# To translate given phrase into an algebraic expression using x

To translate given phrase into an algebraic expression using $$\displaystyle{x}$$ to represent the number.
The given phrase is divide a number by $$\displaystyle-{6}{\frac{{{1}}}{{{11}}}}$$.

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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 $$\displaystyle-{\frac{{{11}}}{{{67}}}}{x}$$.