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

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

Evaluate

$$\frac{25}{11}\approx 2.272727273$$

Solution Steps

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

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

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

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

Add -6 and 1 to get -5.

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

Least common multiple of 5 and 3 is 15. Convert \frac{3}{5} and \frac{4}{3} to fractions with denominator 15.

$$\frac{-\frac{5}{3}}{\frac{9}{15}-\frac{20}{15}}$$

Since \frac{9}{15} and \frac{20}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{5}{3}}{\frac{9-20}{15}}$$

Subtract 20 from 9 to get -11.

$$\frac{-\frac{5}{3}}{-\frac{11}{15}}$$

Divide -\frac{5}{3} by -\frac{11}{15} by multiplying -\frac{5}{3} by the reciprocal of -\frac{11}{15}.

$$-\frac{5}{3}\left(-\frac{15}{11}\right)$$

Multiply -\frac{5}{3} times -\frac{15}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5\left(-15\right)}{3\times 11}$$

Do the multiplications in the fraction \frac{-5\left(-15\right)}{3\times 11}.

$$\frac{75}{33}$$

Reduce the fraction \frac{75}{33} to lowest terms by extracting and canceling out 3.

$$\frac{25}{11}$$

Factor

$$\frac{5 ^ {2}}{11} = 2\frac{3}{11} = 2.272727272727273$$