Solve 2+1/3/7+1-frac{1/4/3}{frac{frac{1}{2}}{frac{1}{4}}-frac{1}{frac{4}{3}}}*(frac{2}{7}+frac{4}{19})

$$\frac { \frac { 2 + \frac { 1 } { 3 } } { 7 } + \frac { 1 - \frac { 1 } { 4 } } { 3 } } { \frac { \frac { 1 } { 2 } } { \frac { 1 } { 4 } } - \frac { 1 } { \frac { 4 } { 3 } } } \times ( \frac { 2 } { 7 } + \frac { 4 } { 19 } )$$

Evaluate

$$\frac{22}{95}\approx 0.231578947$$

Solution Steps

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

$$\frac{\frac{\frac{6}{3}+\frac{1}{3}}{7}+\frac{1-\frac{1}{4}}{3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{1}{\frac{4}{3}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

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

$$\frac{\frac{\frac{6+1}{3}}{7}+\frac{1-\frac{1}{4}}{3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{1}{\frac{4}{3}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Add 6 and 1 to get 7.

$$\frac{\frac{\frac{7}{3}}{7}+\frac{1-\frac{1}{4}}{3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{1}{\frac{4}{3}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

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

$$\frac{\frac{7}{3\times 7}+\frac{1-\frac{1}{4}}{3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{1}{\frac{4}{3}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Cancel out 7 in both numerator and denominator.

$$\frac{\frac{1}{3}+\frac{1-\frac{1}{4}}{3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{1}{\frac{4}{3}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

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

$$\frac{\frac{1}{3}+\frac{\frac{4}{4}-\frac{1}{4}}{3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{1}{\frac{4}{3}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

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

$$\frac{\frac{1}{3}+\frac{\frac{4-1}{4}}{3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{1}{\frac{4}{3}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Subtract 1 from 4 to get 3.

$$\frac{\frac{1}{3}+\frac{\frac{3}{4}}{3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{1}{\frac{4}{3}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

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

$$\frac{\frac{1}{3}+\frac{3}{4\times 3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{1}{\frac{4}{3}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{1}{3}+\frac{1}{4}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{1}{\frac{4}{3}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

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

$$\frac{\frac{4}{12}+\frac{3}{12}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{1}{\frac{4}{3}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

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

$$\frac{\frac{4+3}{12}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{1}{\frac{4}{3}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Add 4 and 3 to get 7.

$$\frac{\frac{7}{12}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{1}{\frac{4}{3}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

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

$$\frac{\frac{7}{12}}{\frac{1}{2}\times 4-\frac{1}{\frac{4}{3}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

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

$$\frac{\frac{7}{12}}{\frac{4}{2}-\frac{1}{\frac{4}{3}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Divide 4 by 2 to get 2.

$$\frac{\frac{7}{12}}{2-\frac{1}{\frac{4}{3}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

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

$$\frac{\frac{7}{12}}{2-1\times \frac{3}{4}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Multiply 1 and \frac{3}{4} to get \frac{3}{4}.

$$\frac{\frac{7}{12}}{2-\frac{3}{4}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Convert 2 to fraction \frac{8}{4}.

$$\frac{\frac{7}{12}}{\frac{8}{4}-\frac{3}{4}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Since \frac{8}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{12}}{\frac{8-3}{4}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Subtract 3 from 8 to get 5.

$$\frac{\frac{7}{12}}{\frac{5}{4}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Divide \frac{7}{12} by \frac{5}{4} by multiplying \frac{7}{12} by the reciprocal of \frac{5}{4}.

$$\frac{7}{12}\times \frac{4}{5}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Multiply \frac{7}{12} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 4}{12\times 5}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Do the multiplications in the fraction \frac{7\times 4}{12\times 5}.

$$\frac{28}{60}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Reduce the fraction \frac{28}{60} to lowest terms by extracting and canceling out 4.

$$\frac{7}{15}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Least common multiple of 7 and 19 is 133. Convert \frac{2}{7} and \frac{4}{19} to fractions with denominator 133.

$$\frac{7}{15}\left(\frac{38}{133}+\frac{28}{133}\right)$$

Since \frac{38}{133} and \frac{28}{133} have the same denominator, add them by adding their numerators.

$$\frac{7}{15}\times \frac{38+28}{133}$$

Add 38 and 28 to get 66.

$$\frac{7}{15}\times \frac{66}{133}$$

Multiply \frac{7}{15} times \frac{66}{133} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 66}{15\times 133}$$

Do the multiplications in the fraction \frac{7\times 66}{15\times 133}.

$$\frac{462}{1995}$$

Reduce the fraction \frac{462}{1995} to lowest terms by extracting and canceling out 21.

$$\frac{22}{95}$$

Factor

$$\frac{2 \cdot 11}{5 \cdot 19} = 0.23157894736842105$$