Respuesta :
To solve each of the given problems we will use the following properties of multiplication and division of fraction:
[tex]\begin{gathered} \frac{a}{b}\times\frac{d}{c}=\frac{a\times d}{b\times c} \\ \\ \frac{\frac{a}{b}}{\frac{d}{c}}=\frac{a}{b}\times\frac{c}{d} \\ \\ A\frac{B}{C}=\frac{A\times C+B}{C} \end{gathered}[/tex]To solve the problem a) we do as follows:
[tex]\frac{21}{\frac{7}{3}}=\frac{\frac{21}{1}}{\frac{7}{3}}=\frac{21}{1}\times\frac{3}{7}=\frac{21\times3}{1\times7}=\frac{63}{7}=9[/tex]From this solution, the answer for problem a) is 9
For the problem b), we proceed as follows:
[tex]\begin{gathered} \frac{4\frac{2}{3}}{\frac{7}{9}}=\frac{\frac{4\times3+2}{3}}{\frac{7}{9}} \\ \\ =\frac{\frac{14}{3}}{\frac{7}{9}} \\ \\ =\frac{14}{3}\times\frac{9}{7} \\ \\ =\frac{14\times9}{3\times7} \\ \\ =\frac{2\times7\times3\times3}{3\times7} \\ \\ =2\times3=6 \end{gathered}[/tex]From this solution, the answer for problem b) is 6
For the problem in the question c), we proceed as follows:
[tex]\frac{\frac{12}{7}}{\frac{2}{7}}=\frac{12}{7}\times\frac{7}{2}=\frac{12\times7}{7\times2}=\frac{12}{2}=6[/tex]From this solution, the answer for problem c) is 6
Now, for the problem d), we proceed as follows:
[tex]\frac{4\frac{1}{2}}{\frac{1}{2}}=\frac{\frac{4\times2+1}{2}}{\frac{1}{2}}=\frac{\frac{8+1}{2}}{\frac{1}{2}}=\frac{\frac{9}{2}}{\frac{1}{2}}=\frac{9}{2}\times\frac{2}{1}=\frac{9\times2}{2\times1}=9[/tex]From this solution, the answer for problem d) is 9
To solve the problem e), we proceed as follows:
[tex]\frac{\frac{72}{7}}{\frac{8}{7}}=\frac{72}{7}\times\frac{7}{8}=\frac{72\times7}{7\times8}=\frac{72}{8}=9[/tex]From this solution, the answer for problem e) is 9
To solve the problem f), we proceed as follows:
[tex]\frac{9}{\frac{3}{2}}=\frac{\frac{9}{1}}{\frac{3}{2}}=\frac{9}{1}\times\frac{2}{3}=\frac{9\times2}{1\times3}=\frac{18}{3}=6[/tex]From this solution, the answer for problem f) is 6
