Question

$5\frac{2}{3} div -\frac{5}{12}$

Explanation:

Step1: Convert mixed - number to improper fraction

$5\frac{2}{3}=\frac{5\times3 + 2}{3}=\frac{17}{3}$
So the expression becomes $\frac{17}{3}\div(-\frac{5}{12})$

Step2: Change division to multiplication

Dividing by a fraction is equivalent to multiplying by its reciprocal. So $\frac{17}{3}\div(-\frac{5}{12})=\frac{17}{3}\times(-\frac{12}{5})$

Step3: Multiply numerators and denominators

$\frac{17\times(- 12)}{3\times5}=\frac{-204}{15}$

Step4: Simplify the fraction

$\frac{-204}{15}=-\frac{68}{5}=-13\frac{3}{5}$

Answer:

$-\frac{68}{5}$ or $-13\frac{3}{5}$