Question

Solve 2 1/2 divided by 5 1/3 = 8/x

Answer 1

`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 } }`

We're dividing fractions, so we will flip the one in the denominator upside down and we will multiply it with the numerator.


`\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 }`

Let's equal this too 8/x


`\frac { 15 }{ 32 } =\frac { 8 }{ x }`

Cross multiply.


`8\cdot 32=15\cdot x\\ \\ 256=15x`

Divide both sides by 15.


`\frac { 256 }{ 15 } =\frac { 15x }{ 15 } \\ \\ \frac { 256 }{ 15 } =x`