Question

Evaluate and simplify the following complex fraction.

Answer 1

Thus,

`((2)/(3))/((4)/(-9))=-(3)/(2)`

Explanation:

Given the expression

`((2)/(3))/((4)/(-9))`

`\mathrm{Apply\:the\:fraction\:rule}:\quad (a)/(-b)=-(a)/(b)`

`=((2)/(3))/(-(4)/(9))`

`\mathrm{Apply\:the\:fraction\:rule}:\quad (a)/(-b)=-(a)/(b)`

`=-((2)/(3))/((4)/(9))`

`\mathrm{Divide\:fractions}:\quad ((a)/(b))/((c)/(d))=(a\cdot \:d)/(b\cdot \:c)`

`=-(2\cdot \:9)/(3\cdot \:4)`

`=-(18)/(12)`

`\mathrm{Cancel\:the\:common\:factor:}\:6`

`=-(3)/(2)`

Thus,

`((2)/(3))/((4)/(-9))=-(3)/(2)`