Question

what is $-\frac{5}{6}div\frac{9}{10}$?
$-\frac{27}{25}$
$-\frac{4}{3}$
$-\frac{25}{27}$
$-\frac{3}{4}$

Explanation:

Step1: Change division to multiplication

Dividing by a fraction is the same as multiplying by its reciprocal. So, $-\frac{5}{6}\div\frac{9}{10}=-\frac{5}{6}\times\frac{10}{9}$.

Step2: Multiply the numerators and denominators

Multiply the numerators $(- 5\times10=-50)$ and the denominators $(6\times9 = 54)$. So we get $-\frac{50}{54}$.

Step3: Simplify the fraction

Divide both the numerator and denominator by their greatest - common divisor, which is 2. $\frac{-50\div2}{54\div2}=-\frac{25}{27}$.

Answer:

$-\frac{25}{27}$