Question

Which expression is equivalent to -2 1/4÷ (-2/3)​

Answer 1

`-2(1)/(4)/\left(-(2)/(3)\right)=(27)/(8)=3(3)/(8)}`

Explanation:

`-2(1)/(4)/\left(-(2)/(3)\right)\qquad\text{the quotient of two negative numbers is positive}\\\\=2(1)/(4)/(2)/(3)\qquad\text{convert the mixed number to the improper fraction}\\\\=(2\cdot4+1)/(4)/(2)/(3)=(9)/(4)/(2)/(3)\\\\\text{dividing by a fraction is the same as multiplying by its reciprocal.}\\\\=(9)/(4)\cdot(3)/(2)=(9\cdot3)/(4\cdot2)=(27)/(8)\qquad\text{convert to the mixed number}\\\\=3(3)/(8)`