
                 \part \(\frac{-4xy}{8x} =\frac{-y}{2}\)                                                        
                 \begin{solutionordottedlines}[1cm]                                                             
                 $\frac{-y}{2}$                                                                                   
                 \end{solutionordottedlines}                                                                    
                 \part \(\frac{2y}{5} \times \frac{y}{4} =\frac{2y^2}{20}=\frac{y^2}{10}\)                      
                 \begin{solutionordottedlines}[1cm]                                                             
                 $\frac{y^2}{10}$                                                                                 
                 \end{solutionordottedlines}                                                                    
                 \part \(\frac{p}{6q} \times \frac{9p}{4q} =\frac{9p^2}{24q^2}=\frac{3p^2}{8q^2}\)              
                 \begin{solutionordottedlines}[1cm]                                                             
                 $\frac{3p^2}{8q^2}$                                                                              
                 \end{solutionordottedlines}                                                                    
                 \part \(\frac{2yz}{5xy} \times \frac{3xy}{4yz} =\frac{6xyz}{20xyz}=\frac{3}{10}\)              
                 \begin{solutionordottedlines}[1cm]                                                             
                 $\frac{3}{10}$                                                                                   
                 \end{solutionordottedlines}                                                                    
                 \part \(\frac{2y}{5} \div \frac{y}{4} =\frac{2y}{5} \times \frac{4}{y}=\frac{8}{5}\)           
                 \begin{solutionordottedlines}[1cm]                                                             
                 $\frac{8}{5}$                                                                                    
                 \end{solutionordottedlines}                                                                    
             \end{parts}                                                                                        
             \end{doublespace}                                                                                  
             \end{multicols}                                                                                    
     \end{questions}                                                                                            
 \end{exercisebox}                                                                                              
