Solve 4/5:[(5/8-1/3)-12]

$$\frac { 4 } { 5 } : [ ( \frac { 5 } { 8 } - \frac { 1 } { 3 } ) - 12 ]$$

Evaluate

$$-\frac{96}{1405}\approx -0.068327402$$

Solution Steps

Least common multiple of 8 and 3 is 24. Convert \frac{5}{8} and \frac{1}{3} to fractions with denominator 24.

$$\frac{\frac{4}{5}}{\frac{15}{24}-\frac{8}{24}-12}$$

Since \frac{15}{24} and \frac{8}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4}{5}}{\frac{15-8}{24}-12}$$

Subtract 8 from 15 to get 7.

$$\frac{\frac{4}{5}}{\frac{7}{24}-12}$$

Convert 12 to fraction \frac{288}{24}.

$$\frac{\frac{4}{5}}{\frac{7}{24}-\frac{288}{24}}$$

Since \frac{7}{24} and \frac{288}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4}{5}}{\frac{7-288}{24}}$$

Subtract 288 from 7 to get -281.

$$\frac{\frac{4}{5}}{-\frac{281}{24}}$$

Divide \frac{4}{5} by -\frac{281}{24} by multiplying \frac{4}{5} by the reciprocal of -\frac{281}{24}.

$$\frac{4}{5}\left(-\frac{24}{281}\right)$$

Multiply \frac{4}{5} times -\frac{24}{281} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\left(-24\right)}{5\times 281}$$

Do the multiplications in the fraction \frac{4\left(-24\right)}{5\times 281}.

$$\frac{-96}{1405}$$

Fraction \frac{-96}{1405} can be rewritten as -\frac{96}{1405} by extracting the negative sign.

$$-\frac{96}{1405}$$

Factor

$$-\frac{96}{1405} = -0.06832740213523132$$