Answer: [tex]1\dfrac{4}{21}[/tex] .
Step-by-step explanation:
Given problem : [tex]\left(-5\dfrac{5}{6}\right)\div\left(-4\dfrac{9}{10}\right)[/tex]
First we convert mixed fraction into improper fractions as
[tex]-5\dfrac{5}{6}=-\dfrac{5\times6+5}{6}=-\dfrac{30+5}{6}=-\dfrac{35}{6}\\-4\dfrac{9}{10}=-\dfrac{10\times4+9}{10}=-\dfrac{40+9}{10}=-\dfrac{49}{10}[/tex]
Now , plug these values in the given expression , we get
[tex]\left(-5\dfrac{5}{6}\right)\div\left(-4\dfrac{9}{10}\right)=-\dfrac{35}{6}\div\left(-\dfrac{49}{10}\right)\\\\=\dfrac{-35}{6}\times\dfrac{-10}{49}\ \ \ [\text{By Property of fraction}]\\\\=\dfrac{350}{294}\\\\=\dfrac{25}{21}=1\dfrac{4}{21}[/tex]
Hence, the answer is [tex]1\dfrac{4}{21}[/tex] .
