Solve 3/4-1/3:(1-2/5)/frac{3{7}-frac{1}{2}*(frac{2}{3}+frac{7}{2})}

$$\frac { \frac { 3 } { 4 } - \frac { 1 } { 3 } : ( 1 - \frac { 2 } { 5 } ) } { \frac { 3 } { 7 } - \frac { 1 } { 2 } \cdot ( \frac { 2 } { 3 } + \frac { 7 } { 2 } ) }$$

Evaluate

$$-\frac{49}{417}\approx -0.117505995$$

Solution Steps

Convert 1 to fraction \frac{5}{5}.

$$\frac{\frac{3}{4}-\frac{\frac{1}{3}}{\frac{5}{5}-\frac{2}{5}}}{\frac{3}{7}-\frac{1}{2}\left(\frac{2}{3}+\frac{7}{2}\right)}$$

Since \frac{5}{5} and \frac{2}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3}{4}-\frac{\frac{1}{3}}{\frac{5-2}{5}}}{\frac{3}{7}-\frac{1}{2}\left(\frac{2}{3}+\frac{7}{2}\right)}$$

Subtract 2 from 5 to get 3.

$$\frac{\frac{3}{4}-\frac{\frac{1}{3}}{\frac{3}{5}}}{\frac{3}{7}-\frac{1}{2}\left(\frac{2}{3}+\frac{7}{2}\right)}$$

Divide \frac{1}{3} by \frac{3}{5} by multiplying \frac{1}{3} by the reciprocal of \frac{3}{5}.

$$\frac{\frac{3}{4}-\frac{1}{3}\times \frac{5}{3}}{\frac{3}{7}-\frac{1}{2}\left(\frac{2}{3}+\frac{7}{2}\right)}$$

Multiply \frac{1}{3} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3}{4}-\frac{1\times 5}{3\times 3}}{\frac{3}{7}-\frac{1}{2}\left(\frac{2}{3}+\frac{7}{2}\right)}$$

Do the multiplications in the fraction \frac{1\times 5}{3\times 3}.

$$\frac{\frac{3}{4}-\frac{5}{9}}{\frac{3}{7}-\frac{1}{2}\left(\frac{2}{3}+\frac{7}{2}\right)}$$

Least common multiple of 4 and 9 is 36. Convert \frac{3}{4} and \frac{5}{9} to fractions with denominator 36.

$$\frac{\frac{27}{36}-\frac{20}{36}}{\frac{3}{7}-\frac{1}{2}\left(\frac{2}{3}+\frac{7}{2}\right)}$$

Since \frac{27}{36} and \frac{20}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{27-20}{36}}{\frac{3}{7}-\frac{1}{2}\left(\frac{2}{3}+\frac{7}{2}\right)}$$

Subtract 20 from 27 to get 7.

$$\frac{\frac{7}{36}}{\frac{3}{7}-\frac{1}{2}\left(\frac{2}{3}+\frac{7}{2}\right)}$$

Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{7}{2} to fractions with denominator 6.

$$\frac{\frac{7}{36}}{\frac{3}{7}-\frac{1}{2}\left(\frac{4}{6}+\frac{21}{6}\right)}$$

Since \frac{4}{6} and \frac{21}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7}{36}}{\frac{3}{7}-\frac{1}{2}\times \frac{4+21}{6}}$$

Add 4 and 21 to get 25.

$$\frac{\frac{7}{36}}{\frac{3}{7}-\frac{1}{2}\times \frac{25}{6}}$$

Multiply \frac{1}{2} times \frac{25}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{7}{36}}{\frac{3}{7}-\frac{1\times 25}{2\times 6}}$$

Do the multiplications in the fraction \frac{1\times 25}{2\times 6}.

$$\frac{\frac{7}{36}}{\frac{3}{7}-\frac{25}{12}}$$

Least common multiple of 7 and 12 is 84. Convert \frac{3}{7} and \frac{25}{12} to fractions with denominator 84.

$$\frac{\frac{7}{36}}{\frac{36}{84}-\frac{175}{84}}$$

Since \frac{36}{84} and \frac{175}{84} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{36}}{\frac{36-175}{84}}$$

Subtract 175 from 36 to get -139.

$$\frac{\frac{7}{36}}{-\frac{139}{84}}$$

Divide \frac{7}{36} by -\frac{139}{84} by multiplying \frac{7}{36} by the reciprocal of -\frac{139}{84}.

$$\frac{7}{36}\left(-\frac{84}{139}\right)$$

Multiply \frac{7}{36} times -\frac{84}{139} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\left(-84\right)}{36\times 139}$$

Do the multiplications in the fraction \frac{7\left(-84\right)}{36\times 139}.

$$\frac{-588}{5004}$$

Reduce the fraction \frac{-588}{5004} to lowest terms by extracting and canceling out 12.

$$-\frac{49}{417}$$

Factor

$$-\frac{49}{417} = -0.11750599520383694$$