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

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

Evaluate

$$-\frac{85}{63}\approx -1.349206349$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{4}{3} to fractions with denominator 6.

$$\frac{\frac{9}{6}-\frac{8}{6}+\frac{5}{4}}{\frac{\frac{3}{5}}{\frac{-4}{7}}}$$

Since \frac{9}{6} and \frac{8}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9-8}{6}+\frac{5}{4}}{\frac{\frac{3}{5}}{\frac{-4}{7}}}$$

Subtract 8 from 9 to get 1.

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

Least common multiple of 6 and 4 is 12. Convert \frac{1}{6} and \frac{5}{4} to fractions with denominator 12.

$$\frac{\frac{2}{12}+\frac{15}{12}}{\frac{\frac{3}{5}}{\frac{-4}{7}}}$$

Since \frac{2}{12} and \frac{15}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2+15}{12}}{\frac{\frac{3}{5}}{\frac{-4}{7}}}$$

Add 2 and 15 to get 17.

$$\frac{\frac{17}{12}}{\frac{\frac{3}{5}}{\frac{-4}{7}}}$$

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

$$\frac{\frac{17}{12}}{\frac{3\times 7}{5\left(-4\right)}}$$

Multiply 3 and 7 to get 21.

$$\frac{\frac{17}{12}}{\frac{21}{5\left(-4\right)}}$$

Multiply 5 and -4 to get -20.

$$\frac{\frac{17}{12}}{\frac{21}{-20}}$$

Fraction \frac{21}{-20} can be rewritten as -\frac{21}{20} by extracting the negative sign.

$$\frac{\frac{17}{12}}{-\frac{21}{20}}$$

Divide \frac{17}{12} by -\frac{21}{20} by multiplying \frac{17}{12} by the reciprocal of -\frac{21}{20}.

$$\frac{17}{12}\left(-\frac{20}{21}\right)$$

Multiply \frac{17}{12} times -\frac{20}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{17\left(-20\right)}{12\times 21}$$

Do the multiplications in the fraction \frac{17\left(-20\right)}{12\times 21}.

$$\frac{-340}{252}$$

Reduce the fraction \frac{-340}{252} to lowest terms by extracting and canceling out 4.

$$-\frac{85}{63}$$

Factor

$$-\frac{85}{63} = -1\frac{22}{63} = -1.3492063492063493$$