Given: The expression below
[tex]\frac{1}{10}\div-\frac{8}{9}[/tex]To Determine: The value of the given expression
Step 1: Change the division sign to multiplication sign and interchange the numerator and the denominator of the fraction to the right as shown below
[tex]\frac{1}{10}\times-\frac{9}{8}[/tex]Step 2: Simplify into a simple fraction
[tex]\frac{1\times-9}{10\times8}=-\frac{9}{80}[/tex]Hence, the simplest form of the given statement is
[tex]-\frac{9}{80}[/tex]