[tex]2\frac { 1 }{ 2 } \quad divided\quad by\quad 5\frac { 1 }{ 3 } \\ \\ 2\frac { 1 }{ 2 } =2+\frac { 1 }{ 2 } =\frac { 5 }{ 2 } \\ \\ 5\frac { 1 }{ 3 } =5+\frac { 1 }{ 3 } =\frac { 15+1 }{ 3 } =\frac { 16 }{ 3 } \\ \\ \\ \frac { \frac { 5 }{ 2 } }{ \frac { 16 }{ 3 } } [/tex]
We're dividing fractions, so we will flip the one in the denominator upside down and we will multiply it with the numerator.
[tex]\frac { \frac { 5 }{ 2 } }{ \frac { 16 }{ 3 } } \quad =\quad \frac { 5 }{ 2 } \cdot \frac { 3 }{ 16 } =\frac { 5\cdot 3 }{ 2\cdot 16 } =\frac { 15 }{ 32 } [/tex]
Let's equal this too 8/x
[tex]\frac { 15 }{ 32 } =\frac { 8 }{ x } [/tex]
Cross multiply.
[tex]8\cdot 32=15\cdot x\\ \\ 256=15x[/tex]
Divide both sides by 15.
[tex]\frac { 256 }{ 15 } =\frac { 15x }{ 15 } \\ \\ \frac { 256 }{ 15 } =x[/tex]
