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

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

Evaluate

$$\frac{21}{124}\approx 0.169354839$$

Solution Steps

Divide 2 by 2 to get 1.

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

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

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

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

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

Add 6 and 1 to get 7.

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

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

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

Cancel out 7 in both numerator and denominator.

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

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

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

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

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

Subtract 1 from 4 to get 3.

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

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

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

Cancel out 3 in both numerator and denominator.

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

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

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

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

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

Add 4 and 3 to get 7.

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

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

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

Multiply 1 and 4 to get 4.

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

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

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

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

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

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

$$\frac{\frac{7}{12}}{4-\frac{5}{9}}$$

Convert 4 to fraction \frac{36}{9}.

$$\frac{\frac{7}{12}}{\frac{36}{9}-\frac{5}{9}}$$

Since \frac{36}{9} and \frac{5}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{12}}{\frac{36-5}{9}}$$

Subtract 5 from 36 to get 31.

$$\frac{\frac{7}{12}}{\frac{31}{9}}$$

Divide \frac{7}{12} by \frac{31}{9} by multiplying \frac{7}{12} by the reciprocal of \frac{31}{9}.

$$\frac{7}{12}\times \frac{9}{31}$$

Multiply \frac{7}{12} times \frac{9}{31} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 9}{12\times 31}$$

Do the multiplications in the fraction \frac{7\times 9}{12\times 31}.

$$\frac{63}{372}$$

Reduce the fraction \frac{63}{372} to lowest terms by extracting and canceling out 3.

$$\frac{21}{124}$$

Factor

$$\frac{3 \cdot 7}{2 ^ {2} \cdot 31} = 0.1693548387096774$$