Solve 3/4*(1/1-12/1*frac{1/18)}{frac{15}{-4}*(frac{1}{frac{1}{1}}*frac{1}{4}-frac{1}{5}-frac{1}{16})}

$$\frac { \frac { 3 } { 4 } \cdot ( \frac { 1 } { 1 } - \frac { 12 } { 1 } \cdot \frac { 1 } { 18 } ) } { \frac { 15 } { - 4 } \cdot ( \frac { 1 } { \frac { 1 } { 1 } } \cdot \frac { 1 } { 4 } - \frac { 1 } { 5 } - \frac { 1 } { 16 } ) }$$

Evaluate

$$\frac{16}{3}\approx 5.333333333$$

Solution Steps

Divide 1 by 1 to get 1.

$$\frac{\frac{3}{4}\left(1-\frac{12}{1}\times \frac{1}{18}\right)}{\frac{15}{-4}\left(\frac{1}{\frac{1}{1}}\times \frac{1}{4}-\frac{1}{5}-\frac{1}{16}\right)}$$

Divide 1 by 1 to get 1.

$$\frac{\frac{3}{4}\left(1-\frac{12}{1}\times \frac{1}{18}\right)}{\frac{15}{-4}\left(\frac{1}{1}\times \frac{1}{4}-\frac{1}{5}-\frac{1}{16}\right)}$$

Divide 1 by 1 to get 1.

$$\frac{\frac{3}{4}\left(1-\frac{12}{1}\times \frac{1}{18}\right)}{\frac{15}{-4}\left(1\times \frac{1}{4}-\frac{1}{5}-\frac{1}{16}\right)}$$

Anything divided by one gives itself.

$$\frac{\frac{3}{4}\left(1-12\times \frac{1}{18}\right)}{\frac{15}{-4}\left(1\times \frac{1}{4}-\frac{1}{5}-\frac{1}{16}\right)}$$

Multiply 12 and \frac{1}{18} to get \frac{12}{18}.

$$\frac{\frac{3}{4}\left(1-\frac{12}{18}\right)}{\frac{15}{-4}\left(1\times \frac{1}{4}-\frac{1}{5}-\frac{1}{16}\right)}$$

Reduce the fraction \frac{12}{18} to lowest terms by extracting and canceling out 6.

$$\frac{\frac{3}{4}\left(1-\frac{2}{3}\right)}{\frac{15}{-4}\left(1\times \frac{1}{4}-\frac{1}{5}-\frac{1}{16}\right)}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{\frac{3}{4}\left(\frac{3}{3}-\frac{2}{3}\right)}{\frac{15}{-4}\left(1\times \frac{1}{4}-\frac{1}{5}-\frac{1}{16}\right)}$$

Since \frac{3}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3}{4}\times \frac{3-2}{3}}{\frac{15}{-4}\left(1\times \frac{1}{4}-\frac{1}{5}-\frac{1}{16}\right)}$$

Subtract 2 from 3 to get 1.

$$\frac{\frac{3}{4}\times \frac{1}{3}}{\frac{15}{-4}\left(1\times \frac{1}{4}-\frac{1}{5}-\frac{1}{16}\right)}$$

Multiply \frac{3}{4} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\times 1}{4\times 3}}{\frac{15}{-4}\left(1\times \frac{1}{4}-\frac{1}{5}-\frac{1}{16}\right)}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{1}{4}}{\frac{15}{-4}\left(1\times \frac{1}{4}-\frac{1}{5}-\frac{1}{16}\right)}$$

Fraction \frac{15}{-4} can be rewritten as -\frac{15}{4} by extracting the negative sign.

$$\frac{\frac{1}{4}}{-\frac{15}{4}\left(\frac{1}{4}-\frac{1}{5}-\frac{1}{16}\right)}$$

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{1}{5} to fractions with denominator 20.

$$\frac{\frac{1}{4}}{-\frac{15}{4}\left(\frac{5}{20}-\frac{4}{20}-\frac{1}{16}\right)}$$

Since \frac{5}{20} and \frac{4}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{4}}{-\frac{15}{4}\left(\frac{5-4}{20}-\frac{1}{16}\right)}$$

Subtract 4 from 5 to get 1.

$$\frac{\frac{1}{4}}{-\frac{15}{4}\left(\frac{1}{20}-\frac{1}{16}\right)}$$

Least common multiple of 20 and 16 is 80. Convert \frac{1}{20} and \frac{1}{16} to fractions with denominator 80.

$$\frac{\frac{1}{4}}{-\frac{15}{4}\left(\frac{4}{80}-\frac{5}{80}\right)}$$

Since \frac{4}{80} and \frac{5}{80} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{4}}{-\frac{15}{4}\times \frac{4-5}{80}}$$

Subtract 5 from 4 to get -1.

$$\frac{\frac{1}{4}}{-\frac{15}{4}\left(-\frac{1}{80}\right)}$$

Multiply -\frac{15}{4} times -\frac{1}{80} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{4}}{\frac{-15\left(-1\right)}{4\times 80}}$$

Do the multiplications in the fraction \frac{-15\left(-1\right)}{4\times 80}.

$$\frac{\frac{1}{4}}{\frac{15}{320}}$$

Reduce the fraction \frac{15}{320} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{1}{4}}{\frac{3}{64}}$$

Divide \frac{1}{4} by \frac{3}{64} by multiplying \frac{1}{4} by the reciprocal of \frac{3}{64}.

$$\frac{1}{4}\times \frac{64}{3}$$

Multiply \frac{1}{4} times \frac{64}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 64}{4\times 3}$$

Do the multiplications in the fraction \frac{1\times 64}{4\times 3}.

$$\frac{64}{12}$$

Reduce the fraction \frac{64}{12} to lowest terms by extracting and canceling out 4.

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

Factor

$$\frac{2 ^ {4}}{3} = 5\frac{1}{3} = 5.333333333333333$$