Step 1

Let us suppose the number be x.

The phrase ''Divide a number by \(\displaystyle-{6}{\frac{{{1}}}{{{11}}}}\).'' means divide the number x by \(\displaystyle-{6}{\frac{{{1}}}{{{11}}}}\)

The following algebraic expression will be formed:

\(\displaystyle{x}\div{\left(-{6}{\frac{{{1}}}{{{11}}}}\right)}\)

\(\displaystyle={x}\div{\left(-{\frac{{{67}}}{{{11}}}}\right)}\)

\(\displaystyle={x}\times{\left(-{\frac{{{11}}}{{{67}}}}\right)}\)

\(\{\text{changing}\ \div\ to\ \div \text{by inverting the fraction\}}\)

\(\displaystyle=-{\frac{{{11}}}{{{67}}}}{x}\)

The algebraic expression is \(\displaystyle-{\frac{{{11}}}{{{67}}}}{x}\).