Solve (-24/5)-(-3/2)/frac{1{2}-21/3}

$$\frac { ( - 2 \frac { 4 } { 5 } ) - ( - \frac { 3 } { 2 } ) } { \frac { 1 } { 2 } - 2 \frac { 1 } { 3 } }$$

Evaluate

$$\frac{39}{55}\approx 0.709090909$$

Solution Steps

Multiply 2 and 5 to get 10.

$$\frac{-\frac{10+4}{5}-\left(-\frac{3}{2}\right)}{\frac{1}{2}-\frac{2\times 3+1}{3}}$$

Add 10 and 4 to get 14.

$$\frac{-\frac{14}{5}-\left(-\frac{3}{2}\right)}{\frac{1}{2}-\frac{2\times 3+1}{3}}$$

The opposite of -\frac{3}{2} is \frac{3}{2}.

$$\frac{-\frac{14}{5}+\frac{3}{2}}{\frac{1}{2}-\frac{2\times 3+1}{3}}$$

Least common multiple of 5 and 2 is 10. Convert -\frac{14}{5} and \frac{3}{2} to fractions with denominator 10.

$$\frac{-\frac{28}{10}+\frac{15}{10}}{\frac{1}{2}-\frac{2\times 3+1}{3}}$$

Since -\frac{28}{10} and \frac{15}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-28+15}{10}}{\frac{1}{2}-\frac{2\times 3+1}{3}}$$

Add -28 and 15 to get -13.

$$\frac{-\frac{13}{10}}{\frac{1}{2}-\frac{2\times 3+1}{3}}$$

Multiply 2 and 3 to get 6.

$$\frac{-\frac{13}{10}}{\frac{1}{2}-\frac{6+1}{3}}$$

Add 6 and 1 to get 7.

$$\frac{-\frac{13}{10}}{\frac{1}{2}-\frac{7}{3}}$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{7}{3} to fractions with denominator 6.

$$\frac{-\frac{13}{10}}{\frac{3}{6}-\frac{14}{6}}$$

Since \frac{3}{6} and \frac{14}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{13}{10}}{\frac{3-14}{6}}$$

Subtract 14 from 3 to get -11.

$$\frac{-\frac{13}{10}}{-\frac{11}{6}}$$

Divide -\frac{13}{10} by -\frac{11}{6} by multiplying -\frac{13}{10} by the reciprocal of -\frac{11}{6}.

$$-\frac{13}{10}\left(-\frac{6}{11}\right)$$

Multiply -\frac{13}{10} times -\frac{6}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-13\left(-6\right)}{10\times 11}$$

Do the multiplications in the fraction \frac{-13\left(-6\right)}{10\times 11}.

$$\frac{78}{110}$$

Reduce the fraction \frac{78}{110} to lowest terms by extracting and canceling out 2.

$$\frac{39}{55}$$

Factor

$$\frac{3 \cdot 13}{5 \cdot 11} = 0.7090909090909091$$