Solve (-3/4)+7/6/frac{4{5}-24/5}

$$\frac { ( - \frac { 3 } { 4 } ) + \frac { 7 } { 6 } } { \frac { 4 } { 5 } - 2 \frac { 4 } { 5 } }$$

Evaluate

$$-\frac{5}{24}\approx -0.208333333$$

Solution Steps

Least common multiple of 4 and 6 is 12. Convert -\frac{3}{4} and \frac{7}{6} to fractions with denominator 12.

$$\frac{-\frac{9}{12}+\frac{14}{12}}{\frac{4}{5}-\frac{2\times 5+4}{5}}$$

Since -\frac{9}{12} and \frac{14}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-9+14}{12}}{\frac{4}{5}-\frac{2\times 5+4}{5}}$$

Add -9 and 14 to get 5.

$$\frac{\frac{5}{12}}{\frac{4}{5}-\frac{2\times 5+4}{5}}$$

Multiply 2 and 5 to get 10.

$$\frac{\frac{5}{12}}{\frac{4}{5}-\frac{10+4}{5}}$$

Add 10 and 4 to get 14.

$$\frac{\frac{5}{12}}{\frac{4}{5}-\frac{14}{5}}$$

Since \frac{4}{5} and \frac{14}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{12}}{\frac{4-14}{5}}$$

Subtract 14 from 4 to get -10.

$$\frac{\frac{5}{12}}{\frac{-10}{5}}$$

Divide -10 by 5 to get -2.

$$\frac{\frac{5}{12}}{-2}$$

Express \frac{\frac{5}{12}}{-2} as a single fraction.

$$\frac{5}{12\left(-2\right)}$$

Multiply 12 and -2 to get -24.

$$\frac{5}{-24}$$

Fraction \frac{5}{-24} can be rewritten as -\frac{5}{24} by extracting the negative sign.

$$-\frac{5}{24}$$

Factor

$$-\frac{5}{24} = -0.20833333333333334$$