Solve (9divfrac{1/frac{1{8}}*4/5)5/12}{6div1/frac{1{2}}}

$$\frac{ (9 \div \frac{ 1 }{ \frac{ 1 }{ 8 } } \times \frac{ 4 }{ 5 } ) \frac{ 5 }{ 12 } }{ 6 \div \frac{ 1 }{ \frac{ 1 }{ 2 } } }$$

Evaluate

$$\frac{1}{8}=0.125$$

Solution Steps

Divide 9 by \frac{1}{\frac{1}{8}} by multiplying 9 by the reciprocal of \frac{1}{\frac{1}{8}}.

$$\frac{9\times \frac{1}{8}\times \frac{4}{5}\times \frac{5}{12}}{\frac{6}{\frac{1}{\frac{1}{2}}}}$$

Multiply 9 and \frac{1}{8} to get \frac{9}{8}.

$$\frac{\frac{9}{8}\times \frac{4}{5}\times \frac{5}{12}}{\frac{6}{\frac{1}{\frac{1}{2}}}}$$

Multiply \frac{9}{8} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9\times 4}{8\times 5}\times \frac{5}{12}}{\frac{6}{\frac{1}{\frac{1}{2}}}}$$

Do the multiplications in the fraction \frac{9\times 4}{8\times 5}.

$$\frac{\frac{36}{40}\times \frac{5}{12}}{\frac{6}{\frac{1}{\frac{1}{2}}}}$$

Reduce the fraction \frac{36}{40} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{9}{10}\times \frac{5}{12}}{\frac{6}{\frac{1}{\frac{1}{2}}}}$$

Multiply \frac{9}{10} times \frac{5}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9\times 5}{10\times 12}}{\frac{6}{\frac{1}{\frac{1}{2}}}}$$

Do the multiplications in the fraction \frac{9\times 5}{10\times 12}.

$$\frac{\frac{45}{120}}{\frac{6}{\frac{1}{\frac{1}{2}}}}$$

Reduce the fraction \frac{45}{120} to lowest terms by extracting and canceling out 15.

$$\frac{\frac{3}{8}}{\frac{6}{\frac{1}{\frac{1}{2}}}}$$

Divide 6 by \frac{1}{\frac{1}{2}} by multiplying 6 by the reciprocal of \frac{1}{\frac{1}{2}}.

$$\frac{\frac{3}{8}}{6\times \frac{1}{2}}$$

Multiply 6 and \frac{1}{2} to get \frac{6}{2}.

$$\frac{\frac{3}{8}}{\frac{6}{2}}$$

Divide 6 by 2 to get 3.

$$\frac{\frac{3}{8}}{3}$$

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

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

Cancel out 3 in both numerator and denominator.

$$\frac{1}{8}$$

Factor

$$\frac{1}{2 ^ {3}} = 0.125$$