Solve 4/5+2/3*(-12)div(-6)-(-3)^2|+|24+(-3)^3|*(-5)

$$\frac { 4 } { 5 } + \frac { 2 } { 3 } \times ( - 12 ) \div ( - 6 ) - ( - 3 ) ^ { 2 } | + | 24 + ( - 3 ) ^ { 3 } | \times ( - 5 )$$

Evaluate

$$-\frac{1993}{15}\approx -132.866666667$$

Solution Steps

Express \frac{2}{3}\left(-12\right) as a single fraction.

$$\frac{4}{5}+\frac{\frac{2\left(-12\right)}{3}}{-6}-\left(-3\right)^{2}||24+\left(-3\right)^{3}|\left(-5\right)|$$

Multiply 2 and -12 to get -24.

$$\frac{4}{5}+\frac{\frac{-24}{3}}{-6}-\left(-3\right)^{2}||24+\left(-3\right)^{3}|\left(-5\right)|$$

Divide -24 by 3 to get -8.

$$\frac{4}{5}+\frac{-8}{-6}-\left(-3\right)^{2}||24+\left(-3\right)^{3}|\left(-5\right)|$$

Reduce the fraction \frac{-8}{-6} to lowest terms by extracting and canceling out -2.

$$\frac{4}{5}+\frac{4}{3}-\left(-3\right)^{2}||24+\left(-3\right)^{3}|\left(-5\right)|$$

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

$$\frac{12}{15}+\frac{20}{15}-\left(-3\right)^{2}||24+\left(-3\right)^{3}|\left(-5\right)|$$

Since \frac{12}{15} and \frac{20}{15} have the same denominator, add them by adding their numerators.

$$\frac{12+20}{15}-\left(-3\right)^{2}||24+\left(-3\right)^{3}|\left(-5\right)|$$

Add 12 and 20 to get 32.

$$\frac{32}{15}-\left(-3\right)^{2}||24+\left(-3\right)^{3}|\left(-5\right)|$$

Calculate -3 to the power of 2 and get 9.

$$\frac{32}{15}-9||24+\left(-3\right)^{3}|\left(-5\right)|$$

Calculate -3 to the power of 3 and get -27.

$$\frac{32}{15}-9||24-27|\left(-5\right)|$$

Subtract 27 from 24 to get -3.

$$\frac{32}{15}-9||-3|\left(-5\right)|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -3 is 3.

$$\frac{32}{15}-9|3\left(-5\right)|$$

Multiply 3 and -5 to get -15.

$$\frac{32}{15}-9|-15|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -15 is 15.

$$\frac{32}{15}-9\times 15$$

Multiply 9 and 15 to get 135.

$$\frac{32}{15}-135$$

Convert 135 to fraction \frac{2025}{15}.

$$\frac{32}{15}-\frac{2025}{15}$$

Since \frac{32}{15} and \frac{2025}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{32-2025}{15}$$

Subtract 2025 from 32 to get -1993.

$$-\frac{1993}{15}$$

Factor

$$-\frac{1993}{15} = -132\frac{13}{15} = -132.86666666666667$$