Solve 2+1/3/7+1-frac{1/4/3}{frac{frac{1}{2}}{frac{1}{4}}-frac{frac{4}{3}}{frac{3}{5}}}

$$\frac { \frac { 2 + \frac { 1 } { 3 } } { 7 } + \frac { 1 - \frac { 1 } { 4 } } { 3 } } { \frac { \frac { 1 } { 2 } } { \frac { 1 } { 4 } } - \frac { \frac { 4 } { 3 } } { \frac { 3 } { 5 } } }$$

Evaluate

$$-\frac{21}{8}=-2.625$$

Solution Steps

Convert 2 to fraction \frac{6}{3}.

$$\frac{\frac{\frac{6}{3}+\frac{1}{3}}{7}+\frac{1-\frac{1}{4}}{3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{4}{3}}{\frac{3}{5}}}$$

Since \frac{6}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\frac{6+1}{3}}{7}+\frac{1-\frac{1}{4}}{3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{4}{3}}{\frac{3}{5}}}$$

Add 6 and 1 to get 7.

$$\frac{\frac{\frac{7}{3}}{7}+\frac{1-\frac{1}{4}}{3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{4}{3}}{\frac{3}{5}}}$$

Express \frac{\frac{7}{3}}{7} as a single fraction.

$$\frac{\frac{7}{3\times 7}+\frac{1-\frac{1}{4}}{3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{4}{3}}{\frac{3}{5}}}$$

Cancel out 7 in both numerator and denominator.

$$\frac{\frac{1}{3}+\frac{1-\frac{1}{4}}{3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{4}{3}}{\frac{3}{5}}}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{\frac{1}{3}+\frac{\frac{4}{4}-\frac{1}{4}}{3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{4}{3}}{\frac{3}{5}}}$$

Since \frac{4}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{3}+\frac{\frac{4-1}{4}}{3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{4}{3}}{\frac{3}{5}}}$$

Subtract 1 from 4 to get 3.

$$\frac{\frac{1}{3}+\frac{\frac{3}{4}}{3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{4}{3}}{\frac{3}{5}}}$$

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

$$\frac{\frac{1}{3}+\frac{3}{4\times 3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{4}{3}}{\frac{3}{5}}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{1}{3}+\frac{1}{4}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{4}{3}}{\frac{3}{5}}}$$

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{\frac{4}{12}+\frac{3}{12}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{4}{3}}{\frac{3}{5}}}$$

Since \frac{4}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4+3}{12}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{4}{3}}{\frac{3}{5}}}$$

Add 4 and 3 to get 7.

$$\frac{\frac{7}{12}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{4}{3}}{\frac{3}{5}}}$$

Divide \frac{1}{2} by \frac{1}{4} by multiplying \frac{1}{2} by the reciprocal of \frac{1}{4}.

$$\frac{\frac{7}{12}}{\frac{1}{2}\times 4-\frac{\frac{4}{3}}{\frac{3}{5}}}$$

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

$$\frac{\frac{7}{12}}{\frac{4}{2}-\frac{\frac{4}{3}}{\frac{3}{5}}}$$

Divide 4 by 2 to get 2.

$$\frac{\frac{7}{12}}{2-\frac{\frac{4}{3}}{\frac{3}{5}}}$$

Divide \frac{4}{3} by \frac{3}{5} by multiplying \frac{4}{3} by the reciprocal of \frac{3}{5}.

$$\frac{\frac{7}{12}}{2-\frac{4}{3}\times \frac{5}{3}}$$

Multiply \frac{4}{3} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{7}{12}}{2-\frac{4\times 5}{3\times 3}}$$

Do the multiplications in the fraction \frac{4\times 5}{3\times 3}.

$$\frac{\frac{7}{12}}{2-\frac{20}{9}}$$

Convert 2 to fraction \frac{18}{9}.

$$\frac{\frac{7}{12}}{\frac{18}{9}-\frac{20}{9}}$$

Since \frac{18}{9} and \frac{20}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{12}}{\frac{18-20}{9}}$$

Subtract 20 from 18 to get -2.

$$\frac{\frac{7}{12}}{-\frac{2}{9}}$$

Divide \frac{7}{12} by -\frac{2}{9} by multiplying \frac{7}{12} by the reciprocal of -\frac{2}{9}.

$$\frac{7}{12}\left(-\frac{9}{2}\right)$$

Multiply \frac{7}{12} times -\frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\left(-9\right)}{12\times 2}$$

Do the multiplications in the fraction \frac{7\left(-9\right)}{12\times 2}.

$$\frac{-63}{24}$$

Reduce the fraction \frac{-63}{24} to lowest terms by extracting and canceling out 3.

$$-\frac{21}{8}$$

Factor

$$-\frac{21}{8} = -2\frac{5}{8} = -2.625$$