Question

How do you divide `\frac { 3} { 8} \div \frac { 5} { 6}`?

Answer 1

`3/8div5/6=color(green)(4/9)`

Explanation:

Division is identical to multiplication by the (multiplicative) inverse.

The (multiplicative) inverse of `5/6` is `6/5`.

So
`color(white)("XXX")3/8 div 5/6 = 3/8 xx 6/5`

`color(white)("XXXXXXXX") = 3/4xx3/5`

`color(white)("XXXXXXXX")=9/20`

Answer 2

`3/8-:5/6`

Instead of dividing, make them multiply by doing so,

`3/cancel(8)_4xxcancel(6)^3/5`

Multiply numerators and denominators,

`(3xx3)/(4xx5)`

Hence, the answer is `9/20`.