Solve [4/7-frac{1/5/frac{7{3}}}{5/frac{5{7}-frac{14}{5}}}]div[frac{frac{14}{7}}{1+frac{4}{3}}]

$$[ \frac { \frac { \frac { 4 } { 7 } - \frac { 1 } { 5 } } { \frac { 7 } { 3 } } } { \frac { 5 } { \frac { 5 } { 7 } - \frac { 14 } { 5 } } } ] \div [ \frac { \frac { 14 } { 7 } } { 1 + \frac { 4 } { 3 } } ]$$

Evaluate

$$-\frac{949}{12250}\approx -0.077469388$$

Solution Steps

Divide \frac{\frac{\frac{4}{7}-\frac{1}{5}}{\frac{7}{3}}}{\frac{5}{\frac{5}{7}-\frac{14}{5}}} by \frac{\frac{14}{7}}{1+\frac{4}{3}} by multiplying \frac{\frac{\frac{4}{7}-\frac{1}{5}}{\frac{7}{3}}}{\frac{5}{\frac{5}{7}-\frac{14}{5}}} by the reciprocal of \frac{\frac{14}{7}}{1+\frac{4}{3}}.

$$\frac{\frac{\frac{4}{7}-\frac{1}{5}}{\frac{7}{3}}\left(1+\frac{4}{3}\right)}{\frac{5}{\frac{5}{7}-\frac{14}{5}}\times \frac{14}{7}}$$

Least common multiple of 7 and 5 is 35. Convert \frac{4}{7} and \frac{1}{5} to fractions with denominator 35.

$$\frac{\frac{\frac{20}{35}-\frac{7}{35}}{\frac{7}{3}}\left(1+\frac{4}{3}\right)}{\frac{5}{\frac{5}{7}-\frac{14}{5}}\times \frac{14}{7}}$$

Since \frac{20}{35} and \frac{7}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{20-7}{35}}{\frac{7}{3}}\left(1+\frac{4}{3}\right)}{\frac{5}{\frac{5}{7}-\frac{14}{5}}\times \frac{14}{7}}$$

Subtract 7 from 20 to get 13.

$$\frac{\frac{\frac{13}{35}}{\frac{7}{3}}\left(1+\frac{4}{3}\right)}{\frac{5}{\frac{5}{7}-\frac{14}{5}}\times \frac{14}{7}}$$

Divide \frac{13}{35} by \frac{7}{3} by multiplying \frac{13}{35} by the reciprocal of \frac{7}{3}.

$$\frac{\frac{13}{35}\times \frac{3}{7}\left(1+\frac{4}{3}\right)}{\frac{5}{\frac{5}{7}-\frac{14}{5}}\times \frac{14}{7}}$$

Multiply \frac{13}{35} times \frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{13\times 3}{35\times 7}\left(1+\frac{4}{3}\right)}{\frac{5}{\frac{5}{7}-\frac{14}{5}}\times \frac{14}{7}}$$

Do the multiplications in the fraction \frac{13\times 3}{35\times 7}.

$$\frac{\frac{39}{245}\left(1+\frac{4}{3}\right)}{\frac{5}{\frac{5}{7}-\frac{14}{5}}\times \frac{14}{7}}$$

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

$$\frac{\frac{39}{245}\left(\frac{3}{3}+\frac{4}{3}\right)}{\frac{5}{\frac{5}{7}-\frac{14}{5}}\times \frac{14}{7}}$$

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

$$\frac{\frac{39}{245}\times \frac{3+4}{3}}{\frac{5}{\frac{5}{7}-\frac{14}{5}}\times \frac{14}{7}}$$

Add 3 and 4 to get 7.

$$\frac{\frac{39}{245}\times \frac{7}{3}}{\frac{5}{\frac{5}{7}-\frac{14}{5}}\times \frac{14}{7}}$$

Multiply \frac{39}{245} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{39\times 7}{245\times 3}}{\frac{5}{\frac{5}{7}-\frac{14}{5}}\times \frac{14}{7}}$$

Do the multiplications in the fraction \frac{39\times 7}{245\times 3}.

$$\frac{\frac{273}{735}}{\frac{5}{\frac{5}{7}-\frac{14}{5}}\times \frac{14}{7}}$$

Reduce the fraction \frac{273}{735} to lowest terms by extracting and canceling out 21.

$$\frac{\frac{13}{35}}{\frac{5}{\frac{5}{7}-\frac{14}{5}}\times \frac{14}{7}}$$

Least common multiple of 7 and 5 is 35. Convert \frac{5}{7} and \frac{14}{5} to fractions with denominator 35.

$$\frac{\frac{13}{35}}{\frac{5}{\frac{25}{35}-\frac{98}{35}}\times \frac{14}{7}}$$

Since \frac{25}{35} and \frac{98}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{13}{35}}{\frac{5}{\frac{25-98}{35}}\times \frac{14}{7}}$$

Subtract 98 from 25 to get -73.

$$\frac{\frac{13}{35}}{\frac{5}{-\frac{73}{35}}\times \frac{14}{7}}$$

Divide 5 by -\frac{73}{35} by multiplying 5 by the reciprocal of -\frac{73}{35}.

$$\frac{\frac{13}{35}}{5\left(-\frac{35}{73}\right)\times \frac{14}{7}}$$

Express 5\left(-\frac{35}{73}\right) as a single fraction.

$$\frac{\frac{13}{35}}{\frac{5\left(-35\right)}{73}\times \frac{14}{7}}$$

Multiply 5 and -35 to get -175.

$$\frac{\frac{13}{35}}{\frac{-175}{73}\times \frac{14}{7}}$$

Fraction \frac{-175}{73} can be rewritten as -\frac{175}{73} by extracting the negative sign.

$$\frac{\frac{13}{35}}{-\frac{175}{73}\times \frac{14}{7}}$$

Divide 14 by 7 to get 2.

$$\frac{\frac{13}{35}}{-\frac{175}{73}\times 2}$$

Express -\frac{175}{73}\times 2 as a single fraction.

$$\frac{\frac{13}{35}}{\frac{-175\times 2}{73}}$$

Multiply -175 and 2 to get -350.

$$\frac{\frac{13}{35}}{\frac{-350}{73}}$$

Fraction \frac{-350}{73} can be rewritten as -\frac{350}{73} by extracting the negative sign.

$$\frac{\frac{13}{35}}{-\frac{350}{73}}$$

Divide \frac{13}{35} by -\frac{350}{73} by multiplying \frac{13}{35} by the reciprocal of -\frac{350}{73}.

$$\frac{13}{35}\left(-\frac{73}{350}\right)$$

Multiply \frac{13}{35} times -\frac{73}{350} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\left(-73\right)}{35\times 350}$$

Do the multiplications in the fraction \frac{13\left(-73\right)}{35\times 350}.

$$\frac{-949}{12250}$$

Fraction \frac{-949}{12250} can be rewritten as -\frac{949}{12250} by extracting the negative sign.

$$-\frac{949}{12250}$$

Factor

$$-\frac{949}{12250} = -0.07746938775510204$$