Question

$$\begin{gathered} Forrationalnumbers1/2and1/3show \\ a)Commutativepropertyofaddition. \\ b)commutativepropertyofmultiplication \\ c)Writeadditiveinverseofbothnumbers \\ d)Multiplicativeinverseofbothnumbers \end{gathered}$$

Answer 1

Dear student,
$$\begin{gathered} a)Commutativepropertyofadditioni.e.a+b=b+a \\ Here,\frac{1}{2}+\frac{1}{3}=\frac{3+2}{6}=\frac{5}{6} \\ also,\frac{1}{3}+\frac{1}{2}=\frac{2+3}{6}=\frac{5}{6} \\ thus,\frac{1}{2}+\frac{1}{3}=\frac{1}{3}+\frac{1}{2} \\ Hencecommutativepropertyofadditionisverified. \\ b)Commutativepropertyofmultiplicationi.e.a\times b=b\times a \\ Here,\frac{1}{2}\times \frac{1}{3}=\frac{1}{6} \\ also,\frac{1}{3}\times \frac{1}{2}=\frac{1}{6} \\ thus,\frac{1}{2}\times \frac{1}{3}=\frac{1}{3}\times \frac{1}{2} \\ Hencecommutativepropertyofmultipliactionisverified. \\ c)Additiveinverseof\frac{1}{2}isgivenby \\ \frac{1}{2}+a=0 \\ \Rightarrow a=-\frac{1}{2} \\ Additiveinverseof\frac{1}{3}isgivenby \\ \frac{1}{3}+a=0 \\ \Rightarrow a=-\frac{1}{3} \\ d)Multiplicativeinverseof\frac{1}{2} \\ \frac{1}{2}\times a=1 \\ \Rightarrow a=2 \\ Multiplicativeinverseof\frac{1}{3} \\ \frac{1}{3}\times a=1 \\ \Rightarrow a=3 \end{gathered}$$

Regards