Solve (6/11div3/22)div4/3=6/11div(frac{3}{22}divfrac{4}{3})

$$( \frac{ 6 }{ 11 } \div \frac{ 3 }{ 22 } ) \div \frac{ 4 }{ 3 } = \frac{ 6 }{ 11 } \div ( \frac{ 3 }{ 22 } \div \frac{ 4 }{ 3 } )$$

Verify

Solution Steps

Divide \frac{\frac{6}{11}}{\frac{3}{22}} by \frac{4}{3} by multiplying \frac{\frac{6}{11}}{\frac{3}{22}} by the reciprocal of \frac{4}{3}.

$$\frac{\frac{6}{11}\times 3}{\frac{3}{22}\times 4}=\frac{\frac{6}{11}}{\frac{\frac{3}{22}}{\frac{4}{3}}}$$

Express \frac{6}{11}\times 3 as a single fraction.

$$\frac{\frac{6\times 3}{11}}{\frac{3}{22}\times 4}=\frac{\frac{6}{11}}{\frac{\frac{3}{22}}{\frac{4}{3}}}$$

Multiply 6 and 3 to get 18.

$$\frac{\frac{18}{11}}{\frac{3}{22}\times 4}=\frac{\frac{6}{11}}{\frac{\frac{3}{22}}{\frac{4}{3}}}$$

Express \frac{3}{22}\times 4 as a single fraction.

$$\frac{\frac{18}{11}}{\frac{3\times 4}{22}}=\frac{\frac{6}{11}}{\frac{\frac{3}{22}}{\frac{4}{3}}}$$

Multiply 3 and 4 to get 12.

$$\frac{\frac{18}{11}}{\frac{12}{22}}=\frac{\frac{6}{11}}{\frac{\frac{3}{22}}{\frac{4}{3}}}$$

Reduce the fraction \frac{12}{22} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{18}{11}}{\frac{6}{11}}=\frac{\frac{6}{11}}{\frac{\frac{3}{22}}{\frac{4}{3}}}$$

Divide \frac{18}{11} by \frac{6}{11} by multiplying \frac{18}{11} by the reciprocal of \frac{6}{11}.

$$\frac{18}{11}\times \frac{11}{6}=\frac{\frac{6}{11}}{\frac{\frac{3}{22}}{\frac{4}{3}}}$$

Multiply \frac{18}{11} times \frac{11}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{18\times 11}{11\times 6}=\frac{\frac{6}{11}}{\frac{\frac{3}{22}}{\frac{4}{3}}}$$

Cancel out 11 in both numerator and denominator.

$$\frac{18}{6}=\frac{\frac{6}{11}}{\frac{\frac{3}{22}}{\frac{4}{3}}}$$

Divide 18 by 6 to get 3.

$$3=\frac{\frac{6}{11}}{\frac{\frac{3}{22}}{\frac{4}{3}}}$$

Divide \frac{6}{11} by \frac{\frac{3}{22}}{\frac{4}{3}} by multiplying \frac{6}{11} by the reciprocal of \frac{\frac{3}{22}}{\frac{4}{3}}.

$$3=\frac{6\times \frac{4}{3}}{11\times \frac{3}{22}}$$

Express 6\times \frac{4}{3} as a single fraction.

$$3=\frac{\frac{6\times 4}{3}}{11\times \frac{3}{22}}$$

Multiply 6 and 4 to get 24.

$$3=\frac{\frac{24}{3}}{11\times \frac{3}{22}}$$

Divide 24 by 3 to get 8.

$$3=\frac{8}{11\times \frac{3}{22}}$$

Express 11\times \frac{3}{22} as a single fraction.

$$3=\frac{8}{\frac{11\times 3}{22}}$$

Multiply 11 and 3 to get 33.

$$3=\frac{8}{\frac{33}{22}}$$

Reduce the fraction \frac{33}{22} to lowest terms by extracting and canceling out 11.

$$3=\frac{8}{\frac{3}{2}}$$

Divide 8 by \frac{3}{2} by multiplying 8 by the reciprocal of \frac{3}{2}.

$$3=8\times \frac{2}{3}$$

Express 8\times \frac{2}{3} as a single fraction.

$$3=\frac{8\times 2}{3}$$

Multiply 8 and 2 to get 16.

$$3=\frac{16}{3}$$

Convert 3 to fraction \frac{9}{3}.

$$\frac{9}{3}=\frac{16}{3}$$

Compare \frac{9}{3} and \frac{16}{3}.

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